A Quality Analyst wants to construct a control chart for determining whether three machines,all producing the same product,are under control with regard to a particular quality variable.Accordingly,he sampled four units of output from each machine,with the following results: Using the factors for three sigma control limits,what are the x-bar chart upper and lower control limits?
A)24.33 and 15.67
B)23.29 and 16.71
C)23.5 and 16.5
D)23.16 and 16.84
E)24.42 and 17.67

Question

A Quality Analyst wants to construct a control chart for determining whether three machines,all producing the same product,are under control with regard to a particular quality variable.Accordingly,he sampled four units of output from each machine,with the following results:  Using the factors for three sigma control limits,what are the x-bar chart upper and lower control limits?
A)24.33 and 15.67 
B)23.29 and 16.71 
C)23.5 and 16.5 
D)23.16 and 16.84 
E)24.42 and 17.67

Quizplus · Accepted Answer

To calculate the control limits for the x-bar chart, we first compute the average (x-bar) of each sample and then calculate the average of these x-bars.

The average x-bar is:

(20+22.5+21+19.5)/4 = 20.75

Next, we need to calculate the standard deviation of the x-bars, which is given by:

sqrt[(sum of (x-bar - x-double-bar)^2) / (k-1)]

Where k is the number of samples (in this case, 3).

Plugging in the values, we get:

sqrt[((20-20.75)^2 + (22.5-20.75)^2 + (21-20.75)^2 + (19.5-20.75)^2) / (3-1)] = 1.479

Finally, we can calculate the control limits using the formula:

Upper control limit = x-double-bar + 3 * (standard deviation of x-bar)

Lower control limit = x-double-bar - 3 * (standard deviation of x-bar)

Plugging in the values, we get:

Upper control limit = 20.75 + 3 * 1.479 = 24.19

Lower control limit = 20.75 - 3 * 1.479 = 17.31

Therefore, the x-bar chart upper and lower control limits are 24.19 and 17.31 respectively. The closest choice to these values is D.

A Quality Analyst Wants to Construct a Control Chart for Determining