250+ TOP MCQs on Process Capability Ratios – 4 and Answers

Statistical Quality Control Multiple Choice Questions 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
Answer: d
Clarification: 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
Answer: c
Clarification: 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
Answer: a
Clarification: 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
Answer: d
Clarification: 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
Answer: d
Clarification: 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}{6sqrt{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|}})
Answer: b
Clarification: 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)
Answer: a
Clarification: 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
Answer: c
Clarification: 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
Answer: c
Clarification: 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
Answer: a
Clarification: 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
Answer: c
Clarification: 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
Answer: b
Clarification: 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})
Answer: d
Clarification: 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
Answer: b
Clarification: 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
Answer: a
Clarification: 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
Answer: a
Clarification: 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.