This set of Statistical Quality Control Multiple Choice Questions & Answers (MCQs) focuses on “Process Capability Ratios – 4”.

1. To remove the errors in the estimation of the PCR, the _________ is used.

a) Acceptance Sampling

b) Sample mean

c) Sample variance

d) Confidence intervals

View Answer

Explanation: In actual practice, we only observe the estimate of PCR, not the real PCR. As the estimate can have a large error probability, it is always a good idea to use confidence intervals.

2. Which of these measures the actual capability of the process?

a) C_{p}

b) C_{pu}

c) C_{pk}

d) C_{pl}

View Answer

Explanation: C

_{pk}always shows the actual capability as by interpretation of it, we can sense the potential improvement possible in the process by centering it.

3. Which of these measures the potential capability of the process?

a) C_{p}

b) C_{pu}

c) C_{pk}

d) C_{pl}

View Answer

Explanation: Actual process capability can only be measured using the process capability ratio C

_{p}as it does not take process centering into account. It ignores the potential improvement possible.

4. If a process actual fallout is 1350 ppm, and its C_{p}=2.0, what will be its fallout after centering?

a) 1 ppm

b) 4 ppm

c) 0.009 ppm

d) 0.0018 ppm

View Answer

Explanation: Process fallout is 1350, so its C

_{pk}=1.0. So after potential improvement, when its C

_{pk}= C

_{p}, we get the process fallout = 0.0018 ppm.

5. Which of these can be used to analyze the process capability of the process which has the quality characteristic distributed non-normally?

a) C_{p}

b) C_{pk}

c) C_{pl}

d) C_{pc}

View Answer

Explanation: There have been many attempts to extend the definition of the standard capability indices to the case of non-normal distribution. One of them is C

_{pc}.

6. How is C_{pc} expressed?

a) \(C_{pc}=\frac{USL+LSL}{6\sqrt{\frac{π}{2} E|X-T|}}\)

b) \(C_{pc}=\frac{USL-LSL}{6 \sqrt{\frac{π}{2} E|X-T|}}\)

c) \(C_{pc}=\frac{USL-LSL}{6 \sqrt{\frac{π}{2} E|X+T|}}\)

d) \(C_{pc}=\frac{USL-LSL}{\sqrt{\frac{π}{2} E|X-T|}}\)

View Answer

Explanation: C

_{pc}is expressed as,

\(C_{pc}=\frac{USL-LSL}{6 \sqrt{\frac{π}{2} E|X-T|}}\)

7. What is the value of T in the expression of C_{pc}?

a) T=\(\frac{1}{2}\)(USL+LSL)

b) T=(USL+LSL)

c) T=\(\frac{1}{3}\)(USL+LSL)

d) T=\(\frac{1}{2}\)(USL-LSL)

View Answer

Explanation: The value of T in the expression of C

_{pc}is as follows.

T=\(\frac{1}{2}\)(USL+LSL)

8. What does the second subscript in C_{pc}?

a) Course

b) Capability

c) Confidence

d) Clarity

View Answer

Explanation: In the process capability index C

_{pc}, designed by Lucin ̃o, which takes process non-normality into account, the second subscript denotes confidence as in Confidence intervals.

9. Which of these is not desirable to be worked alone with?

a) C_{p}

b) C_{pc }

c) C_{pk}

d) C_{pu}

View Answer

Explanation: Two processes having different centering can have a same C

_{pk}. So we need to evaluate C

_{p}to check the equality of PCR C

_{pk}with it. This way we get perfect centering between the specifications.

10. For any fixed value between LSL and USL, C_{pk} depends _________ on σ.

a) Inversely

b) Directly

c) Negatively

d) Positively

View Answer

Explanation: As we know,

C

_{pc}=min(C

_{pu},C

_{pl})

Where, C

_{pu}and C

_{pl}, both vary inversely according to σ. So C

_{pc}is inversely dependent on σ.

11. What will be the value of C_{pc} as σ approaches to zero?

a) Zero

b) One

c) Infinity

d) Minus Infinity

View Answer

Explanation: As Process Capability Ratio C

_{pc}varies inversely with σ, when the value of σ approaches zero, the value of the PCR C

_{pc}becomes infinity.

12. Which of these besides the PCR C_{pc} can be used to know more about the process centering?

a) C_{p}

b) C_{pm}

c) C_{pu}

d) C_{pl}

View Answer

Explanation: As C

_{pc}also needs some complementary process capability ratio such as C

_{p}, to know more about process centering, another PCR C

_{pm}is developed to know more about process centering.

13. What is the value of C_{pm}?

a) \(C_{pm}=\frac{USL+LSl}{6σ}\)

b) \(C_{pm}=\frac{USL-LSl}{6σ}\)

c) \(C_{pm}=\frac{USL+LSl}{6τ}\)

d) \(C_{pm}=\frac{USL-LSl}{6τ}\)

View Answer

Explanation: The value of C

_{pm}Process capability ratio is given as,

\(C_{pm}=\frac{USL-LSl}{6τ}\)

14. ‘C_{pk}’ can also be used to determine the process capability of non-normal data.

a) True

b) False

View Answer

Explanation: C

_{pk}and C

_{p}are based on an assumption that the quality characteristic varies on a normal distribution. So we cannot use the process capability ratio C

_{pk}to determine the process capability of the non-normal data.

15. ‘C_{p}’ and ‘C_{pk}’ both can’t be used alone to make decisions about the process centering.

a) True

b) False

View Answer

Explanation: To predict the process centering, we must have information about C

_{p}and C

_{pk}. This way we can check the equality between C

_{p}and C

_{pk}and say if the process is centered.

16. Kotz and Lovelace were in strong opposition of _______________

a) P_{p}

b) C_{p}

c) C_{pk}

d) C_{pm}

View Answer

Explanation: Kotz and Lovelace were in strong opposition of P

_{p}because they were used when the process was not in control. They said no index can give useful predictive information about process capability.

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