# Statistical Quality Control Questions and Answers – Control Charting Techniques – Statistical Process Control for Short Production Runs – 5

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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 – 5”.

1. When the type I error is specified, which of these is correct expression for the UCL of the modified control charts?
a) $$UCL=USL-\left(Z_δ+\frac{Z_α}{\sqrt{n}}\right) \sigma$$
b) $$UCL=USL-\left(Z_δ-\frac{Z_α}{\sqrt{n}}\right) \sigma$$
c) $$UCL=USL+\left(Z_δ+\frac{Z_α}{\sqrt{n}}\right) \sigma$$
d) $$UCL=USL+\left(Z_δ-\frac{Z_α}{\sqrt{n}}\right) \sigma$$

Explanation: The modified control charts are the alternatives of ordinary Shewhart control charts, when the process capability is high. These have UCL as,
$$UCL=USL-\left(Z_δ-\frac{Z_α}{\sqrt{n}}\right) \sigma$$

2. Which of these is a correct expression for the UCL of the modified control charts when the type I error is not specified?
a) $$UCL=USL+\left(Z_δ+\frac{3}{\sqrt{n}}\right) \sigma$$
b) $$UCL=USL+\left(Z_δ-\frac{3}{\sqrt{n}}\right) \sigma$$
c) $$UCL=USL-\left(Z_δ-\frac{3}{\sqrt{n}}\right) \sigma$$
d) $$UCL=USL-\left(Z_δ+\frac{3}{\sqrt{n}}\right) \sigma$$

Explanation: The UCL of the modified control charts can be done by both, specifying the type I error or by not specifying the type I error. When the type I error is not specified, the UCL is,
$$UCL=USL-\left(Z_δ-\frac{3}{\sqrt{n}}\right) \sigma$$

3. When the type I error is not specified, the value of LCL of the modified control charts is ____________
a) $$LCL=LSL+\left(Z_δ-\frac{3}{\sqrt{n}}\right) \sigma$$
b) $$LCL=LSL-\left(Z_δ+\frac{3}{\sqrt{n}}\right) \sigma$$
c) $$LCL=LSL-\left(Z_δ-\frac{3}{\sqrt{n}}\right) \sigma$$
d) $$LCL=LSL+\left(Z_δ+\frac{3}{\sqrt{n}}\right) \sigma$$

Explanation: The LCL of the modified control chart also uses the type I error. If the type I error is not to be specified. Its value is written by the expression,
$$LCL=LSL+\left(Z_δ-\frac{3}{\sqrt{n}}\right) \sigma$$

4. ____________ sigma limits are recommended for modified control charts.
a) 4
b) 2
c) 3
d) 6

Explanation: The modified control charts are effective when the spread of process is quite less than the limits used. So 2-sigma limits are recommended for the modified control charts.

5. Which of the hypothesis can be tested using the modified control charts?
a) μL ≤ μ ≤ μU
b) μL ≤ μ
c) μ ≤ μU
d) μL = μ = μU

Explanation: The modified control charts allow the mean shift between two particular mean values. This means that the hypothesis μL ≤ μ ≤ μU can be tested using the modified control charts.

6. To design a modified control chart, we must have a good estimate of _________ available.
a) μ
b) σ
c) μ2
d) process variance

Explanation: The modified control chart limits are totally based upon the estimate of the process standard deviation. So, to design a modified control chart, we must have a good estimate of σ available.

7. If process variability shifts, the modified control charts are ____________
a) Not appropriate
b) Totally appropriate
c) Good to use
d) Perfect for the mapping the shifts

Explanation: A modified control chart needs a good estimate of the process standard deviation. As the process standard deviation is depended upon the process variability, the modified control charts are not appropriate to use.

8. If there is a chance of shifting of the process variability, which chart may be used with the modified control chart?
a) c-chart
b) p-chart
c) R-chart
d) x̅ -chart

Explanation: As the process variability shifts can be monitored using a Shewhart R chart or an s-chart, if there is a chance of shifting of the process variability, they can be used in conjunction with modified control charts.

9. From which chart the initial estimate of the process variability is determined?
a) R-chart
b) c-chart
c) p-chart
d) Cusum charts

Explanation: As R charts and s-charts are good ways to estimate the process standard deviation, hence the process variability too, they are used to determine the initial estimate of the process variability.

10. When the type I error is specified, the LCL of the modified control chart is ___________
a) $$LCL=LSL-\left(Z_δ-\frac{Z}{\sqrt{n}}\right)$$
b) $$LCL=LSL-\left(Z_δ+\frac{Z}{\sqrt{n}}\right)$$
c) $$LCL=LSL+\left(Z_δ+\frac{Z}{\sqrt{n}}\right)$$
d) $$LCL=LSL+\left(Z_δ-\frac{Z}{\sqrt{n}}\right)$$

Explanation: As the type I error is not specified, the value of the 100(1-δ) percentage point of the normal distribution Zδ is used. The LCL is,
$$LCL=LSL+\left(Z_δ-\frac{Z}{\sqrt{n}}\right)$$

11. The approach of using a x chart to monitor the fraction of nonconforming units or the fraction of the units exceeding the specifications, is called the ___________
a) Shewhart control charts
b) Cusum charts
c) EWMA charts
d) Acceptance control charts

Explanation: There is an approach to using an x chart to monitor the fraction of nonconforming or defective units, or the fraction of the units exceeding the specifications, which is called Acceptance control chart.

12. Who was the first person to develop the acceptance control charts?
a) Astern
b) Roy
c) Freund
d) Crowder

Explanation: The first person, to develop a method to use the x chart to monitor the fraction of defective units, was Freund (1957). He first developed the technique of the acceptance control charts.

13. A modified control charts limit expression does not contain ___________
a) δ
b) σ
c) μ
d) α

Explanation: The modified control charts was based on a specific sample size n, a process nonconforming δ, and type I error probability α. It does not depend on μ.

14. The p-chart is the only chart to monitor the fraction of nonconforming units.
a) True
b) False

Explanation: The acceptance charts is based on the approach of using the x̅ chart to monitor the fraction of nonconforming units. So p-chart is not the only chart to monitor the fraction nonconforming units.

15. If the process mean increases very much, the modified control charts are not appropriate.
a) True
b) False 