# Statistical Quality Control Questions and Answers – Variable Charts – Control Charts for x̅ and R – 4

This set of Statistical Quality Control online quiz focuses on “Variable Charts – Control Charts for x̅ and R – 4”.

1. The assumption that links normality to the control charts is ___________
a) The underlying distribution of the quality characteristic is normal
b) The normal mean will be equal to the process mean
c) The normal distribution is not the correct distribution for all the quality characteristic
d) Every distribution is a part of normal distribution

Explanation: There is an assumption that links the normality to the control charts in the development of the performance properties of x bar and R charts; that is, the underlying distribution of the quality characteristic is normal.

2. The probability of not detecting “an in-control shift” of the mean of the process is said to be the _____
a) α – Risk
b) β – Risk
c) γ – Risk
d) δ – Risk

Explanation: If the mean of a process shifts from one value to another value with process being in-control, and shift is not detected on the control chart, the probability of this event is called the β – Risk.

3. If the sample size is 7 and the Average run length is 122 for a process, what will be the expected number of the individual units sampled?
a) 850
b) 854
c) 867
d) 844

Explanation: We know,
I=nARL
Putting n=7 and ARL=122, we get, I = 854.

4. If β- risk of any process is 0.75, what will be the ARL for that process?
a) 4
b) 1.33
c) 0.86
d) 2

Explanation: ARL is given by,
ARL=$$\frac{1}{1-β}$$
Putting β=0.75, we get ARL=4.

5. Slope of OC curve for x bar chart will _________ when sample size is increased.
a) Decrease
b) Increase
c) Remain same
d) Decrease then increase

Explanation: The OC curve is the curve between the β- risk against the magnitude of the shift in mean expressed in std. deviation units for different sample size. Its slope decreases as the sample size is increased.
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6. If the probability of one point plotting out of control limits of a X bar control charts is 0.0143, what will be its expected number of individual units sampled with subgroup size 8?
a) 559
b) 544
c) 530
d) 580

Explanation: We know, ARL=1α and I=nARL. From question we get, α=0.0143 and n=8.
Using this data we get; I≈559.

7. A mixture pattern in the control chart points is exhibited when __________ occurs.
a) Operator fatigue
b) Change of raw materials
c) Continuous wear of tool
d) Adjustments too often responding to random variation

Explanation: When the “Over-control” occurs, i.e. the operator adjusts the processes very frequently and recurrently, the random pattern of the process data vanishes and a mixed pattern is obtained.

8. If the means for sample 1 to 4 for a process are, 12.67, 22.32, 14.53, 12.11; what value will be the center line of x chart indicating?
a) 15.2
b) 15.4
c) 14.8
d) 14.9

Explanation: The center line of the x chart, indicates the mean of all means of samples; i.e.,
CL=$$\bar{\bar{x}} = \frac{\sum \bar{x}}{N}$$=15.4

9. A permanent change in the sample size is made only because of cost or because has exhibited good stability and fewer resources are allocated for process monitoring.
a) True
b) False

Explanation: The permanent change in sample size is not a frequent activity. So it is done because of some major reasons like cost or extraordinary good performance of process on control chart.

10. Which of these should be plotted on the x bar chart?
a) Counts
b) Defects
c) Problems Solved
d) Measurements

Explanation: Counts, defects and problems solved are all quantities which increase in a discrete amount. Measurements increase in a continuous way. Only Continuous quantities are plotted on the x bar chart.

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