This set of Statistical Quality Control Multiple Choice Questions & Answers (MCQs) focuses on “Control Charts for x̅ and S – 1”.

1. What is the estimator of standard deviation in the x bar and R charts?

a) Mean of one sample

b) Mean of whole process

c) Range

d) Process capability ratio

View Answer

Explanation: In x bar and R charts, process standard deviation is estimated indirectly through the use of the range R. x bar is used as an estimator of mean.

2. What does “s” denote in x bar and s charts?

a) Sample

b) Sample standard deviation

c) Process standard deviation

d) Statistics

View Answer

Explanation: Process standard deviation in the x bar and s charts, is estimated directly instead of indirectly through the use of Range as in x bar and R charts. Here “s” denotes the sample standard deviation.

3. What is an unbiased estimator of unknown variance of a probability distribution?

a) Sample mean

b) Sample standard deviation

c) Sample variance

d) Sample range

View Answer

Explanation: If σ

_{2}is the unknown variance of a probability distribution, then an unbiased estimator must be used to estimate σ

_{2}. In this case, sample variance is used as the required estimator.

4. What is the standard formula of sample variance?

View Answer

5. Which of these formulas gives the exact equation for the UCL of s chart with a std. value for σ given?

a) B_{6} σ

b) B_{5} σ

c) c_{4} σ

d) c_{3} σ

View Answer

Explanation: The UCL parameter of the s chart with a std. value for σ given, is expressed by

UCL=B

_{6}σ.

6. The center line of the s chart with a standard value for σ given, denotes the value of _____

a) B_{6} σ

b) c_{4} σ

c) B_{5} σ

d) c_{5} σ

View Answer

Explanation: The center line of the s chart with a standard value for σ given, denotes the value equal to,

CL=B

_{6}σ

7. If the sample standard deviations for a process are 1.567, 1.429, 1.323, 1.525, 1.989, 1.457, what will be the mean standard deviation?

a) 1.548

b) 1.858

c) 1.327

d) 1.967

View Answer

Explanation: The mean standard deviation of the sample standard deviations is given by,

Where s

_{i}denotes the standard deviation of ith sample. Calculating the mean using the above formaula gives, s=1.548.

8. What is the value of B_{5} in the terms of c_{4}?

View Answer

9. The center line of the s chart denotes ____

a) Standard deviation of the process

b) Mean of m number of standard deviations, where m is the number of samples

c) c_{4} s

d) B_{5} s

View Answer

Explanation: The center line of the s chart denotes the mean of m number of standard deviations, where m is the number of samples. This is the desired value of the sample standard deviation for the process to be in control.

10. What is the value of LCL for the s chart when the standard value for σ is not given?

a) B_{5} s

b) B_{4} s

c) B_{6} s

d) B_{3} s

View Answer

Explanation: The LCL of the s chart gives the value equal to, B

_{3}s when the standard value for σ is not given. This is the lowest the value of s can be, for the process to be in-control.

11. What is the value of B_{3} in the terms of c_{4}?

View Answer

12. What is the formula for UCL for x bar chart when s is known?

View Answer

Explanation: The formula of UCL for x bar and s chart construction when s is known, is given by

13. For mean of all sample standard deviations=0.0094 and the sample size= 5, what will be the estimate of process standard deviation?

a) 100

b) 0.01

c) 0.0094

d) 94

View Answer

Explanation: We know that estimate of the process standard deviation,

Here for sample size=5, c

_{4}=0.94, and s = 0.0094, we get σ = 0.01.

14. Process standard deviation is the mean of all sample standard deviations.

a) True

b) False

View Answer

Explanation: It is not necessary that process standard deviation is the mean of all sample deviations. This is because there is some inherent and natural variability in the process. This may or may not appear in every sample.

15. X bar and R charts are highly favorable when the sample size is high.

a) True

b) False

View Answer

Explanation: X bar and R charts are not used for high sample sizes- say, n>10 or 12. This is because, the range method for estimating σ loses its efficiency for moderate to large samples.

16. Which of this is a situation when x bar and s charts should be utilized instead of x bar and R charts?

a) When sample size is constant

b) When sample standard deviation is less than 1

c) When sample range is more than 1

d) When sample size is variable

View Answer

Explanation: It is favorable to use the x bar and s charts over x bar and R charts when the sample size is variable. This is because when sample size is variable, it leads to a changing center line of R chart, which is difficult to interpret.

**Sanfoundry Global Education & Learning Series – Statistical Quality Control.**

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