Deck 14: Statistical Process Control

ملء الشاشة (f)
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سؤال
A machine that is supposed to fill small bottles to contain 20 ml yields the following data from a test of 4 bottles every hour.
SAMR119.920.120.220.320.1250.4220.420.020.320.320.250.4320.020.720.420.320.350.7420.420.120.119.920.1250.5519.919.819.619.519.70.4619.419.419.619.719.5250.3719.819.419.619.719.6250.4819.919.820.020.019.9250.2920.220.320.120.320.2250.21020.020.320.020.220.1250.31120.320.520.120.220.2750.41220.119.919.819.719.8750.41319.519.819.719.619.650.31419.419.819.819.419.40.41519.519.619.619.919.650.4\begin{array}{l|llll|l|l}S&&&A&&M&R\\\hline1 & 19.9 & 20.1 & 20.2 & 20 . 3& 20.125 & 0.4 \\2 & 20.4 & 20.0 & 20.3 & 20.3 & 20.25 & 0.4 \\3 & 20.0 & 20.7 & 20.4 & 20.3 & 20.35 & 0.7 \\4 & 20.4 & 20.1 & 20.1 & 19.9&20 .125&0 .5\\5 & 19.9 & 19.8 & 19.6 & 19.5 & 19.7 & 0.4 \\6 & 19.4 & 19.4 & 19.6 & 19.7&19 .525&0 .3 \\7 & 19.8 & 19.4 & 19.6 & 19.7&19 .625&0 .4 \\8 & 19.9 & 19.8 & 20.0 & 20.0 & 19.925&0 .2 \\9 & 20.2 & 20.3 & 20.1 & 20.3&20 .225&0 .2\\10 & 20.0 & 20.3 & 20.0 & 20.2 & 20.125&0 .3 \\11 & 20.3 & 20.5 & 20.1 & 20.2&20.275&0 .4 \\12 & 20.1 & 19.9 & 19.8 & 19.7&19 .875&0 .4\\13 & 19.5 & 19.8 & 19.7 & 19.6 & 19.65 & 0.3 \\14 & 19.4 & 19.8 & 19.8 & 19.4 & 19.4 & 0.4 \\15 & 19.5 & 19.6 & 19.6 & 19.9 & 19.65 & 0.4\\\end{array}
 A machine that is supposed to fill small bottles to contain 20 ml yields the following data from a test of 4 bottles every hour.  \begin{array}{l|llll|l|l} S&&&A&&M&R\\\hline 1 & 19.9 & 20.1 & 20.2 & 20 . 3& 20.125 & 0.4 \\ 2 & 20.4 & 20.0 & 20.3 & 20.3 & 20.25 & 0.4 \\ 3 & 20.0 & 20.7 & 20.4 & 20.3 & 20.35 & 0.7 \\ 4 & 20.4 & 20.1 & 20.1 & 19.9&20 .125&0 .5\\ 5 & 19.9 & 19.8 & 19.6 & 19.5 & 19.7 & 0.4 \\ 6 & 19.4 & 19.4 & 19.6 & 19.7&19 .525&0 .3 \\ 7 & 19.8 & 19.4 & 19.6 & 19.7&19 .625&0 .4 \\ 8 & 19.9 & 19.8 & 20.0 & 20.0 & 19.925&0 .2 \\ 9 & 20.2 & 20.3 & 20.1 & 20.3&20 .225&0 .2\\ 10 & 20.0 & 20.3 & 20.0 & 20.2 & 20.125&0 .3 \\ 11 & 20.3 & 20.5 & 20.1 & 20.2&20.275&0 .4 \\ 12 & 20.1 & 19.9 & 19.8 & 19.7&19 .875&0 .4\\ 13 & 19.5 & 19.8 & 19.7 & 19.6 & 19.65 & 0.3 \\ 14 & 19.4 & 19.8 & 19.8 & 19.4 & 19.4 & 0.4 \\ 15 & 19.5 & 19.6 & 19.6 & 19.9 & 19.65 & 0.4\\ \end{array}   <div style=padding-top: 35px>
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لقلب البطاقة.
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A machine that is supposed to produce ball bearings with a diameter of 7 mm yields the following data from a test of 5 ball bearings every 20 minutes.
SAMR16.36.86.96.86.96.740.626.36.66.66.37.06.560.736.86.77.06.57.06.80.547.06.76.76.86.86.80.356.86.86.66.56.46.620.466.86.76.66.36.96.660.677.37.37.47.47.07.280.487.27.07.26.97.17.080.397.37.67.17.47.67.40.5107.27.67.57.67.17.40.5117.27.27.47.07.07.160.4127.57.47.47.67.17.40.5\begin{array} { l|lllll|l| } S&&&A&&&M&R\\\hline 1&6.3&6.8&6.9&6.8&6.9&6.74&0.6\\2&6.3&6.6&6.6&6.3&7.0&6.56&0.7\\3&6.8&6.7&7.0&6.5&7.0&6.8&0.5\\4&7.0&6.7&6.7&6.8&6.8&6.8&0.3\\5&6.8&6.8&6.6&6.5&6.4&6.62&0.4\\6&6.8&6.7&6.6&6.3&6.9&6.66&0.6\\7&7.3&7.3&7.4&7.4&7.0&7.28&0.4\\8&7.2&7.0&7.2&6.9&7.1&7.08&0.3\\9&7.3&7.6&7.1&7.4&7.6&7.4&0.5\\10&7.2&7.6&7.5&7.6&7.1&7.4&0.5\\11&7.2&7.2&7.4&7.0&7.0&7.16&0.4\\12&7.5&7.4&7.4&7.6&7.1&7.4&0.5\\\end{array}
 Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A machine that is supposed to produce ball bearings with a diameter of 7 mm yields the following data from a test of 5 ball bearings every 20 minutes.  \begin{array} { l|lllll|l|  } S&&&A&&&M&R\\ \hline 1&6.3&6.8&6.9&6.8&6.9&6.74&0.6\\2&6.3&6.6&6.6&6.3&7.0&6.56&0.7\\ 3&6.8&6.7&7.0&6.5&7.0&6.8&0.5\\4&7.0&6.7&6.7&6.8&6.8&6.8&0.3\\ 5&6.8&6.8&6.6&6.5&6.4&6.62&0.4\\6&6.8&6.7&6.6&6.3&6.9&6.66&0.6\\ 7&7.3&7.3&7.4&7.4&7.0&7.28&0.4\\8&7.2&7.0&7.2&6.9&7.1&7.08&0.3\\ 9&7.3&7.6&7.1&7.4&7.6&7.4&0.5\\10&7.2&7.6&7.5&7.6&7.1&7.4&0.5\\ 11&7.2&7.2&7.4&7.0&7.0&7.16&0.4\\12&7.5&7.4&7.4&7.6&7.1&7.4&0.5\\ \end{array}   <div style=padding-top: 35px>
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Describe a run chart and give an example. Refer to the values on each of the axes as you describe the run chart.
سؤال
A machine is supposed to fill boxes to a weight of 50 lbs. Every 30 minutes a sample of four boxes is tested; the results are given below.
SAMR14938394542.751125251436151.7518356603252502844459464949.51555161484551.251664550464847.2557525145550.751084050534847.751394867605156.519104350504747.57114830383938.7518125046485349.25713505856645714144752474948.755155257585254.756\begin{array} { r | r r r r | r | r } \mathrm { S } &&& { \mathrm { A } } && \mathrm { M } & \mathrm { R } \\\hline 1 & 49 & 38 & 39 & 45 & 42.75 & 11 \\2 & 52 & 51 & 43 & 61 & 51.75 & 18 \\3 & 56 & 60 & 32 & 52 & 50 & 28 \\4 & 44 & 59 & 46 & 49 & 49.5 & 15\\5 & 51 & 61 & 48 & 45 & 51.25 & 16 \\6 & 45 & 50 & 46 & 4 8& 47.25 & 5 \\7 & 52 & 51 & 45 & 5 & 50.75 & 10 \\8 & 40 & 50 & 53 & 48&47.75 & 13\\9 & 48 & 67 & 60 & 5 1& 56.5 & 19 \\10 & 43 & 50 & 50 & 47 & 47.5 & 7 \\11 & 48 & 30 & 38 & 39 & 38.75 & 18 \\12 & 50 & 46 & 48 & 53 & 49.25 & 7\\13 & 50 & 58 & 56 & 64 & 57 & 14 \\14 & 47 & 52 & 47 & 49 & 48.75 & 5 \\15 & 52 & 57 & 58 & 52&54.75 & 6\\\end{array}
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Relate the concept of control charts to the concept of confidence intervals.
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A machine that is supposed to fill small bottles to contain 20 ml yields the following data from a test of 4 bottles every hour.
SAMR119.920.120.220.320.1250.4220.420.020.320.320.250.4320.020.720.420.320.350.7420.420.120.119.920.1250.5519.919.819.619.519.70.4619.419.419.619.719.5250.3719.819.419.619.719.6250.4819.919.820.020.019.9250.2920.220.320.120.320.2250.21020.020.320.020.220.1250.31120.320.520.120.220.2750.41220.119.919.819.719.8750.41319.519.819.719.619.650.31419.419.819.819.419.40.41519.519.619.619.919.650.4\begin{array}{l|llll|l|l}S&&&A&&M&R\\\hline1 & 19.9 & 20.1 & 20.2 & 20.3&20 .125 & 0.4 \\2 & 20.4 & 20.0 & 20.3 & 20.3 & 20.25 & 0.4 \\3 & 20.0 & 20.7 & 20.4 & 20.3 & 20.35 & 0.7\\4 & 20.4 & 20.1 & 20.1 & 19.9&20 .125 & 0.5 \\5 & 19.9 & 19.8 & 19.6 & 19.5 & 19.7 & 0.4 \\6 & 19.4 & 19.4 & 19.6 & 19.7&19 .525 & 0.3\\7 & 19.8 & 19.4 & 19.6 & 19.7&19 .625&0 .4 \\8 & 19.9 & 19.8 & 20.0 & 20.0&19 .925 & 0.2 \\9 & 20.2 & 20.3 & 20.1 & 20.3&20 .225 & 0.2\\10 & 20.0 & 20.3 & 20.0 & 20.2&20 .125&0 .3 \\11 & 20.3 & 20.5 & 20.1 & 20.2&20 .275&0 .4 \\12 & 20.1 & 19.9 & 19.8 & 19.7&19 .875&0 .4\\13 & 19.5 & 19.8 & 19.7 & 19.6 & 19.65 & 0.3 \\14 & 19.4 & 19.8 & 19.8 & 19.4 & 19.4 & 0.4 \\15 & 19.5 & 19.6 & 19.6 & 19.9 & 19.65 & 0.4\\\end{array}
 Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A machine that is supposed to fill small bottles to contain 20 ml yields the following data from a test of 4 bottles every hour.  \begin{array}{l|llll|l|l} S&&&A&&M&R\\\hline 1 & 19.9 & 20.1 & 20.2 & 20.3&20 .125 & 0.4 \\ 2 & 20.4 & 20.0 & 20.3 & 20.3 & 20.25 & 0.4 \\ 3 & 20.0 & 20.7 & 20.4 & 20.3 & 20.35 & 0.7\\ 4 & 20.4 & 20.1 & 20.1 & 19.9&20 .125 & 0.5 \\ 5 & 19.9 & 19.8 & 19.6 & 19.5 & 19.7 & 0.4 \\ 6 & 19.4 & 19.4 & 19.6 & 19.7&19 .525 & 0.3\\ 7 & 19.8 & 19.4 & 19.6 & 19.7&19 .625&0 .4 \\ 8 & 19.9 & 19.8 & 20.0 & 20.0&19 .925 & 0.2 \\ 9 & 20.2 & 20.3 & 20.1 & 20.3&20 .225 & 0.2\\ 10 & 20.0 & 20.3 & 20.0 & 20.2&20 .125&0 .3 \\ 11 & 20.3 & 20.5 & 20.1 & 20.2&20 .275&0 .4 \\ 12 & 20.1 & 19.9 & 19.8 & 19.7&19 .875&0 .4\\ 13 & 19.5 & 19.8 & 19.7 & 19.6 & 19.65 & 0.3 \\ 14 & 19.4 & 19.8 & 19.8 & 19.4 & 19.4 & 0.4 \\ 15 & 19.5 & 19.6 & 19.6 & 19.9 & 19.65 & 0.4\\ \end{array}   <div style=padding-top: 35px>
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A machine that is supposed to fill small bottles to contain 20 ml yields the following data from a test of 4 bottles every hour.
SAMR119.920.120.220.320.1250.4220.420.020.320.320.250.4320.020.720.420.320.350.7420.420.120.119.920.1250.5519.919.819.619.519.70.4619.419.419.619.719.5250.3719.819.419.619.719.6250.4819.919.820.020.019.9250.2920.220.320.120.320.2250.21020.020.320.020.220.1250.31120.320.520.120.220.2750.41220.119.919.819.719.8750.41319.519.819.719.619650.31419.419.819.819.419.40.41519.519.619.619.919.650.4\begin{array} { l|llll|l| } S&&A&&&M&R\\\hline 1&19.9&20.1&20.2&20.3&20.125&0.4\\2&20.4&20.0&20.3&20.3&20.25&0.4\\3&20.0&20.7&20.4&20.3&20.35&0.7\\4&20.4&20.1&20.1&19.9&20.125&0.5\\5&19.9&19.8&19.6&19.5&19.7&0.4\\6&19.4&19.4&19.6&19.7&19.525&0.3\\7&19.8&19.4&19.6&19.7&19.625&0.4\\8&19.9&19.8&20.0&20.0&19.925&0.2\\9&20.2&20.3&20.1&20.3&20.225&0.2\\10&20.0&20.3&20.0&20.2&20.125&0.3\\11&20.3&20.5&20.1&20.2&20.275&0.4\\12&20.1&19.9&19.8&19.7&19.875&0.4\\13&19.5&19.8&19.7&19.6&1965&0.3\\14&19.4&19.8&19.8&19.4&19.4&0.4\\15&19.5&19.6&19.6&19.9&19.65&0.4\end{array}
 Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A machine that is supposed to fill small bottles to contain 20 ml yields the following data from a test of 4 bottles every hour.  \begin{array} { l|llll|l|  } S&&A&&&M&R\\ \hline 1&19.9&20.1&20.2&20.3&20.125&0.4\\2&20.4&20.0&20.3&20.3&20.25&0.4\\ 3&20.0&20.7&20.4&20.3&20.35&0.7\\4&20.4&20.1&20.1&19.9&20.125&0.5\\ 5&19.9&19.8&19.6&19.5&19.7&0.4\\6&19.4&19.4&19.6&19.7&19.525&0.3\\ 7&19.8&19.4&19.6&19.7&19.625&0.4\\8&19.9&19.8&20.0&20.0&19.925&0.2\\ 9&20.2&20.3&20.1&20.3&20.225&0.2\\10&20.0&20.3&20.0&20.2&20.125&0.3\\ 11&20.3&20.5&20.1&20.2&20.275&0.4\\12&20.1&19.9&19.8&19.7&19.875&0.4\\ 13&19.5&19.8&19.7&19.6&1965&0.3\\14&19.4&19.8&19.8&19.4&19.4&0.4\\ 15&19.5&19.6&19.6&19.9&19.65&0.4 \end{array}   <div style=padding-top: 35px>
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Define statistically stable (or "within statistical control"). Show examples of run charts which illustrate processes which are not statistically controlled. Discuss the pattern which indicates the process is not statistically controlled for each example.
سؤال
A machine is supposed to fill cans that contain 12 oz. Each hour, a sample of four cans is tested; the results of 15 consecutive hours are given below. SAMR111.211.711.811.711.60.6211.811.311.611.661.5750.5311.312.011.811.711.70.7412.111.612.112.011.950.5511.811.811.911.911.850.1612.011.911.811.711.850.3711.612.011.911.811.8250.4811.512.111.912.011.8750.6912.112.111.711.911.950.41011.712.011.611.911.80.41112.112.411.912.212.150.51212.512.012.412.312.30.51312.512.012.112.112.1750.51412.412.012.012.412.20.41512.412.412.61212.3750.5\begin{array}{l|llll|l|l}S&&&A&&M&R\\\hline1 & 11.2 & 11.7 & 11.8 & 11 .7 & 11.6 & 0.6 \\2 & 11.8 & 11.3 & 11.6 & 11 .6 & 61.575 & 0.5 \\3 & 11.3 & 12.0 & 11.8 & 11.7 & 11.7 & 0.7 \\4 & 12.1 & 11.6 & 12.1 & 12 . 0& 11.95 & 0.5 \\5 & 11.8 & 11.8 & 11.9 & 11.9&11 .85 & 0.1\\6 & 12.0 & 11.9 & 11.8 & 11 .7& 11.85&0 .3 \\7 & 11.6 & 12.0 & 11.9 & 11.8 & 11.825&0 .4 \\8 & 11.5 & 12.1 & 11.9 & 12 .0& 11.875&0 .6 \\9 & 12.1 & 12.1 & 11.7 & 11.9&11 .95&0 .4\\10 & 11.7 & 12.0 & 11.6 & 11.9 & 11.8 & 0.4 \\11 & 12.1 & 12.4 & 11.9 & 12.2&12 .15 & 0.5 \\12 & 12.5 & 12.0 & 12.4 & 12.3 & 12.3 & 0.5\\13 & 12.5 & 12.0 & 12.1 & 12 .1& 12.175& 0.5 \\14 & 12.4 & 12.0 & 12.0 & 12.4 & 12.2 & 0.4 \\15 & 12.4 & 12.4 & 12.6 & 12 & 12.375 & 0.5\\\end{array}
 A machine is supposed to fill cans that contain 12 oz. Each hour, a sample of four cans is tested; the results of 15 consecutive hours are given below.  \begin{array}{l|llll|l|l} S&&&A&&M&R\\\hline 1 & 11.2 & 11.7 & 11.8 & 11 .7 & 11.6 & 0.6 \\ 2 & 11.8 & 11.3 & 11.6 & 11 .6 & 61.575 & 0.5 \\ 3 & 11.3 & 12.0 & 11.8 & 11.7 & 11.7 & 0.7 \\ 4 & 12.1 & 11.6 & 12.1 & 12 . 0& 11.95 & 0.5 \\ 5 & 11.8 & 11.8 & 11.9 & 11.9&11 .85 & 0.1\\ 6 & 12.0 & 11.9 & 11.8 & 11 .7& 11.85&0 .3 \\ 7 & 11.6 & 12.0 & 11.9 & 11.8 & 11.825&0 .4 \\ 8 & 11.5 & 12.1 & 11.9 & 12 .0& 11.875&0 .6 \\ 9 & 12.1 & 12.1 & 11.7 & 11.9&11 .95&0 .4\\ 10 & 11.7 & 12.0 & 11.6 & 11.9 & 11.8 & 0.4 \\ 11 & 12.1 & 12.4 & 11.9 & 12.2&12 .15 & 0.5 \\ 12 & 12.5 & 12.0 & 12.4 & 12.3 & 12.3 & 0.5\\ 13 & 12.5 & 12.0 & 12.1 & 12 .1& 12.175& 0.5 \\ 14 & 12.4 & 12.0 & 12.0 & 12.4 & 12.2 & 0.4 \\ 15 & 12.4 & 12.4 & 12.6 & 12 & 12.375 & 0.5\\ \end{array}   <div style=padding-top: 35px>
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A machine is supposed to fill cans that contain 12 oz. Each hour, a sample of four cans is tested; the results of 15 consecutive hours are given below. SAMR111.211.711.811.711.60.6211.811.311.611.611.5750.5311.312.011.811.711.70.7412.111.612.112.011.950.5511.811.811.911.911.850.1612.011.911.811.711.850.3711.612.011.911.811.8250.4811.512.111.912.011.8750.6912.112.111.711.911.950.41011.712.011.611.911.80.41112.112.411.912.212.150.51212.512.012.412.312.30.51312.512.012.112.112.1750.51412.412.012.012.412.20.41512.412.412.612.112.3750.5\begin{array} { l|llll|l| } S&&A&&&M&R\\\hline 1&11.2&11.7&11.8&11.7&11.6&0.6\\2&11.8&11.3&11.6&11.6&11.575&0.5\\3&11.3&12.0&11.8&11.7&11.7&0.7\\4&12.1&11.6&12.1&12.0&11.95&0.5\\5&11.8&11.8&11.9&11.9&11.85&0.1\\6&12.0&11.9&11.8&11.7&11.85&0.3\\7&11.6&12.0&11.9&11.8&11.825&0.4\\8&11.5&12.1&11.9&12.0&11.875&0.6\\9&12.1&12.1&11.7&11.9&11.95&0.4\\10&11.7&12.0&11.6&11.9&11.8&0.4\\11&12.1&12.4&11.9&12.2&12.15&0.5\\12&12.5&12.0&12.4&12.3&12.3&0.5\\13&12.5&12.0&12.1&12.1&12.175&0.5\\14&12.4&12.0&12.0&12.4&12.2&0.4\\15&12.4&12.4&12.6&12.1&12.375&0.5\end{array}
 Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A machine is supposed to fill cans that contain 12 oz. Each hour, a sample of four cans is tested; the results of 15 consecutive hours are given below.  \begin{array} { l|llll|l|  } S&&A&&&M&R\\ \hline 1&11.2&11.7&11.8&11.7&11.6&0.6\\ 2&11.8&11.3&11.6&11.6&11.575&0.5\\ 3&11.3&12.0&11.8&11.7&11.7&0.7\\4&12.1&11.6&12.1&12.0&11.95&0.5\\5&11.8&11.8&11.9&11.9&11.85&0.1\\ 6&12.0&11.9&11.8&11.7&11.85&0.3\\ 7&11.6&12.0&11.9&11.8&11.825&0.4\\8&11.5&12.1&11.9&12.0&11.875&0.6\\ 9&12.1&12.1&11.7&11.9&11.95&0.4\\ 10&11.7&12.0&11.6&11.9&11.8&0.4\\11&12.1&12.4&11.9&12.2&12.15&0.5\\ 12&12.5&12.0&12.4&12.3&12.3&0.5\\13&12.5&12.0&12.1&12.1&12.175&0.5\\ 14&12.4&12.0&12.0&12.4&12.2&0.4\\15&12.4&12.4&12.6&12.1&12.375&0.5 \end{array}   <div style=padding-top: 35px>
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Draw a control chart that illustrates a process which is statistically stable and one which illustrates a process which is not statistically stable. Discuss the results.
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A machine that is supposed to produce ball bearings with a diameter of 7 mm yields the following data from a test of 5 ball bearings every 20 minutes.
SAMR16.36.86.96.86.96.740.526.36.66.66.37.06.560.736.86.77.06.57.06.80.547.06.76.76.86.86.80.356.86.86.66.56.46.620.466.86.76.66.36.96.660.677.37.37.47.47.07.280.487.27.07.26.97.17.080.397.37.67.17.47.67.40.5107.27.67.57.67.17.40.5117.27.27.47.07.07.160.4127.57.47.47.67.17.40.5\begin{array}{l|lllll|l|l}S&&&A&&&M&R\\\hline1&6.3&6.8&6.9&6.8&6.9&6.74&0.5\\2 & 6.3 & 6.6 & 6.6 & 6.3 & 7.0&6 .56 & 0.7 \\3 & 6.8 & 6.7 & 7.0 & 6.5 & 7.0 & 6.8 & 0.5\\4 & 7.0 & 6.7 & 6.7 & 6.8 & 6.8 & 6.8 & 0.3 \\5 & 6.8 & 6.8 & 6.6 & 6.5 & 6.4&6 .62 & 0.4 \\6 & 6.8 & 6.7 & 6.6 & 6.3 & 6.9&6 .66 & 0.6\\7 & 7.3 & 7.3 & 7.4 & 7.4 & 7.0&7 .28 & 0.4 \\8 & 7.2 & 7.0 & 7.2 & 6.9 & 7.1&7 .08 & 0.3 \\9 & 7.3 & 7.6 & 7.1 & 7.4 & 7.6 & 7.4 & 0.5\\10 & 7.2 & 7.6 & 7.5 & 7.6 & 7.1 & 7.4 & 0.5 \\11 & 7.2 & 7.2 & 7.4 & 7.0 & 7.0&7 .16 & 0.4 \\12 & 7.5 & 7.4 & 7.4 & 7.6 & 7.1 & 7.4 & 0.5\\\end{array}
 Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A machine that is supposed to produce ball bearings with a diameter of 7 mm yields the following data from a test of 5 ball bearings every 20 minutes.  \begin{array}{l|lllll|l|l} S&&&A&&&M&R\\\hline 1&6.3&6.8&6.9&6.8&6.9&6.74&0.5\\ 2 & 6.3 & 6.6 & 6.6 & 6.3 & 7.0&6 .56 & 0.7 \\ 3 & 6.8 & 6.7 & 7.0 & 6.5 & 7.0 & 6.8 & 0.5\\ 4 & 7.0 & 6.7 & 6.7 & 6.8 & 6.8 & 6.8 & 0.3 \\ 5 & 6.8 & 6.8 & 6.6 & 6.5 & 6.4&6 .62 & 0.4 \\ 6 & 6.8 & 6.7 & 6.6 & 6.3 & 6.9&6 .66 & 0.6\\ 7 & 7.3 & 7.3 & 7.4 & 7.4 & 7.0&7 .28 & 0.4 \\ 8 & 7.2 & 7.0 & 7.2 & 6.9 & 7.1&7 .08 & 0.3 \\ 9 & 7.3 & 7.6 & 7.1 & 7.4 & 7.6 & 7.4 & 0.5\\ 10 & 7.2 & 7.6 & 7.5 & 7.6 & 7.1 & 7.4 & 0.5 \\ 11 & 7.2 & 7.2 & 7.4 & 7.0 & 7.0&7 .16 & 0.4 \\ 12 & 7.5 & 7.4 & 7.4 & 7.6 & 7.1 & 7.4 & 0.5\\ \end{array}   <div style=padding-top: 35px>
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A machine is supposed to fill boxes to a weight of 50 lbs. Every 30 minutes a sample of four boxes is tested; the results are given below. SAMR14938394542.75112525143651.7518356603252502844459464949.51555161484551.251664550464847.25575251455550.751084050534847.751394867605156.519104350504747.57114830383938.7518125046485349.25713505856645714144752474948.755155257585254.756\begin{array}{l|llll|l|l}S&&&A&&M&R\\\hline1 & 49 & 38 & 39 & 45 & 42.75 & 11 \\2 & 52 & 51 & 43 & 6 & 51.75 & 18 \\3 & 56 & 60 & 32 & 52 & 50 & 28\\4 & 44 & 59 & 46 & 49 & 49.5 & 15 \\5 & 51 & 61 & 48 & 45 & 51.25 & 16 \\6 & 45 & 50 & 46 & 48& 47.25 & 5 \\7 & 52 & 51 & 45 & 55& 50.75 & 10\\8 & 40 & 50 & 53 & 48 & 47.75 & 13 \\9 & 48 & 67 & 60 & 51 & 56.5 & 19 \\10 & 43 & 50 & 50 & 47 & 47.5 & 7 \\11 & 48 & 30 & 38 & 39 & 38.75 & 18\\12 & 50 & 46 & 48 & 53 & 49.25 & 7 \\13 & 50 & 58 & 56 & 64 & 57 & 14 \\14 & 47 & 52 & 47 & 49&48.75 & 5 \\15 & 52 & 57 & 58 & 52&54.75 & 6\\\end{array}
 Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A machine is supposed to fill boxes to a weight of 50 lbs. Every 30 minutes a sample of four boxes is tested; the results are given below.  \begin{array}{l|llll|l|l} S&&&A&&M&R\\\hline 1 & 49 & 38 & 39 & 45 & 42.75 & 11 \\ 2 & 52 & 51 & 43 & 6 & 51.75 & 18 \\ 3 & 56 & 60 & 32 & 52 & 50 & 28\\ 4 & 44 & 59 & 46 & 49 & 49.5 & 15 \\ 5 & 51 & 61 & 48 & 45 & 51.25 & 16 \\ 6 & 45 & 50 & 46 & 48& 47.25 & 5 \\ 7 & 52 & 51 & 45 & 55& 50.75 & 10\\ 8 & 40 & 50 & 53 & 48 & 47.75 & 13 \\ 9 & 48 & 67 & 60 & 51 & 56.5 & 19 \\ 10 & 43 & 50 & 50 & 47 & 47.5 & 7 \\ 11 & 48 & 30 & 38 & 39 & 38.75 & 18\\ 12 & 50 & 46 & 48 & 53 & 49.25 & 7 \\ 13 & 50 & 58 & 56 & 64 & 57 & 14 \\ 14 & 47 & 52 & 47 & 49&48.75 & 5 \\ 15 & 52 & 57 & 58 & 52&54.75 & 6\\ \end{array}   <div style=padding-top: 35px>
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A machine is supposed to fill cans that contain 12 oz. Each hour, a sample of four cans is tested; the results of 15 consecutive hours are given below. SAMR111.211.711.811.711.60.6211.811.311.611.61.5750.5311.312.011.811.711.70.7412.111.612.112.011.950.5511.811.811.911.911.850.1612.011.911.811.711.850.3711.612.011.911.81.8250.4811.512.111.912.011.8750.6912.112.111.711.911.950.41011.712.011.611.911.80.41112.112.411.912.212.150.51212.512.012.412.312.30.51312.512.012.112.112.1750.51412.412.012.012.412.20.41512.412.412.612.112.3750.5\begin{array}{c|cccc|c|c}\mathrm{S} & & \mathrm{A} &&& \mathrm{M} & \mathrm{R} \\\hline 1 & 11.2 & 11.7 & 11.8 & 11 .7 & 11.6 & 0.6 \\2 & 11.8 & 11.3 & 11.6 & 11 . 6& 1.575 & 0.5 \\3 & 11.3 & 12.0 & 11.8 & 11.7 & 11.7 & 0.7 \\4 & 12.1 & 11.6 & 12.1 & 12.0&11 .95 & 0.5 \\5 & 11.8 & 11.8 & 11.9 & 11.9&11 .85 & 0.1\\6 & 12.0 & 11.9 & 11.8 & 11.7&11 .85&0 .3 \\7 & 11.6 & 12.0 & 11.9 & 11.8&1 .825&0 .4 \\8 & 11.5 & 12.1 & 11.9 & 12.0&11 .875&0 .6\\9 & 12.1 & 12.1 & 11.7 & 11.9&11 .95&0 .4 \\10 & 11.7 & 12.0 & 11.6 & 11.9 & 11.8 & 0.4 \\11 & 12.1 & 12.4 & 11.9 & 12.2&12 .15&0 .5\\12 & 12.5 & 12.0 & 12.4 & 12 .3& 12.3 & 0.5 \\13 & 12.5 & 12.0 & 12.1 & 12.1 & 12.175 & 0.5 \\14 & 12.4 & 12.0 & 12.0 & 12 . 4& 12.2 & 0.4 \\15 & 12.4 & 12.4 & 12.6 & 12 .1 & 12.375 & 0.5\\\end{array}
 Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A machine is supposed to fill cans that contain 12 oz. Each hour, a sample of four cans is tested; the results of 15 consecutive hours are given below.  \begin{array}{c|cccc|c|c} \mathrm{S} & & \mathrm{A} &&& \mathrm{M} & \mathrm{R} \\ \hline 1 & 11.2 & 11.7 & 11.8 & 11 .7 & 11.6 & 0.6 \\ 2 & 11.8 & 11.3 & 11.6 & 11 . 6& 1.575 & 0.5 \\ 3 & 11.3 & 12.0 & 11.8 & 11.7 & 11.7 & 0.7 \\ 4 & 12.1 & 11.6 & 12.1 & 12.0&11 .95 & 0.5 \\ 5 & 11.8 & 11.8 & 11.9 & 11.9&11 .85 & 0.1\\ 6 & 12.0 & 11.9 & 11.8 & 11.7&11 .85&0 .3 \\ 7 & 11.6 & 12.0 & 11.9 & 11.8&1 .825&0 .4 \\ 8 & 11.5 & 12.1 & 11.9 & 12.0&11 .875&0 .6\\ 9 & 12.1 & 12.1 & 11.7 & 11.9&11 .95&0 .4 \\ 10 & 11.7 & 12.0 & 11.6 & 11.9 & 11.8 & 0.4 \\ 11 & 12.1 & 12.4 & 11.9 & 12.2&12 .15&0 .5\\ 12 & 12.5 & 12.0 & 12.4 & 12 .3& 12.3 & 0.5 \\ 13 & 12.5 & 12.0 & 12.1 & 12.1 & 12.175 & 0.5 \\ 14 & 12.4 & 12.0 & 12.0 & 12 . 4& 12.2 & 0.4 \\ 15 & 12.4 & 12.4 & 12.6 & 12 .1 & 12.375 & 0.5\\ \end{array}   <div style=padding-top: 35px>
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Describe a control chart. Complete the table to identify the important parts of different types of control charts.
 Center line and Upper  Lower  Points plotted how to compute control limitcontrol limit  Control char  for R Control char  for Xˉ Control char  for p\begin{array}{r|c}&&\text { Center line and } &\text {Upper } &\text { Lower } \\&\text { Points plotted } &\text {how to compute} &\text { control limit} &\text {control limit }\\\hline \text { Control char } \\\text { for } R \\\\\text { Control char } \\\text { for } \bar{X} \\\\\text { Control char } \\\text { for } p\end{array}
سؤال
A machine that is supposed to produce ball bearings with a diameter of 7 mm yields the following data from a test of 5 ball bearings every 20 minutes. SAMR16.36.86.96.86.96.740.626.36.66.66.37.06.560.736.86.77.06.57.06.80.547.06.76.76.86.86.80.356.86.86.66.56.46.620.466.86.76.66.36.96.660.677.37.37.47.47.07.280.487.27.07.26.97.17.080.397.37.67.17.47.67.40.5107.27.67.57.67.17.40.5117.27.27.47.07.07.160.4127.57.47.47.67.17.40.5\begin{array}{l|lllll|l|l}S&&&A&&&M&R\\\hline1 & 6.3 & 6.8 & 6.9 & 6.8 & 6.9&6 .74 & 0.6 \\2 & 6.3 & 6.6 & 6.6 & 6.3 & 7.0&6 .56 & 0.7 \\3 & 6.8 & 6.7 & 7.0 & 6.5 & 7.0 & 6.8 & 0.5 \\4 & 7.0 & 6.7 & 6.7 & 6.8 & 6.8 & 6.8 & 0.3\\5 & 6.8 & 6.8 & 6.6 & 6.5 & 6.4&6 .62 & 0.4 \\6 & 6.8 & 6.7 & 6.6 & 6.3 & 6.9&6 .66 & 0.6 \\7 & 7.3 & 7.3 & 7.4 & 7.4 & 7.0&7 .28 & 0.4 \\8 & 7.2 & 7.0 & 7.2 & 6.9 & 7.1&7 .08&0 .3\\9 & 7.3 & 7.6 & 7.1 & 7.4 & 7.6 & 7.4 & 0.5 \\10 & 7.2 & 7.6 & 7.5 & 7.6 & 7.1 & 7.4 & 0.5 \\11 & 7.2 & 7.2 & 7.4 & 7.0 & 7.0&7 .16 & 0.4 \\12 & 7.5 & 7.4 & 7.4 & 7.6 & 7.1 & 7.4 & 0.5\\\end{array}
 A machine that is supposed to produce ball bearings with a diameter of 7 mm yields the following data from a test of 5 ball bearings every 20 minutes.  \begin{array}{l|lllll|l|l} S&&&A&&&M&R\\\hline 1 & 6.3 & 6.8 & 6.9 & 6.8 & 6.9&6 .74 & 0.6 \\ 2 & 6.3 & 6.6 & 6.6 & 6.3 & 7.0&6 .56 & 0.7 \\ 3 & 6.8 & 6.7 & 7.0 & 6.5 & 7.0 & 6.8 & 0.5 \\ 4 & 7.0 & 6.7 & 6.7 & 6.8 & 6.8 & 6.8 & 0.3\\ 5 & 6.8 & 6.8 & 6.6 & 6.5 & 6.4&6 .62 & 0.4 \\ 6 & 6.8 & 6.7 & 6.6 & 6.3 & 6.9&6 .66 & 0.6 \\ 7 & 7.3 & 7.3 & 7.4 & 7.4 & 7.0&7 .28 & 0.4 \\ 8 & 7.2 & 7.0 & 7.2 & 6.9 & 7.1&7 .08&0 .3\\ 9 & 7.3 & 7.6 & 7.1 & 7.4 & 7.6 & 7.4 & 0.5 \\ 10 & 7.2 & 7.6 & 7.5 & 7.6 & 7.1 & 7.4 & 0.5 \\ 11 & 7.2 & 7.2 & 7.4 & 7.0 & 7.0&7 .16 & 0.4 \\ 12 & 7.5 & 7.4 & 7.4 & 7.6 & 7.1 & 7.4 & 0.5\\ \end{array}   <div style=padding-top: 35px>
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A machine is supposed to fill boxes to a weight of 50 lbs. Every 30 minutes a sample of four boxes is tested; the results are given below.
SAMR14938394542.751125251436151.7518356603252502844459454949.51555161484551.251664550464847.25575251455550.751184050534847.751394867605156.519104350504747.57114830383938.7518125046485349.25713505856645714144752474948.755155257585254.756\begin{array} { l|llll|l| } S&&A&&&M&R\\\hline 1&49&38&39&45&42.75&11\\2&52&51&43&61&51.75&18\\3&56&60&32&52&50&28\\4&44&59&45&49&49.5&15\\5&51&61&48&45&51.25&16\\6&45&50&46&48&47.25&5\\7&52&51&45&55&50.75&11\\8&40&50&53&48&47.75&13\\9&48&67&60&51&56.5&19\\10&43&50&50&47&47.5&7\\11&48&30&38&39&38.75&18\\12&50&46&48&53&49.25&7\\13&50&58&56&64&57&14\\14&47&52&47&49&48.75&5\\15&52&57&58&52&54.75&6\end{array}
 Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A machine is supposed to fill boxes to a weight of 50 lbs. Every 30 minutes a sample of four boxes is tested; the results are given below.  \begin{array} { l|llll|l|  } S&&A&&&M&R\\ \hline 1&49&38&39&45&42.75&11\\2&52&51&43&61&51.75&18\\ 3&56&60&32&52&50&28\\4&44&59&45&49&49.5&15\\ 5&51&61&48&45&51.25&16\\6&45&50&46&48&47.25&5\\ 7&52&51&45&55&50.75&11\\8&40&50&53&48&47.75&13\\ 9&48&67&60&51&56.5&19\\10&43&50&50&47&47.5&7\\11&48&30&38&39&38.75&18\\12&50&46&48&53&49.25&7\\ 13&50&58&56&64&57&14\\14&47&52&47&49&48.75&5\\15&52&57&58&52&54.75&6 \end{array}   <div style=padding-top: 35px>
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Describe the three criteria used to determine if a control chart indicates a process which is not statistically stable.
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Describe what process data are. Why are process data important to businesses? What is a common goal of businesses using quality control?
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A common goal of quality control is to reduce variation in a product or service. List and describe the two types of variability. Give an example of each.
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  - <div style=padding-top: 35px>
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A control chart for xˉ\bar x is shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.  Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A control chart for  \bar x  is shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.  <div style=padding-top: 35px>
سؤال
Solve the Problem.

-A control chart for monitoring variation and center can be based on standard deviations instead of on ranges. An s chart for monitoring variation is made by plotting sample standard deviations with a center line at sˉ\bar { s } (the mean of the sample standard deviations) and control limits at B4sˉB _ { 4 } \bar { s } and B3sˉB _ { 3 } \bar { s } , where B4B _ { 4 } sˉ\bar { s } and B3B _ { 3 }sˉ\bar { s } are found in the Control Chart Constants table. Construct an s chart for the data below.

A manufacturer of lightbulbs picks 10 lightbulbs at random each day for quality control. The mean, standard de and range (in hours) of the lifetimes of the 10 lightbulbs are calculated. The results for 12 consecutive days are sh the table below.
 Day xˉ Range  s 1201.13.41.22203.44.71.73200.93.10.94205.66.22.35201.34.71.36200.53.71.77205.85.82.18203.76.22.99199.82.10.810202.74.41.611200.02.70.712204.67.83.0\begin{array}{lcll}\text { Day } & \bar{x} & \text { Range } & \text { s } \\\hline 1 & 201.1 & 3.4 & 1.2 \\2 & 203.4 & 4.7 & 1.7 \\3 & 200.9 & 3.1 & 0.9 \\4 & 205.6 & 6.2 & 2.3 \\5 & 201.3 & 4.7 & 1.3\\6 & 200.5 & 3.7 & 1.7 \\7 & 205.8 & 5.8 & 2.1 \\8 & 203.7 & 6.2 & 2.9 \\9 & 199.8 & 2.1 & 0.8 \\10 & 202.7 & 4.4 & 1.6 \\11 & 200.0 & 2.7 & 0.7 \\12 & 204.6 & 7.8 & 3.0\\\end{array}
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A control chart for R is shown below. Determine whether the process variation is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of statistically stable variation. Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A control chart for R is shown below. Determine whether the process variation is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of statistically stable variation.  <div style=padding-top: 35px>
سؤال
Solve the Problem.

-An xˉ\bar { x } chart based on standard deviations (instead of ranges) is made by plotting sample means with a centerline at xˉˉ\bar {\bar { x} } and control limits at xˉˉ+A3sˉ\bar {\bar { x} } + A _ { 3 } \bar { s } and xˉˉA3sˉ\bar {\bar { x} } - A _ { 3 } \bar { s } where A3A _ { 3 } is found in the Control Chart Constants table and sˉ\bar { s } is the mean of the sample standard deviations. Construct an xˉ\bar { x } chart based on standard deviations for the data belo
A manufacturer of high intensity video projector lightbulbs picks 6 lightbulbs at random each day for quality cor The mean, standard deviation, and range (in hours) of the lifetimes of the 6 lightbulbs are calculated. The results consecutive days are shown in the table below.
 Day xˉ Range  s 121.13.41.2223.44.71.7320.93.10.9425.66.22.3521.34.71.3620.53.71.7725.85.82.1823.76.22.9929.82.10.81022.74.41.61120.02.70.71224.67.83.0\begin{array}{lllll}\text { Day } & \bar{x} & \text { Range } & \text { s } \\1 & 21.13 .4 & & 1.2 & \\2 & 23.44 .7 & & 1.7 & \\3 & 20.93 .1 & & 0.9 & \\4 & 25.66 .2 & & 2.3 & \\5 & 21.3 & 4.7 &{1.3} \\6 & 20.5 & 3.7 &{1.7} \\7 & 25.85 .8 & &2.1 & \\8 & 23.76 .2 & & 2.9 & \\9 & 29.82 .1 & & 0.8 & \\10 & 22.7 & 4.4 &{1.6} \\11 & 20.02 .7 & & 0.7 & \\12 & 24.67 .8 & & 3.0\end{array}  Answer: \text { Answer: }
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A run chart for individual values is shown below. Does there appear to be a pattern suggesting that the process is not within statistical control? If so, describe the pattern. Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A run chart for individual values is shown below. Does there appear to be a pattern suggesting that the process is not within statistical control? If so, describe the pattern.  <div style=padding-top: 35px>
سؤال
Use the given process data to construct a control chart for p

-If the weight of cereal in a particular packet is less than 14 oz, the packet is considered nonconforming. Each week, the manufacturer randomly selects 1,000 cereal packets and determines the number that are nonconforming. The results for 12 consecutive weeks are shown below. 46&nbsp;32&nbsp;21&nbsp;30&nbsp;47&nbsp;31&nbsp;32&nbsp;52&nbsp;48&nbsp;45&nbsp;62&nbsp;58
 Use the given process data to construct a control chart for p  -If the weight of cereal in a particular packet is less than 14 oz, the packet is considered nonconforming. Each week, the manufacturer randomly selects 1,000 cereal packets and determines the number that are nonconforming. The results for 12 consecutive weeks are shown below.  46 32 21 30 47 31 32 52 48 45 62 58   <div style=padding-top: 35px>
سؤال
Solve the Problem.

-A control chart for attributes is to be constructed. Which process would have wider control limits, a process which has been having a 5% rate of nonconforming items, or a process which has been having a 10% of nonconforming items? Assume that both processes have the same sample sizes. For a given sample size, would it be easier to detect a shift from 5% to 10% or a shift from 10% to 15%? Explain your reasoning.
سؤال
Use the given process data to construct a control chart for p

-A drugstore considers a wait of more than 5 minutes to be a defect. Each week 100 customers are randomly selected and timed at the checkout line. The numbers of defects for 20 consecutive weeks are given below. 4&nbsp;4&nbsp;5&nbsp;5&nbsp;5&nbsp;5&nbsp;5&nbsp;5&nbsp;6&nbsp;6&nbsp;6&nbsp;6&nbsp;12&nbsp;6&nbsp;6&nbsp;6&nbsp;7&nbsp;6&nbsp;7&nbsp;8&nbsp;7
 Use the given process data to construct a control chart for p  -A drugstore considers a wait of more than 5 minutes to be a defect. Each week 100 customers are randomly selected and timed at the checkout line. The numbers of defects for 20 consecutive weeks are given below.  4 4 5 5 5 5 5 5 6 6 6 6 12 6 6 6 7 6 7 8 7   <div style=padding-top: 35px>
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  - <div style=padding-top: 35px>
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

- A control chart for xˉ\bar x is shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.  Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  - A control chart for  \bar x  is shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.  <div style=padding-top: 35px>
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A control chart for R is shown below. Determine whether the process variation is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of statistically stable variation. Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A control chart for R is shown below. Determine whether the process variation is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of statistically stable variation.  <div style=padding-top: 35px>
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  - <div style=padding-top: 35px>
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  - <div style=padding-top: 35px>
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A control chart for xˉ\bar x is shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.  Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A control chart for \bar x   is shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.  <div style=padding-top: 35px>
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A control chart fo xˉ\bar x s shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.  Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A control chart fo  \bar x  s shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.  <div style=padding-top: 35px>
سؤال
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A run chart for individual values is shown below. Does there appear to be a pattern suggesting that the process is not within statistical control? If so, describe the pattern. Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A run chart for individual values is shown below. Does there appear to be a pattern suggesting that the process is not within statistical control? If so, describe the pattern.  <div style=padding-top: 35px>
سؤال
Use the given process data to construct a control chart for p

-A manufacturer monitors the level of defects in the television sets that it produces. Each week, 200 television sets are randomly selected and tested and the number of defects is recorded. The results for 12 consecutive weeks are shown below. 4&nbsp;7&nbsp;5&nbsp;6&nbsp;8&nbsp;3&nbsp;12&nbsp;4&nbsp;4&nbsp;5&nbsp;6&nbsp;2
 Use the given process data to construct a control chart for p  -A manufacturer monitors the level of defects in the television sets that it produces. Each week, 200 television sets are randomly selected and tested and the number of defects is recorded. The results for 12 consecutive weeks are shown below.  4 7 5 6 8 3 12 4 4 5 6 2   <div style=padding-top: 35px>
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Deck 14: Statistical Process Control
1
A machine that is supposed to fill small bottles to contain 20 ml yields the following data from a test of 4 bottles every hour.
SAMR119.920.120.220.320.1250.4220.420.020.320.320.250.4320.020.720.420.320.350.7420.420.120.119.920.1250.5519.919.819.619.519.70.4619.419.419.619.719.5250.3719.819.419.619.719.6250.4819.919.820.020.019.9250.2920.220.320.120.320.2250.21020.020.320.020.220.1250.31120.320.520.120.220.2750.41220.119.919.819.719.8750.41319.519.819.719.619.650.31419.419.819.819.419.40.41519.519.619.619.919.650.4\begin{array}{l|llll|l|l}S&&&A&&M&R\\\hline1 & 19.9 & 20.1 & 20.2 & 20 . 3& 20.125 & 0.4 \\2 & 20.4 & 20.0 & 20.3 & 20.3 & 20.25 & 0.4 \\3 & 20.0 & 20.7 & 20.4 & 20.3 & 20.35 & 0.7 \\4 & 20.4 & 20.1 & 20.1 & 19.9&20 .125&0 .5\\5 & 19.9 & 19.8 & 19.6 & 19.5 & 19.7 & 0.4 \\6 & 19.4 & 19.4 & 19.6 & 19.7&19 .525&0 .3 \\7 & 19.8 & 19.4 & 19.6 & 19.7&19 .625&0 .4 \\8 & 19.9 & 19.8 & 20.0 & 20.0 & 19.925&0 .2 \\9 & 20.2 & 20.3 & 20.1 & 20.3&20 .225&0 .2\\10 & 20.0 & 20.3 & 20.0 & 20.2 & 20.125&0 .3 \\11 & 20.3 & 20.5 & 20.1 & 20.2&20.275&0 .4 \\12 & 20.1 & 19.9 & 19.8 & 19.7&19 .875&0 .4\\13 & 19.5 & 19.8 & 19.7 & 19.6 & 19.65 & 0.3 \\14 & 19.4 & 19.8 & 19.8 & 19.4 & 19.4 & 0.4 \\15 & 19.5 & 19.6 & 19.6 & 19.9 & 19.65 & 0.4\\\end{array}
 A machine that is supposed to fill small bottles to contain 20 ml yields the following data from a test of 4 bottles every hour.  \begin{array}{l|llll|l|l} S&&&A&&M&R\\\hline 1 & 19.9 & 20.1 & 20.2 & 20 . 3& 20.125 & 0.4 \\ 2 & 20.4 & 20.0 & 20.3 & 20.3 & 20.25 & 0.4 \\ 3 & 20.0 & 20.7 & 20.4 & 20.3 & 20.35 & 0.7 \\ 4 & 20.4 & 20.1 & 20.1 & 19.9&20 .125&0 .5\\ 5 & 19.9 & 19.8 & 19.6 & 19.5 & 19.7 & 0.4 \\ 6 & 19.4 & 19.4 & 19.6 & 19.7&19 .525&0 .3 \\ 7 & 19.8 & 19.4 & 19.6 & 19.7&19 .625&0 .4 \\ 8 & 19.9 & 19.8 & 20.0 & 20.0 & 19.925&0 .2 \\ 9 & 20.2 & 20.3 & 20.1 & 20.3&20 .225&0 .2\\ 10 & 20.0 & 20.3 & 20.0 & 20.2 & 20.125&0 .3 \\ 11 & 20.3 & 20.5 & 20.1 & 20.2&20.275&0 .4 \\ 12 & 20.1 & 19.9 & 19.8 & 19.7&19 .875&0 .4\\ 13 & 19.5 & 19.8 & 19.7 & 19.6 & 19.65 & 0.3 \\ 14 & 19.4 & 19.8 & 19.8 & 19.4 & 19.4 & 0.4 \\ 15 & 19.5 & 19.6 & 19.6 & 19.9 & 19.65 & 0.4\\ \end{array}
2
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A machine that is supposed to produce ball bearings with a diameter of 7 mm yields the following data from a test of 5 ball bearings every 20 minutes.
SAMR16.36.86.96.86.96.740.626.36.66.66.37.06.560.736.86.77.06.57.06.80.547.06.76.76.86.86.80.356.86.86.66.56.46.620.466.86.76.66.36.96.660.677.37.37.47.47.07.280.487.27.07.26.97.17.080.397.37.67.17.47.67.40.5107.27.67.57.67.17.40.5117.27.27.47.07.07.160.4127.57.47.47.67.17.40.5\begin{array} { l|lllll|l| } S&&&A&&&M&R\\\hline 1&6.3&6.8&6.9&6.8&6.9&6.74&0.6\\2&6.3&6.6&6.6&6.3&7.0&6.56&0.7\\3&6.8&6.7&7.0&6.5&7.0&6.8&0.5\\4&7.0&6.7&6.7&6.8&6.8&6.8&0.3\\5&6.8&6.8&6.6&6.5&6.4&6.62&0.4\\6&6.8&6.7&6.6&6.3&6.9&6.66&0.6\\7&7.3&7.3&7.4&7.4&7.0&7.28&0.4\\8&7.2&7.0&7.2&6.9&7.1&7.08&0.3\\9&7.3&7.6&7.1&7.4&7.6&7.4&0.5\\10&7.2&7.6&7.5&7.6&7.1&7.4&0.5\\11&7.2&7.2&7.4&7.0&7.0&7.16&0.4\\12&7.5&7.4&7.4&7.6&7.1&7.4&0.5\\\end{array}
 Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A machine that is supposed to produce ball bearings with a diameter of 7 mm yields the following data from a test of 5 ball bearings every 20 minutes.  \begin{array} { l|lllll|l|  } S&&&A&&&M&R\\ \hline 1&6.3&6.8&6.9&6.8&6.9&6.74&0.6\\2&6.3&6.6&6.6&6.3&7.0&6.56&0.7\\ 3&6.8&6.7&7.0&6.5&7.0&6.8&0.5\\4&7.0&6.7&6.7&6.8&6.8&6.8&0.3\\ 5&6.8&6.8&6.6&6.5&6.4&6.62&0.4\\6&6.8&6.7&6.6&6.3&6.9&6.66&0.6\\ 7&7.3&7.3&7.4&7.4&7.0&7.28&0.4\\8&7.2&7.0&7.2&6.9&7.1&7.08&0.3\\ 9&7.3&7.6&7.1&7.4&7.6&7.4&0.5\\10&7.2&7.6&7.5&7.6&7.1&7.4&0.5\\ 11&7.2&7.2&7.4&7.0&7.0&7.16&0.4\\12&7.5&7.4&7.4&7.6&7.1&7.4&0.5\\ \end{array}
3
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Describe a run chart and give an example. Refer to the values on each of the axes as you describe the run chart.
A run chart is a sequential plot of individual data values over time. The horizontal axis typically is used for the time sequence, and the vertical axis is used for the values of the data.
4
A machine is supposed to fill boxes to a weight of 50 lbs. Every 30 minutes a sample of four boxes is tested; the results are given below.
SAMR14938394542.751125251436151.7518356603252502844459464949.51555161484551.251664550464847.2557525145550.751084050534847.751394867605156.519104350504747.57114830383938.7518125046485349.25713505856645714144752474948.755155257585254.756\begin{array} { r | r r r r | r | r } \mathrm { S } &&& { \mathrm { A } } && \mathrm { M } & \mathrm { R } \\\hline 1 & 49 & 38 & 39 & 45 & 42.75 & 11 \\2 & 52 & 51 & 43 & 61 & 51.75 & 18 \\3 & 56 & 60 & 32 & 52 & 50 & 28 \\4 & 44 & 59 & 46 & 49 & 49.5 & 15\\5 & 51 & 61 & 48 & 45 & 51.25 & 16 \\6 & 45 & 50 & 46 & 4 8& 47.25 & 5 \\7 & 52 & 51 & 45 & 5 & 50.75 & 10 \\8 & 40 & 50 & 53 & 48&47.75 & 13\\9 & 48 & 67 & 60 & 5 1& 56.5 & 19 \\10 & 43 & 50 & 50 & 47 & 47.5 & 7 \\11 & 48 & 30 & 38 & 39 & 38.75 & 18 \\12 & 50 & 46 & 48 & 53 & 49.25 & 7\\13 & 50 & 58 & 56 & 64 & 57 & 14 \\14 & 47 & 52 & 47 & 49 & 48.75 & 5 \\15 & 52 & 57 & 58 & 52&54.75 & 6\\\end{array}
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5
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Relate the concept of control charts to the concept of confidence intervals.
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6
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A machine that is supposed to fill small bottles to contain 20 ml yields the following data from a test of 4 bottles every hour.
SAMR119.920.120.220.320.1250.4220.420.020.320.320.250.4320.020.720.420.320.350.7420.420.120.119.920.1250.5519.919.819.619.519.70.4619.419.419.619.719.5250.3719.819.419.619.719.6250.4819.919.820.020.019.9250.2920.220.320.120.320.2250.21020.020.320.020.220.1250.31120.320.520.120.220.2750.41220.119.919.819.719.8750.41319.519.819.719.619.650.31419.419.819.819.419.40.41519.519.619.619.919.650.4\begin{array}{l|llll|l|l}S&&&A&&M&R\\\hline1 & 19.9 & 20.1 & 20.2 & 20.3&20 .125 & 0.4 \\2 & 20.4 & 20.0 & 20.3 & 20.3 & 20.25 & 0.4 \\3 & 20.0 & 20.7 & 20.4 & 20.3 & 20.35 & 0.7\\4 & 20.4 & 20.1 & 20.1 & 19.9&20 .125 & 0.5 \\5 & 19.9 & 19.8 & 19.6 & 19.5 & 19.7 & 0.4 \\6 & 19.4 & 19.4 & 19.6 & 19.7&19 .525 & 0.3\\7 & 19.8 & 19.4 & 19.6 & 19.7&19 .625&0 .4 \\8 & 19.9 & 19.8 & 20.0 & 20.0&19 .925 & 0.2 \\9 & 20.2 & 20.3 & 20.1 & 20.3&20 .225 & 0.2\\10 & 20.0 & 20.3 & 20.0 & 20.2&20 .125&0 .3 \\11 & 20.3 & 20.5 & 20.1 & 20.2&20 .275&0 .4 \\12 & 20.1 & 19.9 & 19.8 & 19.7&19 .875&0 .4\\13 & 19.5 & 19.8 & 19.7 & 19.6 & 19.65 & 0.3 \\14 & 19.4 & 19.8 & 19.8 & 19.4 & 19.4 & 0.4 \\15 & 19.5 & 19.6 & 19.6 & 19.9 & 19.65 & 0.4\\\end{array}
 Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A machine that is supposed to fill small bottles to contain 20 ml yields the following data from a test of 4 bottles every hour.  \begin{array}{l|llll|l|l} S&&&A&&M&R\\\hline 1 & 19.9 & 20.1 & 20.2 & 20.3&20 .125 & 0.4 \\ 2 & 20.4 & 20.0 & 20.3 & 20.3 & 20.25 & 0.4 \\ 3 & 20.0 & 20.7 & 20.4 & 20.3 & 20.35 & 0.7\\ 4 & 20.4 & 20.1 & 20.1 & 19.9&20 .125 & 0.5 \\ 5 & 19.9 & 19.8 & 19.6 & 19.5 & 19.7 & 0.4 \\ 6 & 19.4 & 19.4 & 19.6 & 19.7&19 .525 & 0.3\\ 7 & 19.8 & 19.4 & 19.6 & 19.7&19 .625&0 .4 \\ 8 & 19.9 & 19.8 & 20.0 & 20.0&19 .925 & 0.2 \\ 9 & 20.2 & 20.3 & 20.1 & 20.3&20 .225 & 0.2\\ 10 & 20.0 & 20.3 & 20.0 & 20.2&20 .125&0 .3 \\ 11 & 20.3 & 20.5 & 20.1 & 20.2&20 .275&0 .4 \\ 12 & 20.1 & 19.9 & 19.8 & 19.7&19 .875&0 .4\\ 13 & 19.5 & 19.8 & 19.7 & 19.6 & 19.65 & 0.3 \\ 14 & 19.4 & 19.8 & 19.8 & 19.4 & 19.4 & 0.4 \\ 15 & 19.5 & 19.6 & 19.6 & 19.9 & 19.65 & 0.4\\ \end{array}
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7
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A machine that is supposed to fill small bottles to contain 20 ml yields the following data from a test of 4 bottles every hour.
SAMR119.920.120.220.320.1250.4220.420.020.320.320.250.4320.020.720.420.320.350.7420.420.120.119.920.1250.5519.919.819.619.519.70.4619.419.419.619.719.5250.3719.819.419.619.719.6250.4819.919.820.020.019.9250.2920.220.320.120.320.2250.21020.020.320.020.220.1250.31120.320.520.120.220.2750.41220.119.919.819.719.8750.41319.519.819.719.619650.31419.419.819.819.419.40.41519.519.619.619.919.650.4\begin{array} { l|llll|l| } S&&A&&&M&R\\\hline 1&19.9&20.1&20.2&20.3&20.125&0.4\\2&20.4&20.0&20.3&20.3&20.25&0.4\\3&20.0&20.7&20.4&20.3&20.35&0.7\\4&20.4&20.1&20.1&19.9&20.125&0.5\\5&19.9&19.8&19.6&19.5&19.7&0.4\\6&19.4&19.4&19.6&19.7&19.525&0.3\\7&19.8&19.4&19.6&19.7&19.625&0.4\\8&19.9&19.8&20.0&20.0&19.925&0.2\\9&20.2&20.3&20.1&20.3&20.225&0.2\\10&20.0&20.3&20.0&20.2&20.125&0.3\\11&20.3&20.5&20.1&20.2&20.275&0.4\\12&20.1&19.9&19.8&19.7&19.875&0.4\\13&19.5&19.8&19.7&19.6&1965&0.3\\14&19.4&19.8&19.8&19.4&19.4&0.4\\15&19.5&19.6&19.6&19.9&19.65&0.4\end{array}
 Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A machine that is supposed to fill small bottles to contain 20 ml yields the following data from a test of 4 bottles every hour.  \begin{array} { l|llll|l|  } S&&A&&&M&R\\ \hline 1&19.9&20.1&20.2&20.3&20.125&0.4\\2&20.4&20.0&20.3&20.3&20.25&0.4\\ 3&20.0&20.7&20.4&20.3&20.35&0.7\\4&20.4&20.1&20.1&19.9&20.125&0.5\\ 5&19.9&19.8&19.6&19.5&19.7&0.4\\6&19.4&19.4&19.6&19.7&19.525&0.3\\ 7&19.8&19.4&19.6&19.7&19.625&0.4\\8&19.9&19.8&20.0&20.0&19.925&0.2\\ 9&20.2&20.3&20.1&20.3&20.225&0.2\\10&20.0&20.3&20.0&20.2&20.125&0.3\\ 11&20.3&20.5&20.1&20.2&20.275&0.4\\12&20.1&19.9&19.8&19.7&19.875&0.4\\ 13&19.5&19.8&19.7&19.6&1965&0.3\\14&19.4&19.8&19.8&19.4&19.4&0.4\\ 15&19.5&19.6&19.6&19.9&19.65&0.4 \end{array}
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8
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Define statistically stable (or "within statistical control"). Show examples of run charts which illustrate processes which are not statistically controlled. Discuss the pattern which indicates the process is not statistically controlled for each example.
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9
A machine is supposed to fill cans that contain 12 oz. Each hour, a sample of four cans is tested; the results of 15 consecutive hours are given below. SAMR111.211.711.811.711.60.6211.811.311.611.661.5750.5311.312.011.811.711.70.7412.111.612.112.011.950.5511.811.811.911.911.850.1612.011.911.811.711.850.3711.612.011.911.811.8250.4811.512.111.912.011.8750.6912.112.111.711.911.950.41011.712.011.611.911.80.41112.112.411.912.212.150.51212.512.012.412.312.30.51312.512.012.112.112.1750.51412.412.012.012.412.20.41512.412.412.61212.3750.5\begin{array}{l|llll|l|l}S&&&A&&M&R\\\hline1 & 11.2 & 11.7 & 11.8 & 11 .7 & 11.6 & 0.6 \\2 & 11.8 & 11.3 & 11.6 & 11 .6 & 61.575 & 0.5 \\3 & 11.3 & 12.0 & 11.8 & 11.7 & 11.7 & 0.7 \\4 & 12.1 & 11.6 & 12.1 & 12 . 0& 11.95 & 0.5 \\5 & 11.8 & 11.8 & 11.9 & 11.9&11 .85 & 0.1\\6 & 12.0 & 11.9 & 11.8 & 11 .7& 11.85&0 .3 \\7 & 11.6 & 12.0 & 11.9 & 11.8 & 11.825&0 .4 \\8 & 11.5 & 12.1 & 11.9 & 12 .0& 11.875&0 .6 \\9 & 12.1 & 12.1 & 11.7 & 11.9&11 .95&0 .4\\10 & 11.7 & 12.0 & 11.6 & 11.9 & 11.8 & 0.4 \\11 & 12.1 & 12.4 & 11.9 & 12.2&12 .15 & 0.5 \\12 & 12.5 & 12.0 & 12.4 & 12.3 & 12.3 & 0.5\\13 & 12.5 & 12.0 & 12.1 & 12 .1& 12.175& 0.5 \\14 & 12.4 & 12.0 & 12.0 & 12.4 & 12.2 & 0.4 \\15 & 12.4 & 12.4 & 12.6 & 12 & 12.375 & 0.5\\\end{array}
 A machine is supposed to fill cans that contain 12 oz. Each hour, a sample of four cans is tested; the results of 15 consecutive hours are given below.  \begin{array}{l|llll|l|l} S&&&A&&M&R\\\hline 1 & 11.2 & 11.7 & 11.8 & 11 .7 & 11.6 & 0.6 \\ 2 & 11.8 & 11.3 & 11.6 & 11 .6 & 61.575 & 0.5 \\ 3 & 11.3 & 12.0 & 11.8 & 11.7 & 11.7 & 0.7 \\ 4 & 12.1 & 11.6 & 12.1 & 12 . 0& 11.95 & 0.5 \\ 5 & 11.8 & 11.8 & 11.9 & 11.9&11 .85 & 0.1\\ 6 & 12.0 & 11.9 & 11.8 & 11 .7& 11.85&0 .3 \\ 7 & 11.6 & 12.0 & 11.9 & 11.8 & 11.825&0 .4 \\ 8 & 11.5 & 12.1 & 11.9 & 12 .0& 11.875&0 .6 \\ 9 & 12.1 & 12.1 & 11.7 & 11.9&11 .95&0 .4\\ 10 & 11.7 & 12.0 & 11.6 & 11.9 & 11.8 & 0.4 \\ 11 & 12.1 & 12.4 & 11.9 & 12.2&12 .15 & 0.5 \\ 12 & 12.5 & 12.0 & 12.4 & 12.3 & 12.3 & 0.5\\ 13 & 12.5 & 12.0 & 12.1 & 12 .1& 12.175& 0.5 \\ 14 & 12.4 & 12.0 & 12.0 & 12.4 & 12.2 & 0.4 \\ 15 & 12.4 & 12.4 & 12.6 & 12 & 12.375 & 0.5\\ \end{array}
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10
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A machine is supposed to fill cans that contain 12 oz. Each hour, a sample of four cans is tested; the results of 15 consecutive hours are given below. SAMR111.211.711.811.711.60.6211.811.311.611.611.5750.5311.312.011.811.711.70.7412.111.612.112.011.950.5511.811.811.911.911.850.1612.011.911.811.711.850.3711.612.011.911.811.8250.4811.512.111.912.011.8750.6912.112.111.711.911.950.41011.712.011.611.911.80.41112.112.411.912.212.150.51212.512.012.412.312.30.51312.512.012.112.112.1750.51412.412.012.012.412.20.41512.412.412.612.112.3750.5\begin{array} { l|llll|l| } S&&A&&&M&R\\\hline 1&11.2&11.7&11.8&11.7&11.6&0.6\\2&11.8&11.3&11.6&11.6&11.575&0.5\\3&11.3&12.0&11.8&11.7&11.7&0.7\\4&12.1&11.6&12.1&12.0&11.95&0.5\\5&11.8&11.8&11.9&11.9&11.85&0.1\\6&12.0&11.9&11.8&11.7&11.85&0.3\\7&11.6&12.0&11.9&11.8&11.825&0.4\\8&11.5&12.1&11.9&12.0&11.875&0.6\\9&12.1&12.1&11.7&11.9&11.95&0.4\\10&11.7&12.0&11.6&11.9&11.8&0.4\\11&12.1&12.4&11.9&12.2&12.15&0.5\\12&12.5&12.0&12.4&12.3&12.3&0.5\\13&12.5&12.0&12.1&12.1&12.175&0.5\\14&12.4&12.0&12.0&12.4&12.2&0.4\\15&12.4&12.4&12.6&12.1&12.375&0.5\end{array}
 Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A machine is supposed to fill cans that contain 12 oz. Each hour, a sample of four cans is tested; the results of 15 consecutive hours are given below.  \begin{array} { l|llll|l|  } S&&A&&&M&R\\ \hline 1&11.2&11.7&11.8&11.7&11.6&0.6\\ 2&11.8&11.3&11.6&11.6&11.575&0.5\\ 3&11.3&12.0&11.8&11.7&11.7&0.7\\4&12.1&11.6&12.1&12.0&11.95&0.5\\5&11.8&11.8&11.9&11.9&11.85&0.1\\ 6&12.0&11.9&11.8&11.7&11.85&0.3\\ 7&11.6&12.0&11.9&11.8&11.825&0.4\\8&11.5&12.1&11.9&12.0&11.875&0.6\\ 9&12.1&12.1&11.7&11.9&11.95&0.4\\ 10&11.7&12.0&11.6&11.9&11.8&0.4\\11&12.1&12.4&11.9&12.2&12.15&0.5\\ 12&12.5&12.0&12.4&12.3&12.3&0.5\\13&12.5&12.0&12.1&12.1&12.175&0.5\\ 14&12.4&12.0&12.0&12.4&12.2&0.4\\15&12.4&12.4&12.6&12.1&12.375&0.5 \end{array}
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11
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Draw a control chart that illustrates a process which is statistically stable and one which illustrates a process which is not statistically stable. Discuss the results.
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12
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A machine that is supposed to produce ball bearings with a diameter of 7 mm yields the following data from a test of 5 ball bearings every 20 minutes.
SAMR16.36.86.96.86.96.740.526.36.66.66.37.06.560.736.86.77.06.57.06.80.547.06.76.76.86.86.80.356.86.86.66.56.46.620.466.86.76.66.36.96.660.677.37.37.47.47.07.280.487.27.07.26.97.17.080.397.37.67.17.47.67.40.5107.27.67.57.67.17.40.5117.27.27.47.07.07.160.4127.57.47.47.67.17.40.5\begin{array}{l|lllll|l|l}S&&&A&&&M&R\\\hline1&6.3&6.8&6.9&6.8&6.9&6.74&0.5\\2 & 6.3 & 6.6 & 6.6 & 6.3 & 7.0&6 .56 & 0.7 \\3 & 6.8 & 6.7 & 7.0 & 6.5 & 7.0 & 6.8 & 0.5\\4 & 7.0 & 6.7 & 6.7 & 6.8 & 6.8 & 6.8 & 0.3 \\5 & 6.8 & 6.8 & 6.6 & 6.5 & 6.4&6 .62 & 0.4 \\6 & 6.8 & 6.7 & 6.6 & 6.3 & 6.9&6 .66 & 0.6\\7 & 7.3 & 7.3 & 7.4 & 7.4 & 7.0&7 .28 & 0.4 \\8 & 7.2 & 7.0 & 7.2 & 6.9 & 7.1&7 .08 & 0.3 \\9 & 7.3 & 7.6 & 7.1 & 7.4 & 7.6 & 7.4 & 0.5\\10 & 7.2 & 7.6 & 7.5 & 7.6 & 7.1 & 7.4 & 0.5 \\11 & 7.2 & 7.2 & 7.4 & 7.0 & 7.0&7 .16 & 0.4 \\12 & 7.5 & 7.4 & 7.4 & 7.6 & 7.1 & 7.4 & 0.5\\\end{array}
 Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A machine that is supposed to produce ball bearings with a diameter of 7 mm yields the following data from a test of 5 ball bearings every 20 minutes.  \begin{array}{l|lllll|l|l} S&&&A&&&M&R\\\hline 1&6.3&6.8&6.9&6.8&6.9&6.74&0.5\\ 2 & 6.3 & 6.6 & 6.6 & 6.3 & 7.0&6 .56 & 0.7 \\ 3 & 6.8 & 6.7 & 7.0 & 6.5 & 7.0 & 6.8 & 0.5\\ 4 & 7.0 & 6.7 & 6.7 & 6.8 & 6.8 & 6.8 & 0.3 \\ 5 & 6.8 & 6.8 & 6.6 & 6.5 & 6.4&6 .62 & 0.4 \\ 6 & 6.8 & 6.7 & 6.6 & 6.3 & 6.9&6 .66 & 0.6\\ 7 & 7.3 & 7.3 & 7.4 & 7.4 & 7.0&7 .28 & 0.4 \\ 8 & 7.2 & 7.0 & 7.2 & 6.9 & 7.1&7 .08 & 0.3 \\ 9 & 7.3 & 7.6 & 7.1 & 7.4 & 7.6 & 7.4 & 0.5\\ 10 & 7.2 & 7.6 & 7.5 & 7.6 & 7.1 & 7.4 & 0.5 \\ 11 & 7.2 & 7.2 & 7.4 & 7.0 & 7.0&7 .16 & 0.4 \\ 12 & 7.5 & 7.4 & 7.4 & 7.6 & 7.1 & 7.4 & 0.5\\ \end{array}
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13
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A machine is supposed to fill boxes to a weight of 50 lbs. Every 30 minutes a sample of four boxes is tested; the results are given below. SAMR14938394542.75112525143651.7518356603252502844459464949.51555161484551.251664550464847.25575251455550.751084050534847.751394867605156.519104350504747.57114830383938.7518125046485349.25713505856645714144752474948.755155257585254.756\begin{array}{l|llll|l|l}S&&&A&&M&R\\\hline1 & 49 & 38 & 39 & 45 & 42.75 & 11 \\2 & 52 & 51 & 43 & 6 & 51.75 & 18 \\3 & 56 & 60 & 32 & 52 & 50 & 28\\4 & 44 & 59 & 46 & 49 & 49.5 & 15 \\5 & 51 & 61 & 48 & 45 & 51.25 & 16 \\6 & 45 & 50 & 46 & 48& 47.25 & 5 \\7 & 52 & 51 & 45 & 55& 50.75 & 10\\8 & 40 & 50 & 53 & 48 & 47.75 & 13 \\9 & 48 & 67 & 60 & 51 & 56.5 & 19 \\10 & 43 & 50 & 50 & 47 & 47.5 & 7 \\11 & 48 & 30 & 38 & 39 & 38.75 & 18\\12 & 50 & 46 & 48 & 53 & 49.25 & 7 \\13 & 50 & 58 & 56 & 64 & 57 & 14 \\14 & 47 & 52 & 47 & 49&48.75 & 5 \\15 & 52 & 57 & 58 & 52&54.75 & 6\\\end{array}
 Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A machine is supposed to fill boxes to a weight of 50 lbs. Every 30 minutes a sample of four boxes is tested; the results are given below.  \begin{array}{l|llll|l|l} S&&&A&&M&R\\\hline 1 & 49 & 38 & 39 & 45 & 42.75 & 11 \\ 2 & 52 & 51 & 43 & 6 & 51.75 & 18 \\ 3 & 56 & 60 & 32 & 52 & 50 & 28\\ 4 & 44 & 59 & 46 & 49 & 49.5 & 15 \\ 5 & 51 & 61 & 48 & 45 & 51.25 & 16 \\ 6 & 45 & 50 & 46 & 48& 47.25 & 5 \\ 7 & 52 & 51 & 45 & 55& 50.75 & 10\\ 8 & 40 & 50 & 53 & 48 & 47.75 & 13 \\ 9 & 48 & 67 & 60 & 51 & 56.5 & 19 \\ 10 & 43 & 50 & 50 & 47 & 47.5 & 7 \\ 11 & 48 & 30 & 38 & 39 & 38.75 & 18\\ 12 & 50 & 46 & 48 & 53 & 49.25 & 7 \\ 13 & 50 & 58 & 56 & 64 & 57 & 14 \\ 14 & 47 & 52 & 47 & 49&48.75 & 5 \\ 15 & 52 & 57 & 58 & 52&54.75 & 6\\ \end{array}
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14
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A machine is supposed to fill cans that contain 12 oz. Each hour, a sample of four cans is tested; the results of 15 consecutive hours are given below. SAMR111.211.711.811.711.60.6211.811.311.611.61.5750.5311.312.011.811.711.70.7412.111.612.112.011.950.5511.811.811.911.911.850.1612.011.911.811.711.850.3711.612.011.911.81.8250.4811.512.111.912.011.8750.6912.112.111.711.911.950.41011.712.011.611.911.80.41112.112.411.912.212.150.51212.512.012.412.312.30.51312.512.012.112.112.1750.51412.412.012.012.412.20.41512.412.412.612.112.3750.5\begin{array}{c|cccc|c|c}\mathrm{S} & & \mathrm{A} &&& \mathrm{M} & \mathrm{R} \\\hline 1 & 11.2 & 11.7 & 11.8 & 11 .7 & 11.6 & 0.6 \\2 & 11.8 & 11.3 & 11.6 & 11 . 6& 1.575 & 0.5 \\3 & 11.3 & 12.0 & 11.8 & 11.7 & 11.7 & 0.7 \\4 & 12.1 & 11.6 & 12.1 & 12.0&11 .95 & 0.5 \\5 & 11.8 & 11.8 & 11.9 & 11.9&11 .85 & 0.1\\6 & 12.0 & 11.9 & 11.8 & 11.7&11 .85&0 .3 \\7 & 11.6 & 12.0 & 11.9 & 11.8&1 .825&0 .4 \\8 & 11.5 & 12.1 & 11.9 & 12.0&11 .875&0 .6\\9 & 12.1 & 12.1 & 11.7 & 11.9&11 .95&0 .4 \\10 & 11.7 & 12.0 & 11.6 & 11.9 & 11.8 & 0.4 \\11 & 12.1 & 12.4 & 11.9 & 12.2&12 .15&0 .5\\12 & 12.5 & 12.0 & 12.4 & 12 .3& 12.3 & 0.5 \\13 & 12.5 & 12.0 & 12.1 & 12.1 & 12.175 & 0.5 \\14 & 12.4 & 12.0 & 12.0 & 12 . 4& 12.2 & 0.4 \\15 & 12.4 & 12.4 & 12.6 & 12 .1 & 12.375 & 0.5\\\end{array}
 Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A machine is supposed to fill cans that contain 12 oz. Each hour, a sample of four cans is tested; the results of 15 consecutive hours are given below.  \begin{array}{c|cccc|c|c} \mathrm{S} & & \mathrm{A} &&& \mathrm{M} & \mathrm{R} \\ \hline 1 & 11.2 & 11.7 & 11.8 & 11 .7 & 11.6 & 0.6 \\ 2 & 11.8 & 11.3 & 11.6 & 11 . 6& 1.575 & 0.5 \\ 3 & 11.3 & 12.0 & 11.8 & 11.7 & 11.7 & 0.7 \\ 4 & 12.1 & 11.6 & 12.1 & 12.0&11 .95 & 0.5 \\ 5 & 11.8 & 11.8 & 11.9 & 11.9&11 .85 & 0.1\\ 6 & 12.0 & 11.9 & 11.8 & 11.7&11 .85&0 .3 \\ 7 & 11.6 & 12.0 & 11.9 & 11.8&1 .825&0 .4 \\ 8 & 11.5 & 12.1 & 11.9 & 12.0&11 .875&0 .6\\ 9 & 12.1 & 12.1 & 11.7 & 11.9&11 .95&0 .4 \\ 10 & 11.7 & 12.0 & 11.6 & 11.9 & 11.8 & 0.4 \\ 11 & 12.1 & 12.4 & 11.9 & 12.2&12 .15&0 .5\\ 12 & 12.5 & 12.0 & 12.4 & 12 .3& 12.3 & 0.5 \\ 13 & 12.5 & 12.0 & 12.1 & 12.1 & 12.175 & 0.5 \\ 14 & 12.4 & 12.0 & 12.0 & 12 . 4& 12.2 & 0.4 \\ 15 & 12.4 & 12.4 & 12.6 & 12 .1 & 12.375 & 0.5\\ \end{array}
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15
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Describe a control chart. Complete the table to identify the important parts of different types of control charts.
 Center line and Upper  Lower  Points plotted how to compute control limitcontrol limit  Control char  for R Control char  for Xˉ Control char  for p\begin{array}{r|c}&&\text { Center line and } &\text {Upper } &\text { Lower } \\&\text { Points plotted } &\text {how to compute} &\text { control limit} &\text {control limit }\\\hline \text { Control char } \\\text { for } R \\\\\text { Control char } \\\text { for } \bar{X} \\\\\text { Control char } \\\text { for } p\end{array}
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A machine that is supposed to produce ball bearings with a diameter of 7 mm yields the following data from a test of 5 ball bearings every 20 minutes. SAMR16.36.86.96.86.96.740.626.36.66.66.37.06.560.736.86.77.06.57.06.80.547.06.76.76.86.86.80.356.86.86.66.56.46.620.466.86.76.66.36.96.660.677.37.37.47.47.07.280.487.27.07.26.97.17.080.397.37.67.17.47.67.40.5107.27.67.57.67.17.40.5117.27.27.47.07.07.160.4127.57.47.47.67.17.40.5\begin{array}{l|lllll|l|l}S&&&A&&&M&R\\\hline1 & 6.3 & 6.8 & 6.9 & 6.8 & 6.9&6 .74 & 0.6 \\2 & 6.3 & 6.6 & 6.6 & 6.3 & 7.0&6 .56 & 0.7 \\3 & 6.8 & 6.7 & 7.0 & 6.5 & 7.0 & 6.8 & 0.5 \\4 & 7.0 & 6.7 & 6.7 & 6.8 & 6.8 & 6.8 & 0.3\\5 & 6.8 & 6.8 & 6.6 & 6.5 & 6.4&6 .62 & 0.4 \\6 & 6.8 & 6.7 & 6.6 & 6.3 & 6.9&6 .66 & 0.6 \\7 & 7.3 & 7.3 & 7.4 & 7.4 & 7.0&7 .28 & 0.4 \\8 & 7.2 & 7.0 & 7.2 & 6.9 & 7.1&7 .08&0 .3\\9 & 7.3 & 7.6 & 7.1 & 7.4 & 7.6 & 7.4 & 0.5 \\10 & 7.2 & 7.6 & 7.5 & 7.6 & 7.1 & 7.4 & 0.5 \\11 & 7.2 & 7.2 & 7.4 & 7.0 & 7.0&7 .16 & 0.4 \\12 & 7.5 & 7.4 & 7.4 & 7.6 & 7.1 & 7.4 & 0.5\\\end{array}
 A machine that is supposed to produce ball bearings with a diameter of 7 mm yields the following data from a test of 5 ball bearings every 20 minutes.  \begin{array}{l|lllll|l|l} S&&&A&&&M&R\\\hline 1 & 6.3 & 6.8 & 6.9 & 6.8 & 6.9&6 .74 & 0.6 \\ 2 & 6.3 & 6.6 & 6.6 & 6.3 & 7.0&6 .56 & 0.7 \\ 3 & 6.8 & 6.7 & 7.0 & 6.5 & 7.0 & 6.8 & 0.5 \\ 4 & 7.0 & 6.7 & 6.7 & 6.8 & 6.8 & 6.8 & 0.3\\ 5 & 6.8 & 6.8 & 6.6 & 6.5 & 6.4&6 .62 & 0.4 \\ 6 & 6.8 & 6.7 & 6.6 & 6.3 & 6.9&6 .66 & 0.6 \\ 7 & 7.3 & 7.3 & 7.4 & 7.4 & 7.0&7 .28 & 0.4 \\ 8 & 7.2 & 7.0 & 7.2 & 6.9 & 7.1&7 .08&0 .3\\ 9 & 7.3 & 7.6 & 7.1 & 7.4 & 7.6 & 7.4 & 0.5 \\ 10 & 7.2 & 7.6 & 7.5 & 7.6 & 7.1 & 7.4 & 0.5 \\ 11 & 7.2 & 7.2 & 7.4 & 7.0 & 7.0&7 .16 & 0.4 \\ 12 & 7.5 & 7.4 & 7.4 & 7.6 & 7.1 & 7.4 & 0.5\\ \end{array}
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17
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A machine is supposed to fill boxes to a weight of 50 lbs. Every 30 minutes a sample of four boxes is tested; the results are given below.
SAMR14938394542.751125251436151.7518356603252502844459454949.51555161484551.251664550464847.25575251455550.751184050534847.751394867605156.519104350504747.57114830383938.7518125046485349.25713505856645714144752474948.755155257585254.756\begin{array} { l|llll|l| } S&&A&&&M&R\\\hline 1&49&38&39&45&42.75&11\\2&52&51&43&61&51.75&18\\3&56&60&32&52&50&28\\4&44&59&45&49&49.5&15\\5&51&61&48&45&51.25&16\\6&45&50&46&48&47.25&5\\7&52&51&45&55&50.75&11\\8&40&50&53&48&47.75&13\\9&48&67&60&51&56.5&19\\10&43&50&50&47&47.5&7\\11&48&30&38&39&38.75&18\\12&50&46&48&53&49.25&7\\13&50&58&56&64&57&14\\14&47&52&47&49&48.75&5\\15&52&57&58&52&54.75&6\end{array}
 Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A machine is supposed to fill boxes to a weight of 50 lbs. Every 30 minutes a sample of four boxes is tested; the results are given below.  \begin{array} { l|llll|l|  } S&&A&&&M&R\\ \hline 1&49&38&39&45&42.75&11\\2&52&51&43&61&51.75&18\\ 3&56&60&32&52&50&28\\4&44&59&45&49&49.5&15\\ 5&51&61&48&45&51.25&16\\6&45&50&46&48&47.25&5\\ 7&52&51&45&55&50.75&11\\8&40&50&53&48&47.75&13\\ 9&48&67&60&51&56.5&19\\10&43&50&50&47&47.5&7\\11&48&30&38&39&38.75&18\\12&50&46&48&53&49.25&7\\ 13&50&58&56&64&57&14\\14&47&52&47&49&48.75&5\\15&52&57&58&52&54.75&6 \end{array}
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18
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Describe the three criteria used to determine if a control chart indicates a process which is not statistically stable.
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19
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Describe what process data are. Why are process data important to businesses? What is a common goal of businesses using quality control?
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20
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A common goal of quality control is to reduce variation in a product or service. List and describe the two types of variability. Give an example of each.
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21
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -
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22
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A control chart for xˉ\bar x is shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.  Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A control chart for  \bar x  is shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.
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Solve the Problem.

-A control chart for monitoring variation and center can be based on standard deviations instead of on ranges. An s chart for monitoring variation is made by plotting sample standard deviations with a center line at sˉ\bar { s } (the mean of the sample standard deviations) and control limits at B4sˉB _ { 4 } \bar { s } and B3sˉB _ { 3 } \bar { s } , where B4B _ { 4 } sˉ\bar { s } and B3B _ { 3 }sˉ\bar { s } are found in the Control Chart Constants table. Construct an s chart for the data below.

A manufacturer of lightbulbs picks 10 lightbulbs at random each day for quality control. The mean, standard de and range (in hours) of the lifetimes of the 10 lightbulbs are calculated. The results for 12 consecutive days are sh the table below.
 Day xˉ Range  s 1201.13.41.22203.44.71.73200.93.10.94205.66.22.35201.34.71.36200.53.71.77205.85.82.18203.76.22.99199.82.10.810202.74.41.611200.02.70.712204.67.83.0\begin{array}{lcll}\text { Day } & \bar{x} & \text { Range } & \text { s } \\\hline 1 & 201.1 & 3.4 & 1.2 \\2 & 203.4 & 4.7 & 1.7 \\3 & 200.9 & 3.1 & 0.9 \\4 & 205.6 & 6.2 & 2.3 \\5 & 201.3 & 4.7 & 1.3\\6 & 200.5 & 3.7 & 1.7 \\7 & 205.8 & 5.8 & 2.1 \\8 & 203.7 & 6.2 & 2.9 \\9 & 199.8 & 2.1 & 0.8 \\10 & 202.7 & 4.4 & 1.6 \\11 & 200.0 & 2.7 & 0.7 \\12 & 204.6 & 7.8 & 3.0\\\end{array}
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24
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A control chart for R is shown below. Determine whether the process variation is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of statistically stable variation. Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A control chart for R is shown below. Determine whether the process variation is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of statistically stable variation.
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25
Solve the Problem.

-An xˉ\bar { x } chart based on standard deviations (instead of ranges) is made by plotting sample means with a centerline at xˉˉ\bar {\bar { x} } and control limits at xˉˉ+A3sˉ\bar {\bar { x} } + A _ { 3 } \bar { s } and xˉˉA3sˉ\bar {\bar { x} } - A _ { 3 } \bar { s } where A3A _ { 3 } is found in the Control Chart Constants table and sˉ\bar { s } is the mean of the sample standard deviations. Construct an xˉ\bar { x } chart based on standard deviations for the data belo
A manufacturer of high intensity video projector lightbulbs picks 6 lightbulbs at random each day for quality cor The mean, standard deviation, and range (in hours) of the lifetimes of the 6 lightbulbs are calculated. The results consecutive days are shown in the table below.
 Day xˉ Range  s 121.13.41.2223.44.71.7320.93.10.9425.66.22.3521.34.71.3620.53.71.7725.85.82.1823.76.22.9929.82.10.81022.74.41.61120.02.70.71224.67.83.0\begin{array}{lllll}\text { Day } & \bar{x} & \text { Range } & \text { s } \\1 & 21.13 .4 & & 1.2 & \\2 & 23.44 .7 & & 1.7 & \\3 & 20.93 .1 & & 0.9 & \\4 & 25.66 .2 & & 2.3 & \\5 & 21.3 & 4.7 &{1.3} \\6 & 20.5 & 3.7 &{1.7} \\7 & 25.85 .8 & &2.1 & \\8 & 23.76 .2 & & 2.9 & \\9 & 29.82 .1 & & 0.8 & \\10 & 22.7 & 4.4 &{1.6} \\11 & 20.02 .7 & & 0.7 & \\12 & 24.67 .8 & & 3.0\end{array}  Answer: \text { Answer: }
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26
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A run chart for individual values is shown below. Does there appear to be a pattern suggesting that the process is not within statistical control? If so, describe the pattern. Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A run chart for individual values is shown below. Does there appear to be a pattern suggesting that the process is not within statistical control? If so, describe the pattern.
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27
Use the given process data to construct a control chart for p

-If the weight of cereal in a particular packet is less than 14 oz, the packet is considered nonconforming. Each week, the manufacturer randomly selects 1,000 cereal packets and determines the number that are nonconforming. The results for 12 consecutive weeks are shown below. 46&nbsp;32&nbsp;21&nbsp;30&nbsp;47&nbsp;31&nbsp;32&nbsp;52&nbsp;48&nbsp;45&nbsp;62&nbsp;58
 Use the given process data to construct a control chart for p  -If the weight of cereal in a particular packet is less than 14 oz, the packet is considered nonconforming. Each week, the manufacturer randomly selects 1,000 cereal packets and determines the number that are nonconforming. The results for 12 consecutive weeks are shown below.  46 32 21 30 47 31 32 52 48 45 62 58
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28
Solve the Problem.

-A control chart for attributes is to be constructed. Which process would have wider control limits, a process which has been having a 5% rate of nonconforming items, or a process which has been having a 10% of nonconforming items? Assume that both processes have the same sample sizes. For a given sample size, would it be easier to detect a shift from 5% to 10% or a shift from 10% to 15%? Explain your reasoning.
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29
Use the given process data to construct a control chart for p

-A drugstore considers a wait of more than 5 minutes to be a defect. Each week 100 customers are randomly selected and timed at the checkout line. The numbers of defects for 20 consecutive weeks are given below. 4&nbsp;4&nbsp;5&nbsp;5&nbsp;5&nbsp;5&nbsp;5&nbsp;5&nbsp;6&nbsp;6&nbsp;6&nbsp;6&nbsp;12&nbsp;6&nbsp;6&nbsp;6&nbsp;7&nbsp;6&nbsp;7&nbsp;8&nbsp;7
 Use the given process data to construct a control chart for p  -A drugstore considers a wait of more than 5 minutes to be a defect. Each week 100 customers are randomly selected and timed at the checkout line. The numbers of defects for 20 consecutive weeks are given below.  4 4 5 5 5 5 5 5 6 6 6 6 12 6 6 6 7 6 7 8 7
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30
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -
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31
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

- A control chart for xˉ\bar x is shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.  Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  - A control chart for  \bar x  is shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.
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32
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A control chart for R is shown below. Determine whether the process variation is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of statistically stable variation. Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A control chart for R is shown below. Determine whether the process variation is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of statistically stable variation.
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33
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -
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34
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -
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35
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A control chart for xˉ\bar x is shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.  Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A control chart for \bar x   is shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.
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36
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A control chart fo xˉ\bar x s shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.  Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A control chart fo  \bar x  s shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.
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37
Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply

-A run chart for individual values is shown below. Does there appear to be a pattern suggesting that the process is not within statistical control? If so, describe the pattern. Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply  -A run chart for individual values is shown below. Does there appear to be a pattern suggesting that the process is not within statistical control? If so, describe the pattern.
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38
Use the given process data to construct a control chart for p

-A manufacturer monitors the level of defects in the television sets that it produces. Each week, 200 television sets are randomly selected and tested and the number of defects is recorded. The results for 12 consecutive weeks are shown below. 4&nbsp;7&nbsp;5&nbsp;6&nbsp;8&nbsp;3&nbsp;12&nbsp;4&nbsp;4&nbsp;5&nbsp;6&nbsp;2
 Use the given process data to construct a control chart for p  -A manufacturer monitors the level of defects in the television sets that it produces. Each week, 200 television sets are randomly selected and tested and the number of defects is recorded. The results for 12 consecutive weeks are shown below.  4 7 5 6 8 3 12 4 4 5 6 2
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