# Statistical Quality Control Questions and Answers – Attribute Charts – Control Charts for Fraction Nonconforming – 2

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This set of Statistical Quality Control Questions and Answers for Entrance exams focuses on “Attribute Charts – Control Charts for Fraction Nonconforming – 2”.

1. Which of these gives a correct equation for the general model for Shewhart control chart for a “w” quality characteristic statistic?
a) UCL = μw + Lσw
b) UCL = μw – Lσw
c) LCL = μw + Lσw
d) LCL = μw + σw

Explanation: The Upper control limit for constructing a Shewhart control chart for a quality characteristic w, we have;
UCL = μw + Lσw.

2. The value of L=3 in the genera model of control limits for a Shewhart control chart, explains ____________
a) There are 3 sigma limits taken
b) There are 3 quality characteristics
c) There are 6 quality characteristics
d) There are 6 sigma limits taken

Explanation: The value of L=3 in the general model of control limits for a Shewhart control chart signifies that there are 3 sigma limits taken, i.e. the 3 times shift of the standard deviation, of the mean will be measured on either side.

3. When the Lower control limits for a p chart are less than zero, what is done?
a) The value LCL<0 is utilized in control chart
b) There is a certain constant C added to both UCL and LCL, i.e. UCLnew=UCLold+ C and LCLnew=LCLold+C
c) There is certain constant value added to LCL only, i.e. LCLnew=LCLold+C
d) LCL=0 is taken and assumed that control chart only has the upper control limit

Explanation: The value of LCL is taken to be zero when there is a value less than 0 found for LCL. It is also assumed that the control chart only has the upper control limit.

4. LCL for any p chart when the standard values are given are ________
a) LCL=$$p+\sqrt[3]{\frac{p(1-p)}{n}}$$
b) LCL=$$p+3 \sqrt{\frac{p(1-p)}{n}}$$
c) LCL=$$p-3\sqrt[3]{\frac{p(1-p)}{n}}$$
d) LCL=$$p-\sqrt{\frac{p(1-p)}{n}}$$

Explanation: The LCL for any p chart or control chart for fraction nonconforming, when the standard values are given, are written as,
LCL=$$p-\sqrt{\frac{p(1-p)}{n}}$$

5. The UCL for any p chart, when the standard values are not given, for 3 sigma limits, is written as ____
a) UCL=$$\bar{p}+\sqrt[3]{\frac{\bar{p}(1+\bar{p})}{n}}$$
b) UCL=$$\bar{p} – \sqrt{\frac{\bar{p}(1-\bar{p})}{n}}$$
c) UCL=$$\bar{p}+\sqrt[3]{\frac{\bar{p}(1-\bar{p})}{n}}$$
d) UCL=$$\bar{p}-\sqrt[3]{\frac{\bar{p}(1-\bar{p})}{n}}$$

Explanation: The upper control limit for a 3 sigma limit p-chart is expressed by
UCL=$$\bar{p}+\sqrt[3]{\frac{\bar{p}(1-\bar{p})}{n}}$$
when the standard values are not given.

6. What is done when there is a sample plotted out of control limits for a p-chart?
a) The sample is investigated for an assignable cause and then the sample data is eliminated to develop a new p-chart
b) The sample is only investigated for an assignable cause
c) The sample is not investigated at all (It is assumed that there was no assignable cause present)
d) All the samples are investigated

Explanation: When a sample plots out of control in p-chart, it is investigated for an assignable cause and then the sample data is eliminated to develop a new p-chart.

7. Even if the process is in control according to p-chart and the fraction nonconforming is too high, it states that _________
a) The process is not stable
b) The process is stable but there are no operator controllable problems
c) The process is stable but there are some operator controllable problems
d) The process is out of control

Explanation: If the process is in control according to p chart but the fraction nonconforming is too high, it states that the process is stable with no operator controllable problems.

8. If the fraction nonconforming for 7 samples are 0.11,0.24,0.21,0.14,0.24,0.21,0.17, what is the value for the center line for a p-chart?
a) 0.19
b) 0.21
c) 0.12
d) 0.13

Explanation: The center line of a p chart represents the average of the all the fraction nonconforming. This means,
$$CL=\bar{p}=\frac{\sum_{i=0}^n p_i}{n}$$
This gives, CL=0.19 for the above question.

9. If the sample size for a p-chart is 50 and the value for the center line of the chart is 0.2313, what will be the value of the LCL of the chart?
a) 0.4108
b) 0.0524
c) 0.0762
d) 0.0389

Explanation: The LCL of the p chart is given by expression,
LCL=$$p-\sqrt{\frac{p(1-p)}{n}}$$
When we put the value of CL=p=0.2313, we get LCL=0.0524.

10. The control limits for p-chart found from the use of estimated unknown fraction non conforming, are regarded as __________
a) Final limits
b) Concluded limits
c) Trial limits
d) Absolute limits

Explanation: The control limits for p chart, which are not found using the standard values of p, are generally regarded as trial limits. The finalized limits are calculated by first implementing the trial limits.

11. Which of these is not one of the parameters which need to be specified for fraction nonconforming control charts?
a) Sample Size
b) Frequency of sampling
c) Width of control limits
d) Units to be produced

Explanation: the fraction nonconforming chart has 3 parameters which need to be specified: the sample size, the frequency of sampling, and the width of control limits.

12. If δ is the magnitude of the process shift, n must specify __________
a) $$\delta=nL\sqrt{\frac{pn(1-p)}{n}}$$
b) $$\delta=nL\sqrt{\frac{p(n-p)}{n}}$$
c) $$\delta=L\sqrt{\frac{p(1-p)}{n}}$$
d) $$\delta=L\sqrt{\frac{np(1-np)}{n}}$$

Explanation: The magnitude of process shift and the sample size n must satisfy,
$$\delta=L\sqrt{\frac{p(1-p)}{n}}$$
for a process to be in control.

13. Which of these is true?
a) $$n=(\frac{L}{\delta})^2 p(1-p)$$
b) $$n=(\frac{L}{\delta})^2 p(1-np)$$
c) $$n=(\frac{L}{\delta})^2 (1-p)$$
d) $$n=(\frac{L}{\delta})^2 p(1+p)$$

Explanation: The value for sample size of a p-chart is determined by the following expression,
$$n=(\frac{L}{\delta})^2 p(1-p)$$

14. In the p-chart, even if only one point is out of control, we should conclude that the process is out-of-control.
a) True
b) False

Explanation: It is generally not an intelligent decision to conclude the process state as out-of-control by obtaining only one point out of control in p-chart; since for any p>0, there is a probability of producing some defectives.

15. Non-defective term has the same meaning as Nonconforming.
a) True
b) False