# Statistical Quality Control Questions and Answers – Control Charting Techniques – Statistical Process Control for Short Production Runs – 3

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This set of Statistical Quality Control Multiple Choice Questions & Answers (MCQs) focuses on “Control Charting Techniques – Statistical Process Control for Short Production Runs – 3”.

1. What is the statistic used to plot on control chart for a standardized p-chart for short production runs?
a) $$Z_i=\frac{\hat{p}_i+\bar{p}}{\frac{\sqrt{\bar{p}(1+\bar{p})}}{n}}$$
b) $$Z_i=\frac{\hat{p}_i-\bar{p}}{\frac{\sqrt{\bar{p}(1-\bar{p})}}{n}}$$
c) $$Z_i=\frac{\hat{p}_i-\bar{p}}{\frac{\sqrt{\bar{p}(1+\bar{p})}}{n}}$$
d) $$Z_i=\frac{\hat{p}_i+\bar{p}}{\frac{\sqrt{\bar{p}(1-\bar{p})}}{n}}$$

Explanation: The p-charts are plotted on the data of no of samples not conforming. The statistic plotted on the standardized version of it, is expressed as,
$$Z_i=\frac{\hat{p}_i-\bar{p}}{\frac{\sqrt{\bar{p}(1-\bar{p})}}{n}}$$

2. What is the value of standard deviation for the standardized p-chart for short production runs?
a) $$\sqrt{\frac{\bar{p}(1-\bar{p})}{n}}$$
b) $$\sqrt{\frac{\bar{p}(1+\bar{p})}{n}}$$
c) $$\sqrt{\frac{\bar{p}(\bar{p}-1)}{n}}$$
d) $$\sqrt{\frac{\bar{p}(1-\bar{p})}{2n}}$$

Explanation: The standardized control charts are used to monitor processes for short production runs. The standardized p-chart which is used in short production runs is having the standard deviation value equal to,
$$\sqrt{\frac{\bar{p}(1-\bar{p})}{n}}$$

3. What is the standard deviation value for the standardized c chart used for the short production runs?
a) $$\sqrt{c}$$
b) $$\sqrt{\bar{c}}$$
c) $$\bar{c}$$
d) $$\hat{c}$$

Explanation: The standard deviation value for the standardized c chart remains constant if it is used for the short production runs. It is expressed as,
$$\sqrt{\bar{c}}$$

4. What is the value of the statistic to be plotted on the standardized c-chart which is designed to run in the short production?
a) $$Z_i=\frac{c_i+2\bar{c}}{\sqrt{\bar{c}}}$$
b) $$Z_i=\frac{c_i-2\bar{c}}{\sqrt{\bar{c}}}$$
c) $$Z_i=\frac{c_i-\bar{c}}{\sqrt{\bar{c}}}$$
d) $$Z_i=\frac{c_i+\bar{c}}{\sqrt{\bar{c}}}$$

Explanation: The c chart is plotted keeping the nonconformity number data as the observations. The statistic which is to be standardized version of it, when the case is of the short production runs, is
$$Z_i=\frac{c_i-2\bar{c}}{\sqrt{\bar{c}}}$$

5. What is the value of the target value for the number nonconforming chart?
a) np
b) 2p
c) 3p
d) 2np

Explanation: The number nonconforming chart is called the np chart too. It plots the number of nonconforming samples in total samples. The target value for the number nonconforming chart is np.

6. The attribute ui when plotted on standardized control chart for short production runs, the statistic plotted on the chart has the value equal to __________
a) $$Z_i=\frac{u_i-\bar{u}}{\sqrt{\frac{\bar{u}}{n}}}$$
b) $$Z_i=\frac{u_i+2\bar{u}}{\sqrt{\frac{\bar{u}}{n}}}$$
c) $$Z_i=\frac{u_i+\bar{u}}{\sqrt{\frac{\bar{u}}{n}}}$$
d) $$Z_i=\frac{u_i-2\bar{u}}{\sqrt{\frac{\bar{u}}{n}}}$$

Explanation: The attribute u is called the average number of nonconformities per unit. The standardized u-chart is plotted for statistic,
$$Z_i=\frac{u_i-\bar{u}}{\sqrt{\frac{\bar{u}}{n}}}$$

7. What is the standard deviation of the number of nonconformities per unit, when the standardized u-chart is used for monitoring the process?
a) $$\sqrt{\frac{\bar{u}}{2n}}$$
b) $$\sqrt{\frac{\bar{u}}{n}}$$
c) $$\frac{\sqrt{u}}{n}$$
d) $$\sqrt{\bar{u}}$$

Explanation: The deviation of the number of nonconformities per unit is plotted on Shewhart u-chart. Its standard deviation is expressed as,
standard deviation=$$\sqrt{\frac{\bar{u}}{n}}$$

8. What is the value of the statistic plotted on the standardized np-chart?
a) $$z_i=\frac{n\hat{p}_i+n\bar{p}}{\sqrt{n\bar{p}(1+\bar{p})}}$$
b) $$z_i=\frac{n\hat{p}_i-n\bar{p}}{\sqrt{n\bar{p}(1+\bar{p})}}$$
c) $$z_i=\frac{n\hat{p}_i+n\bar{p}}{\sqrt{n\bar{p}(1-\bar{p})}}$$
d) $$z_i=\frac{n\hat{p}_i-n\bar{p}}{\sqrt{n\bar{p}(1-\bar{p})}}$$

Explanation: The np chart monitors the process by using the data of the nonconforming samples. The statistic plotted on the standardized version of it for short production run is,
$$z_i=\frac{n\hat{p}_i-n\bar{p}}{\sqrt{n\bar{p}(1-\bar{p})}}$$

9. The upper limit of the standardized c-chart for short production runs is ________
a) 1
b) 2
c) -3
d) +3

Explanation: The c chart is used to plot the number of nonconformities on the control chart. The standardized version of it has the UCL of +3 and LCL of -3.

10. The LCL of the standardized p-chart is ________
a) -2
b) +3
c) -1
d) -3

Explanation: The LCL and UCL of the standardized p-chart are at the same units away from the center line which is at zero. The UCL and the LCL of the standardized p-chart are ±3.

11. The center line of the np-chart is at _______
a) -2
b) +2
c) 0
d) 3

Explanation: The control chart, which plots the number of nonconforming samples, is called np-chart. This charts when standardized, have their center line at the zero.

12. Which of these correctly shows the correct values for standardized u-chart in the order of CL, UCL and LCL?
a) 0, 3 and -3
b) 3, 0 and -3
c) 0, -3 and 3
d) -3, 0 and 3

Explanation: THE u-chart, when standardized, has the center line at zero value. The values of the UCL and LCL of the standardized version of u-chart, plotted for short production runs, are ±3.

13. Which of these does not have the LCL and UCL at ∓3?
a) Standardized u-chart
b) Standardized R-chart
c) Standardized c-chart
d) Standardized p-chart

Explanation: The standardized attribute charts are the only charts which have their upper and lower control limits at ±3. Variable control charts do not have their control limits at ±3.

14. The values of control limits for the standardized c-chart are different from the control limits of the standardized p-chart.
a) True
b) False

Explanation: Both, the p-chart and the c-chart when standardized, have their control limits at ±3 value. So the values of the control limits for both, standardized c-chart, and standardized p-chart, are same.

15. The control limits for the p-chart and the standardized p-chart are different.
a) True
b) False

Explanation: The p-chart has the control limits at,
$$p \pm 3\sqrt{\frac{p(1-p)}{n}}$$
Here p is the fraction nonconforming value. Whereas, the standardized p-chart has its control limits at ±3 values.

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