# Statistical Quality Control Questions and Answers – Attribute Charts – Control Charts for Nonconformities (Defects) – 2

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This set of Statistical Quality Control Questions and Answers for Campus interviews focuses on “Attribute Charts – Control Charts for Nonconformities (Defects) – 2”.

1. The 3 – sigma upper limit for a control chart for average number of nonconformities per unit, is expressed by ___________
a) UCL=$$\bar{u} + 3\sqrt{\frac{\bar{u}}{n}}$$
b) UCL=$$\bar{u} – 3\sqrt{\frac{\bar{u}}{n}}$$
c) UCL=$$\bar{u} – 2\sqrt{\frac{\bar{u}}{n}}$$
d) UCL=$$\bar{u} – \frac{3}{2} \sqrt{\frac{\bar{u}}{n}}$$

Explanation: The 3 – sigma upper control limit for a control chart for average number of nonconformities per unit, is expressed by the following expression.
UCL=$$\bar{u} + 3\sqrt{\frac{\bar{u}}{n}}$$

2. If the average number of nonconformities per unit per sample is 0.074, what will be the lower control limit for the u-chart?
a) 0.0414
b) 0.0221
c) 0.0
d) -0.0513

Explanation: The lower control limit for the u-chart is expressed by,
LCL = $$\bar{u} – 3\sqrt{\frac{\bar{u}}{n}}$$
Putting $$\bar{u}$$=0.074 we get, LCL=-0.0414. As LCL is less than 0, we use LCL=0.

3. The control chart for total number of events is called ____________
a) g-charts
b) R-charts
c) h-charts
d) c-charts

Explanation: The control charts, which are developed for the total number of events, are called the g-charts. They were first developed by Kaminski et al in 1992.

4. The control charts developed for the average number of events is generally called ______________
a) g-chart
b) h-chart
c) s-chart
d) s-square-charts

Explanation: The control charts, which are based on the average number of events data, are called the h-charts. They were also developed by Kaminski et al.

5. What will be the center line value for a Kaminski et al h-chart when standards are given?
a) $$\frac{1-p}{p}-a$$
b) $$\frac{1+p}{p}+a$$
c) $$\frac{1+p}{p}-a$$
d) $$\frac{1-p}{p}+a$$

Explanation: The center line value for the Kaminski et al h-chart is given by the equation,
CL = $$\frac{1-p}{p}+a$$

6. What is the value of the Upper control limit for the g-chart?
a) $$n(\frac{1-p}{p}-a)+L\sqrt{n(1-p)}{p^2}$$
b) $$n(\frac{1-p}{p}+a)+L\sqrt{n(1+p)}{p^2}$$
c) $$n(\frac{1-p}{p}+a)+L\sqrt{n(1-p)}{p^2}$$
d) $$n(\frac{1-p}{p}+a)+L\sqrt{(1-p)}{p^2}$$

Explanation: The value of upper limit for the g chart given by Kaminski et al is,
$$n(\frac{1-p}{p}+a)+L\sqrt{n(1-p)}{p^2}$$

7. What is the value of the center line of g-chart?
a) $$n(\frac{1+p}{p}+a)$$
b) $$n(\frac{1-p}{p}+a)$$
c) $$n(\frac{1+p}{p}-a)$$
d) $$n(\frac{1-p}{p}-a)$$

Explanation: The center line value for the g-chart construction is calculated by following formula,
$$n(\frac{1-p}{p}+a)$$

8. What is the value of center line of g-chart when there is no standard given?
a) $$\bar{t}+3\sqrt{\bar{t}}$$
b) $$\bar{t}$$
c) $$\bar{t}-3\sqrt{\bar{t}}$$
d) $$\bar{t}+0.5\sqrt{\bar{t}}$$

Explanation: The center line value for the g-chart, when there is no standard given is given by,
Cl=$$\bar{t}=\frac{t_1+t_2+t_3+⋯+t_m}{m}$$
where t1, t2, t3,…,tm are the total numbers of events in m subgroups each.

9. What is the center line value for the average number of events control chart, when there is no standard given?
a) t/n
b) 2t/3n
c) 2 t/n
d) t/2n

Explanation: The center line value for the average number of events control chart or h-chart, when there is no standard given, is expressed by,
CL= t/n.

10. Which of these is used in the standardized chart for u-chart with variable sample size?
a) Zi
b) Mi
c) Ui
d) Ai

Explanation: For the standardized control chart for a u-chart with variable sample size, the construction of the standardized control chart requires plotting a standard statistic written as Zi.

11. What is the value of Zi in the standardized control chart for u-chart with variable sample size?
a) $$\frac{u_i+\bar{u}}{\sqrt{\frac{\bar{u}}{\bar{n}}}}$$
b) $$\frac{u_i+\bar{u}}{\sqrt{\frac{\bar{u}}{n_i}}}$$
c) $$\frac{u_i-\bar{u}}{\sqrt{\frac{\bar{u}}{n_i}}}$$
d) $$\frac{u_i-\bar{u}}{\sqrt{\frac{\bar{u}}{\bar{n}}}}$$

Explanation: The value of a standard statistic used to plot the standardized chart for the u-chart with a variable sample size, is written as,
$$\frac{u_i-\bar{u}}{\sqrt{\frac{\bar{u}}{n_i}}}$$

12. What is the Upper control limit for the standardized control chart for u-chart with variable sample size?
a) 0
b) 1
c) 1.5
d) 3

Explanation: The upper control limit for the standardized control chart, which is designed for u-chart with variable sample size, is generally set to value 3.

13. The center line of the standardized control chart designed for u-chart, is given by _____
a) 1
b) -3
c) 6
d) 0

Explanation: The center line for the standardized control chart is set to zero. That is why this control chart is named the standardized control chart.

14. The Lower control limit has a 6 unit distance from the upper control limit of the standardized control chart.
a) True
b) False

Explanation: The Upper and lower control limits of the standardized control chart designed for u-chart with variable sample size, have a value of 3 and -3, respectively. So the distance between them is 6 units.

15. Defect or nonconformity data are always lesser informative than fraction nonconforming.
a) True
b) False

Explanation: The nonconformity data are always more informative than the fraction nonconforming data, because there will usually be several different nonconformity types. By analyzing all their types, we get more insight into the defect cause which helps in making OCAPs.

16. The OC curve of the c-chart is a curve which plots β-risk against _______
a) Number of defectives per sample
b) True mean number of defects
c) Total number of defects
d) Demerits per unit