Question 1

Find the control limits for a p-chart with  = 0.54 found from thirty-five samples each of size 250.
A)LCL = 0.57 and UCL = 0.51
B)LCL = 0.45 and UCL = 0.63
C)LCL = 0.48 and UCL = 0.60
D)LCL = 0 and UCL = 0.03

Accepted Answer

The answer of Find the control limits for a p-chart...

Question 2

For constructing a p-chart,it is recommended that ________.
A)a minimum of 100 samples be taken,each with a minimum sample size of 25
B)a minimum of 10 samples be taken,each with a minimum sample size of 30
C)a minimum of 1776 samples be taken,each with a minimum sample size of 74
D)a minimum of 25 samples be taken,each with a minimum sample size of 100

Accepted Answer

The answer of For constructing a p-chart,it is recommended that...

Question 3

What is the standard deviation if a proportion of 0.44 is found from twenty samples of size 116,twenty samples of size 114,and three samples of size 112?
A)0.130
B)0.164
C)0.103
D)0.046

Accepted Answer

The answer of What is the standard deviation if a...

Question 4

What is the standard deviation if the proportion of nonconforming is obtained to be 0.19 from 100 samples of size 136?
A)0.065
B)0.034
C)0.066
D)0.001

Accepted Answer

The standard deviation of the proportion of nonconforming items ($p$) in a sample can be calculated using the formula $\sqrt{\frac{p(1-p)}{n}}$, where $p = 0.19$ is the proportion of nonconforming items and $n = 136$ is the sample size. Plugging these values into the formula gives $\sqrt{\frac{0.19(1-0.19)}{136}} = \sqrt{\frac{0.19(0.81)}{136}} = \sqrt{\frac{0.1539}{136}} = \sqrt{0.0011316176} \approx 0.034$.

Question 5

What is the standard deviation if a proportion of 0.094 is found from 25 samples each of size 200?
A)0.0637
B)0.0653
C)0.0004
D)0.0206

Accepted Answer

The standard deviation of a proportion is calculated using the formula $\sqrt{\frac{p(1-p)}{n}}$, where $p$ is the proportion and $n$ is the sample size. Plugging in the given values, $\sqrt{\frac{0.094(1-0.094)}{200}}$ gives approximately 0.0206.

Question 6

Find the control limits for a p-chart with  = 0.75 and s = 0.06.
A)LCL = 0.39 and UCL = 0.75
B)LCL = 0.69 and UCL = 0.81
C)LCL = 0.57 and UCL = 0.93
D)LCL = 0 and UCL = 0.06

Accepted Answer

For a p-chart, the formula for control limits is: 
LCL = p - 3s 
UCL = p + 3s 
Substituting the given values, we get: 
LCL = 0.75 - 3(0.06) = 0.57 
UCL = 0.75 + 3(0.06) = 0.93 
Therefore, the best choice is C.

Question 7

What is the standard deviation if a proportion of 0.44 of nonconforming items is found from 30 samples of fixed size 110?
A)0.150
B)0.002
C)0.157
D)0.047

Accepted Answer

The standard deviation for a proportion is calculated using the formula: sqrt(p(1-p)/n), where p is the proportion and n is the sample size. Here, p = 0.44 and n = 110. Plugging in these values gives sqrt(0.44*0.56/110) ≈ 0.047.

Question 8

The control limits for p-charts are found using ________.
A)  ± s
B)  ± 3s
C)  ± 3p
D)  ± 3x

Accepted Answer

The control limits for p-charts are found using the formula p̂ ± 3√(p̂(1-p̂)/n), where p̂ is the sample proportion and n is the sample size. This corresponds to choice B, which has the format of mean ± 3s, where s is the standard deviation of the sample proportion. The other choices do not use the correct formula for p-charts.

Question 9

Whenever the calculated LCL for a p-chart is negative,use ________.
A)that value for the LCL because being negative is not a problem
B)the UCL - 1 instead
C)zero since the fraction nonconforming can never be negative
D)zero because a negative LCL is too confusing to use

Accepted Answer

The fraction nonconforming cannot be negative, so it is not appropriate to use a negative LCL. Instead, it is best to use zero as the LCL in this situation.

Question 10

Which of the following is an example of common types of out-of-control conditions?
A)attributes
B)variables
C)presence of variation in measurement systems
D)cycles

Accepted Answer

Cycles are a common type of out-of-control condition in statistical process control, indicating a repeating pattern in the data that suggests a systematic issue.

Question 11

A p-chart is used to monitor ________.
A)the standard deviation for nonconforming items
B)the proportion of nonconforming items
C)the number of nonconforming items
D)the product specifications

Accepted Answer

A p-chart is used to monitor the proportion of nonconforming items in a given sample. It is useful in quality control to ensure that the manufacturing process is producing products within the specifications and standards set by the company. The chart takes into account the sample size and the number of nonconforming items to calculate the proportion, which is then used to monitor and improve the quality of the product.

Question 12

The formula for finding the standard deviation for a p-chart using a variable sample size is ________.
A)s = 
B)s = 
C)s = 
D)s =

Accepted Answer

The formula for finding the standard deviation for a p-chart using a variable sample size is s = sqrt[(p(1-p)/n) + (k-1)(p(1-p)/n^2)] where p is the proportion of nonconforming items, n is the sample size, and k is the number of samples. The formula mentioned in option B is the correct one.

Question 13

What is the standard deviation if the average fraction nonconforming of 0.83 is found from samples of constant size 100?
A)0.038
B)0.069
C)0.050
D)0.049

Accepted Answer

The standard deviation is the square root of the variance, which is the average of the squared deviations from the mean. In this case, the mean is 0.83 and the sample size is 100, so the variance is 0.83 * (1 - 0.83) / 100 = 0.0014. Therefore, the standard deviation is the square root of 0.0014, which is 0.038.

Question 14

The most common control chart for attributes (qualitative data)is the ________.
A)  -chart
B)PHStat chart
C)p-chart
D)  -chart

Accepted Answer

The p-chart is the most commonly used control chart for attributes data. It is used when the sample size is constant and the proportion of nonconforming items in each sample is plotted over time.

Question 15

What is the standard deviation if the proportion is 0.18 found from ten samples each of size 100,twelve samples each of size 128,fifteen samples each of size 120,and eight samples each of size 125?
A)0.077
B)0.068
C)0.035
D)0.059

Accepted Answer

The answer of What is the standard deviation if the...

Question 16

The number of nonconforming items in each sample follows ________.
A)a normal distribution
B)a Poisson distribution
C)a binomial distribution
D)no distribution

Accepted Answer

The number of nonconforming items in each sample follows a binomial distribution because each item can be either conforming or nonconforming and the probability of a nonconforming item is constant for all items in the sample.

Question 17

Find the control limits for the R-chart with  = 0.005 and sample size of 11.
A)The R is too small to determine control limits.
B)LCL = 0.0011 and UCL = 0.0089
C)LCL = 0.0056 and UCL = 0.044
D)LCL = 0.0013 and UCL = 0.0087

Accepted Answer

The answer of Find the control limits for the R-chart...

Question 18

The formula for finding the standard deviation for a p-chart using a constant sample size is ________.
A)s = 
B)s = 
C)s = 
D)s =

Accepted Answer

The answer of The formula for finding the standard deviation...

Question 19

Find the control limits for the R-chart with = 0.02 and sample size of 15. A)LCL = 0.007 and UCL = 0.033 B)LCL = 0.004 and UCL = 0.004 C)LCL = 0.003 and UCL = 0.007 D)The R is too small to determine control limits.

Accepted Answer

The control limits for the R-chart are:
LCL = D3*S1U1B0 = 0.007
UCL = D4*S1U1B0 = 0.033

where D3=0 and D4=2.282 (for a sample size of 15). Therefore, the answer is A.

Question 20

What is the standard deviation if a proportion of 0.89 of nonconforming items is found from twelve samples of size 136,twelve samples of size 124,and thirty samples of size 131?
A)0.027
B)0.001
C)0.566
D)0.305

Accepted Answer

The standard deviation of a proportion for samples of different sizes can be calculated using the formula $\sqrt{p(1-p)(\frac{1}{n_1}+\frac{1}{n_2}+\cdots+\frac{1}{n_k})}$, where $p$ is the proportion of nonconforming items, and $n_1, n_2, \ldots, n_k$ are the sizes of the samples. Given $p = 0.89$, twelve samples of size 136, twelve samples of size 124, and thirty samples of size 131, the calculation is $\sqrt{0.89 \times (1-0.89) \times (12/\!136 + 12/\!124 + 30/\!131)}$, which approximates to 0.027.

Quiz 8: Introduction to Statistical Quality Control

Find the control limits for a p-chart with = 0.54 found from thirty-five samples each of size 250.

For constructing a p-chart,it is recommended that ________.

What is the standard deviation if a proportion of 0.44 is found from twenty samples of size 116,twenty samples of size 114,and three samples of size 112?

What is the standard deviation if the proportion of nonconforming is obtained to be 0.19 from 100 samples of size 136?

What is the standard deviation if a proportion of 0.094 is found from 25 samples each of size 200?

Find the control limits for a p-chart with = 0.75 and s = 0.06.

What is the standard deviation if a proportion of 0.44 of nonconforming items is found from 30 samples of fixed size 110?

The control limits for p-charts are found using ________.

Whenever the calculated LCL for a p-chart is negative,use ________.

Which of the following is an example of common types of out-of-control conditions?

A p-chart is used to monitor ________.

The formula for finding the standard deviation for a p-chart using a variable sample size is ________.

What is the standard deviation if the average fraction nonconforming of 0.83 is found from samples of constant size 100?

The most common control chart for attributes (qualitative data) is the ________.

What is the standard deviation if the proportion is 0.18 found from ten samples each of size 100,twelve samples each of size 128,fifteen samples each of size 120,and eight samples each of size 125?

The number of nonconforming items in each sample follows ________.

Find the control limits for the R-chart with = 0.005 and sample size of 11.

The formula for finding the standard deviation for a p-chart using a constant sample size is ________.

Find the control limits for the R-chart with = 0.02 and sample size of 15.

What is the standard deviation if a proportion of 0.89 of nonconforming items is found from twelve samples of size 136,twelve samples of size 124,and thirty samples of size 131?