# Statistical Quality Control Questions and Answers – Variable Charts – Control Charts for x̅ and R -3

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This set of Statistical Quality Control online test focuses on “Variable Charts – Control Charts for x̅ and R -3”.

1. Once a set of reliable control limits is obtained, we use the control chart for monitoring future production. This is called __________
a) Phase I control chart usage
b) Phase II control chart usage
c) Phase III control chart usage
d) Phase IV control chart usage

Explanation: The use of reliable control limits to monitor the future production from a process, is generally mentioned as the Phase II application of control chart while, setting the trial control limits to monitor the process is called the Phase I application.

2. When R chart is out of control, we __________
a) Eliminate the out-of-control points and recalculate the control limits
b) Take one more sample and recalculate the control limits
c) Eliminate the out-of-control points and the nearest two points, and recalculate the control limits
d) Take no action

Explanation: When R chart is out of control, we often eliminate the out-of-control points and recompute a revised value of R bar. This will help us recalculate the control limits.

3. When the upper and lower natural tolerance limits are equal to the upper and lower specification limits, the process capability ratio, cp is ________
a) Greater than 1
b) 0
c) Less than 1
d) Equal to 1

Explanation: When the natural tolerance limits are having a equal value to the specification limits for a quality characteristic, the process capability ratio, cp is having a value equal to 1.

4. X bar chart monitors __________
a) Between-sample variability
b) Within-sample variability
c) Neither between-sample nor within-sample variability
d) Both between-sample variability and within-sample variability

Explanation: A x chart is only used to monitor the variability of a whole process over time. It does not detect variability within a sample but variability between all the samples of a process output.

5. Unlike x chart, which measures between-sample variability only, an R chart is used to monitor ____
a) Both between-sample variability and within-sample variability
b) Within-sample variability only
c) Between-sample variability only
d) Neither between-sample variability nor within-sample variability

Explanation: A R chart is a chart which uses sample ranges to calculate its center line and control charts. So it only measures within-sample variability, i.e. the instantaneous variability at a given time.

6. When using standard values of process mean and standard deviation, the equation of UCL for a x chart is given as, UCL = μ+Aσ
What is the value of A here?
a) 6/√n
b) 3/√n
c) √n/6
d) √n/3

Explanation: When using the standard values of process mean and standard deviation, A in the equation of UCL for x chart is given by
A=$$\frac{3}{n^{0.5}} = \frac{3}{\sqrt{n}}$$

7. For standard values of mean and standard deviation used, what does the center line of the R chart represent?
a) R bar
b) d2 σ
c) D2 σ
d) d2 R

Explanation: For the standard values of mean and standard deviation used, the center line for a R chart is determined by the following formula, d2 σ.

8. The control limits obtained by specifying the type I error level for the test, are called ________
a) Probability limits
b) Trial limits
c) Error limits
d) Unreliable limits

Explanation: It is possible to define the control limits for a control chart by specifying the type I error level. The limits obtained by this way, are called the Probability limits for the control chart.

9. Which chart should be interpreted first when both, x chart, and R chart are indicating a non-random behavior?
a) x chart
b) R chart
c) X and R chart
d) Trial Limits

Explanation: It is a property of control charts for x bar and R, that if they both indicate non-random behavior, and if R chart is interpreted first to delete the assignable causes in it, it will automatically delete assignable causes in x bar chart.

10. Which of these is a cause of trend patterns on a control chart?
a) Gradual wearing out of some critical process component
b) Operator fatigue
c) Environmental changes
d) Over-control

Explanation: A trend or continuous movement in one direction on a control chart is generally caused by gradual wearing out of some critical process component like deterioration of a tool.

11. Shift in process level can be seen on the control charts when __________
a) Operator fatigue occurs
b) Temperature changes
c) Over-control of process
d) New workers introduction

Explanation: Shift in the process level is a phenomenon seen on the control chart patterns. It occurs when there is introduction of new workers, or there is a change of methods.

12. Stratification is defined as ________
a) Tendency for the points to cluster artificially around the center line
b) Shift in the process level
c) Continuous movement of points in one direction
d) When the points fall near or slightly outside the control limits

Explanation: Stratification is defined as the tendency of the points on a control chart, to cluster around the center line of the control chart. It occurs very frequently while applying control charts to a process.

13. Stratification of points on a control chart indicates __________ of natural variability of the process.
a) Lack
b) Increase
c) Constancy
d) Randomness

Explanation: Stratification makes the points in a control chart to be plotted around the control chart center line; which indicates that the randomness is gone and there is a lack in natural variability of the process.

14. Never attempt to interpret the x chart when the R chart indicates the out of control condition.
a) True
b) False

Explanation: It is easy to eliminate the assignable causes in the x chart by eliminating the assignable causes in the R chart. This implies, if there is indication of out-of-control condition of process from the R chart and x chart; then first, R chart must be interpreted.

15. The 3 sigma limits on x bar control charts imply that the type I error probability is __________
a) 0.0012
b) 0.0072
c) 0.0027
d) 0.0037