# Statistical Quality Control Questions and Answers – Variable Charts – Control Charts for x̅ and R – 2

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This set of Statistical Quality Control Multiple Choice Questions & Answers focuses on “Variable Charts – Control Charts for x̅ and R – 2”.

1. LCL for the R chart is given by __________
a) D3 R
b) D2 R
c) R – D3 R
d) d2 R

Explanation: LCL for an R chart is always given by the following equation,
LCL = D3 R.

2. In the general equation of UCL of a control chart, for any x chart, which of these is used as the estimator of μ?
a) $$\bar{x}$$
b) $$\bar{R}$$
c) $$\bar{\bar{x}}$$
d) $$\bar{\bar{R}}$$

Explanation: UCL=μ+ Zα/2 σ is the general equation for UCL for any control chart. For any $$\bar{x}$$ chart, $$\bar{\bar{x}}$$ is used as the estimator of μ in the above mentioned equation.

3. Which of these gives the correct value of A2 used in the equation for control limits of a x control chart?
a) $$\frac{3}{d_2 \sqrt{n}}$$
b) $$\frac{3}{\sqrt{n}}$$
c) $$\frac{3}{d_2}$$
d) $$\frac{3}{\sqrt{d_2}}$$

Explanation: The value of A2 used in the equation of control limits of a x control chart is given by following equation,
$$\frac{3}{d_2 \sqrt{n}}$$

4. In phase I application of x and R chart, the control limits obtained from the equations are treated as ____________
a) Final limits
b) Trial limits
c) Warning limits
d) Pattern limits

Explanation: The obtained limits from the equation of control limits for a x and R chart, are generally treated as Trial limits. They allow us to determine whether the process was in control when the m initial samples were taken.

5. Which term is having a closest meaning as Sampling Distributions?
a) Control charts
b) On site inspection
c) Whole lot inspection
d) Acceptance sampling

Explanation: The term “control charts” is having a closest meaning to “sampling distribution” because, control charts are also plotted on the data obtained from the sample inspection and also, they show variation in sample data.

6. Process capability generally uses __________
a) Specifications
b) Control Limits
c) Process standard deviation
d) Mean of any one sample

Explanation: Process capability studies make use of the specifications of any certain Critical-to-quality characteristic or quality characteristic to estimate the performance of any process.

7. The process standard deviation is given by __________
a) R/d2
b) Rd2
c) 1/d2
d) R/d

Explanation: The process standard deviation may be estimated by using the following equation,
$$\hat{σ} = \frac{\bar{R}}{d_2}$$

8. For any process, the sample ranges are, 1.2,1.5,1.1,1.4,1.5. The subgroup size is 5. What will be the process standard deviation? Given: d2=2.326 and A2=0.577
a) 0.576
b) 2.322
c) 0.511
d) 2.463

Explanation: We know that,
$$\bar{R} = \frac{\sum_{i=0}^{i=n} R_i}{n}$$ and “process standard deviation = $$\frac{\bar{R}}{d_2}$$“, by using the values of R and d2 in the question, we get process standard deviation=0.576

9. A tolerance diagram is also called ____________
a) Scatter diagram
b) Defect concentration diagram
c) Histogram
d) Tier chart

Explanation: The run chart of individual observations in each sample is called the tolerance diagram for any process. The tolerance diagram is also called Tier chart of the process.

10. Is there any relationship between specification limits and control limits of x and R charts?
a) Yes, Specification limits = Control limits
b) Yes, Control limits=Specification limits/2
c) No
d) Yes, Control limits*0.5 = Specification limits

Explanation: There is no certain relationship defined; between the control limits of x and R charts and the specification limits of any quality characteristic.

11. Control limits are ___________
a) Limits defined by customers
b) Limits driven by the natural variability of the process
c) Limits driven by the inherent variability of the process
d) Statistical limits

Explanation: The control limits are the limits for a quality characteristic for a process to be in-control. They are driven by the natural variability of the process.

12. The natural variability of the process is measured by ____________
a) Process mean
b) Sample standard deviation
c) Process standard deviation
d) Sample mean

Explanation: The natural variability of any process is the main factor affecting the control limits of any quality characteristic while plotting a control chart. They are measured by process standard deviation, σ.

13. What type of chart will be used to plot the number of defectives in the output of any process?
a) x bar chart
b) R chart
c) c chart
d) p chart

Explanation: The number of defectives in the samples of the output of a process is monitored by the p chart and the number of defects is monitored by a “c chart”.

14. Process standard deviation is necessarily equal to the sample standard deviation of the same process.
a) True
b) False

Explanation: It is not necessary that the sample standard deviation will always be equal to the process standard deviation, for a same process. This is because; there may be assignable causes of variation while the sample is being produced by the process.

15.“There is no need of revision of control limits once calculated by the equations of control limits.
a) True
b) False 