This set of Statistical Quality Control Multiple Choice Questions & Answers (MCQs) focuses on “Process Capability Ratios – 2”.

1. If the Lower specification limit for one quality characteristic of one product, is 200, and the mean of the process is estimated to be 264 with an estimate of one sided process capability ratio \(\widehat{C_{pl}}\), what will be the estimate of the process standard deviation?

a) 43

b) 59

c) 32

d) 18

View Answer

Explanation: We know that,

We know that,

\(\widehat{C_{pl}} = \frac{\hat{μ}-LSL}{3\hat{σ}}\)

Putting values, we get, The process standard deviation estimate, \(\hat{σ}\)=32.

2. If the LSL of the quality characteristic increases, the process capability ratio C_{p} will ____________

a) Increase

b) Decrease

c) Will remain same

d) Can’t say (can increase as well as decrease)

View Answer

Explanation: We know that,

\(C_p=\frac{USL-LSL}{6σ}\)

So an increase in the LSL value will decrease the PCR.

3. PCR is a measure of __________

a) The ability of the process to manufacture the products that meet the specifications

b) The ability of the operator to remove the variability

c) The probability of the mean to be equal to the USL

d) The probability of the mean to be equal to the LSL

View Answer

Explanation: Process capability ratio is used as the measure of the ability of the process to manufacture the products, which meet the specifications set for it.

4. The process fallout (in ppm) ___________ with increase in the process capability ratio C_{p}, for a normally distributed process.

a) Increases

b) Decreases

c) Remains same

d) Can’t be described an increase or decrease

View Answer

Explanation: The process fallout in ppm decreases with increase in the Process Capability Ratio C

_{p}. This relation can only be applied to the normally distributed processes.

5. A PCR C_{p}=1.00 indicates the fallout rate of ___________ ppm for two-sided specifications.

a) 2

b) 7

c) 967

d) 2700

View Answer

Explanation: A process capability ratio is a measure of the ability of a process to produce products, which meet their specifications. A PCR C

_{p}=1.00 indicates a fallout rate of 2700 ppm for two-sided specifications.

6. A process capability ratio C_{p}=____________ indicates the fallout rate of 1 ppm for one-sided specifications for a normally distributed process.

a) 1.2

b) 1.8

c) 1.9

d) 1.6

View Answer

Explanation: A process capability ratio C

_{p}=1.6 indicates the fallout rate of 1 ppm for the one – sided specifications. It also indicates the fallout rate of 2 ppm for two-sided specifications.

7. A correct interpretation of the PCR C_{p} does not need the consideration of ___________ of process.

a) Operator

b) Mean

c) Variance

d) Stability

View Answer

Explanation: The correct interpretation of the C

_{p}does not need the consideration of the operator of the process, as this factor is already included in the earlier steps taken before this interpretation.

8. What is generally the minimum value of two sided specification PCR C_{p} for a existing process?

a) 1.11

b) 1.33

c) 1.89

d) 1.60

View Answer

Explanation: The minimum value of the two sided specifications PCR C

_{p}for an existing process is generally taken as 1.33. For one sided specifications, PCR C

_{p}is taken as 1.25.

9. What is the minimum value of Process Capability Ratio C_{p} for one sided specifications, for a new process which is normally distributed?

a) 1.45

b) 1.19

c) 1.72

d) 1.5

View Answer

Explanation: The minimum value of the Process Capability Ratio C

_{p}for one sided specifications, is taken as 1.45 for any new process which is assumed to be normally distributed.

10. If the quality characteristic in consideration is a strength parameter of the existing process, what will be the minimum value of C_{p} for two sided specifications for this?

a) 1.22

b) 1.52

c) 1.50

d) 1.36

View Answer

Explanation: If the quality characteristic in consideration is a strength parameter of the existing process, the minimum value of Process Capability Ratio C

_{p}for two sided specifications 1.50.

11. Which of these is a necessary assumption made for the calculation of the PCR C_{p}?

a) The quality characteristic has a normal distribution

b) The quality characteristic has a lognormal distribution

c) The quality characteristic has an exponential distribution

d) The quality characteristic has a Poisson distribution

View Answer

Explanation: For the calculation of the Process capability ratio, it is assumed that the quality characteristic, for which the PCR is to be calculated, should have a normal distribution.

12. What is the minimum two – sided specification PCR for the safety parameter for a new process?

a) 1.48

b) 1.45

c) 1.67

d) 1.32

View Answer

Explanation: For a new process, a two – sided specification Process Capability Ratio for the safety parameter should have a minimum value of 1.67.

13. What is the value of process fallout in defectives ppm for one sided specifications of a PCR C_{p}= 1.10?

a) 484

b) 201

c) 2700

d) 100

View Answer

Explanation: The value of process fallout in defectives ppm for the one – sided specifications of a PCR C

_{p}=1.10 is 484. This value for two sided specifications of the same PCR C

_{p}is 967.

14. For calculating the PCR C_{p}, the process should be in statistical control.

a) True

b) False

View Answer

Explanation: Before calculating Process Capability ratio for a process, it is a necessary assumption that a process should be in the state of statistical control.

15. For the calculation of the PCR C_{p} the process mean must be centered in the case of two-sided specifications.

a) True

b) False

View Answer

Explanation: It is assumed that the process mean is centered between the lower and upper specification in the case of two sided specifications, before the calculation of PCR C

_{p}.

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