# Statistical Quality Control Questions and Answers – SPC Methods and Philosophy – Statistical Basis of the Control Chart – 3

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This set of Statistical Quality Control MCQs focuses on “SPC Methods and Philosophy – Statistical Basis of the Control Chart – 3”.

1. Moving the UCL and LCL line far from the Center line means ____
a) Decreasing the possibility of type I error
b) Increasing the possibility of type II error
c) Increasing the possibility of type I error
d) Decreasing the possibility of type II error

Explanation: Type I error is, “concluding the process to be out-of-control when it is actually in-control”. So, more distance between UCL and LCL means, a point without an assignable cause will lie in between the UCL and LCL, i.e. in-control.

2. If we decrease the distance between LCL and UCL, what will happen?
a) Decreasing the possibility of type I error
b) Increasing the possibility of type II error
c) Increasing the possibility of type I error
d) Decreasing the possibility of type II error

Explanation: Type II error is, “concluding the process to be in-control when it is actually out-of-control”. This means the decreased distance between LCL and UCL will cause a point with assignable cause, lie not in between them, i.e. out-of-control.

3. If “two sets of limits” approach is taken to construct a control chart, what are the outer set of limits called?
a) Action Limits
b) Warning Limits
c) Variable Limits
d) Constant Limits

Explanation: The outer set of limits used in a “two sets of limits” approach of constructing a control chart, are generally called Action limits as action is to be done to correct the assignable cause if any point out-lies the action limits.

4. The inner limits in the “Two sets of limits” approach of the construction of control chart are called _____
a) Action Limits
b) Variable Limits
c) Constant Limits
d) Warning Limits

Explanation: The “two sets of limits” approach utilizes two different sets of UCL and LCL. In those two sets, the inner set of LCL and UCL is called the warning limits.

5. ARL is termed as ____________
a) Average Run Length
b) Allocating Run Length
c) Affected Run Length
d) Assumed Run Length

Explanation: The Average Run Length has an acronym of ARL. It provides useful way to make effective decisions for the sample size to be selected for the construction of the control chart.

6. The probability of a point to exceed the control limits for a control chart is 0.0040. What will be the ARL for this case?
a) 250
b) 278
c) 210
d) 216

Explanation: We define ARL as the reciprocal of the probability of a point falling out of the area between control limits. Here,
ARL=$$\frac{1}{p}=\frac{1}{0.0040}$$=250

7. For an average run length of 370, what will be the probability of a point falling out of the area between the control limits?
a) 0.0027
b) 0.0013
c) 0.0045
d) 0.0040

Explanation: As we know,
ARL = 1p
Putting value of ARL=370, we get, p=0.0027.

8. What is the full-form of ATS?
a) Average time to Stop
b) Average Time to Start
c) Average Time to Signal
d) Average Time to Select

Explanation: ATS is the abbreviation used for the Average Time to Signal. It is a useful way to express the performance of a control chart very effectively and easily.

9. If for a process, the samples are taken 5 hrs apart and its ARL is 24.24, What will be ATS for it?
a) 121.2
b) 110.0
c) 113.3
d) 137.8

Explanation: We know that,
ATS=ARL.h
Putting values h=5,ARL=24.24; we get,
ATS=121.2.

10. Decreasing sample size will ________
a) Decrease the slope of OC curve
b) Increase the slope of OC curve
c) First decrease then increase the slope of OC curve
d) Makes OC curve have 0 slope

Explanation: The slope of OC curve varies inversely with the sample size taken for the control chart construction. The decrease in the size of the sample taken to construct a control chart will increase the slope of OC curve.

11. Which of these statements, correctly describes the concept of rational subgroups?
a) If assignable causes are present, the chances of difference between subgroups should be largest
b) If assignable causes are present, the chances of difference between subgroups must be lowest
c) If assignable causes are present, the chances of difference between the subgroups must be moderate
d) If assignable causes are present, the chances of difference between the subgroups must be zero

Explanation: Rational Subgroups concept says that, for subgroups, if assignable causes are present, the chances of differences between subgroups should be maximized, while the chance for differences due to these causes within a subgroup must be lowest.

12. If the ARL is 34.8 for a process which has ATS=69.6 hrs, what is the time interval before taking samples?
a) 0.5 hrs
b) 8 hrs
c) 2 hrs
d) 4 hrs

Explanation: The time interval before taking samples is given by,
h=$$\frac{ATS}{ARL}$$
Putting values of ATS and ARL, we get h=2 hrs.

13. Which of these is not one of the sensitizing Western Electric rules that indicate “action needed” for Shewhart control charts?
a) One or more points near a warning limit/control limit
b) One point plots outside 3-sigma control limits
c) Eight consecutive points plot on one side of the control line
d) Two of 3 consecutive points plot beyond the 2-sigma warning limits

Explanation: The Western Electric rules which indicate “action needed” for Shewhart control charts do not state that, if one or more points are plotted near a warning limit or control limit will need an action to control the process.

14. 14 points in a row alternating up and down the mean will not indicate action needed for any process for which a control chart is plotted.
a) True
b) False

Explanation: If 14 points in a row, on a control chart, plot alternating up and down the mean, will surely indicate that that process is giving warning signals. This means the process is presently in-control but will go out-of-control in near future.

15. If an assignable cause is expected in the process, the subgroups taken subsequently should have a maximum difference.
a) True
b) False 