# Statistical Quality Control Questions and Answers – Process Capability Ratios – 4

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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

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) Cp
b) Cpu
c) Cpk
d) Cpl

Explanation: Cpk 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) Cp
b) Cpu
c) Cpk
d) Cpl

Explanation: Actual process capability can only be measured using the process capability ratio Cp 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 Cp=2.0, what will be its fallout after centering?
a) 1 ppm
b) 4 ppm
c) 0.009 ppm
d) 0.0018 ppm

Explanation: Process fallout is 1350, so its Cpk=1.0. So after potential improvement, when its Cpk = Cp, 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) Cp
b) Cpk
c) Cpl
d) Cpc

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 Cpc.

6. How is Cpc 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) $$C_{pc}=\frac{USL-LSL}{\sqrt{\frac{π}{2} E|X-T|}}$$

Explanation: Cpc 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 Cpc?
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)

Explanation: The value of T in the expression of Cpc is as follows.
T=$$\frac{1}{2}$$(USL+LSL)

8. What does the second subscript in Cpc?
a) Course
b) Capability
c) Confidence
d) Clarity

Explanation: In the process capability index Cpc, 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) Cp
b) Cpc
c) Cpk
d) Cpu

Explanation: Two processes having different centering can have a same Cpk. So we need to evaluate Cp to check the equality of PCR Cpk with it. This way we get perfect centering between the specifications.

10. For any fixed value between LSL and USL, Cpk depends _________ on σ.
a) Inversely
b) Directly
c) Negatively
d) Positively

Explanation: As we know,
Cpc=min⁡(Cpu,Cpl)
Where, Cpu and Cpl, both vary inversely according to σ. So Cpc is inversely dependent on σ.

11. What will be the value of Cpc as σ approaches to zero?
a) Zero
b) One
c) Infinity
d) Minus Infinity

Explanation: As Process Capability Ratio Cpc varies inversely with σ, when the value of σ approaches zero, the value of the PCR Cpc becomes infinity.

12. Which of these besides the PCR Cpc can be used to know more about the process centering?
a) Cp
b) Cpm
c) Cpu
d) Cpl

Explanation: As Cpc also needs some complementary process capability ratio such as Cp, to know more about process centering, another PCR Cpm is developed to know more about process centering.

13. What is the value of Cpm?
a) $$C_{pm}=\frac{USL+LSl}{6σ}$$
b) $$C_{pm}=\frac{USL-LSl}{6σ}$$
c) $$C_{pm}=\frac{USL+LSl}{6τ}$$
d) $$C_{pm}=\frac{USL-LSl}{6τ}$$

Explanation: The value of Cpm Process capability ratio is given as,
$$C_{pm}=\frac{USL-LSl}{6τ}$$

14. ‘Cpk’ can also be used to determine the process capability of non-normal data.
a) True
b) False

Explanation: Cpk and Cp are based on an assumption that the quality characteristic varies on a normal distribution. So we cannot use the process capability ratio Cpk to determine the process capability of the non-normal data.

15. ‘Cp’ and ‘Cpk’ both can’t be used alone to make decisions about the process centering.
a) True
b) False

Explanation: To predict the process centering, we must have information about Cp and Cpk. This way we can check the equality between Cp and Cpk and say if the process is centered.

16. Kotz and Lovelace were in strong opposition of _______________
a) Pp
b) Cp
c) Cpk
d) Cpm