This set of Statistical Quality Control Problems focuses on “Process Capability Ratios – 5”.

1. What is the value of τ in the expression of C_{pm} process capability ratio?

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Explanation: The value of τ in the expression of C

_{pm}is the square root of expected squared deviation from target T, i.e.

2. Which of these is equal to the squared value of τ?

a) σ^{2}-(μ+T)^{2}

b) σ^{2}+(μ-T)^{2}

c) σ^{2}-(μ-T)^{2}

d) σ^{2}+(μ+T)^{2}

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Explanation: The value of squared value of τ,

τ

^{2}=E[(x-T)

^{2}]=E[(x-μ)

^{2}]+(μ-T)

^{2}=σ

^{2}+(μ-T)

^{2}.

3. Which of these is having same value as C_{pm}?

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4. What is value of ξ in the expression for C_{pm} Process Capability Ratio?

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5. If standard values are not given, the value of C_{pm} is estimated by expression _____

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Explanation: The estimate of C

_{pm}, when the standard values of σ, μ are not given, is calculated by expression,

6. What is the value of V in the expression of the estimate of C_{pm} Process Capability Ratio?

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Explanation: The value of V is used at the place of ξ in the case when the standard values of σ and μ are not available. The value of V is equal to,

7. What is the value of C_{pm} when the value |μ-T|→∞ ?

a) 1

b) 0

c) ∞

d) -∞

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Explanation: The value of C

_{pm}approaches to zero asymptotically as the value |μ-T|→∞. This is because,

8. What is the value of C_{pm} when the value μ=T?

a) C_{pm}=1

b) C_{pm}=0

c) C_{pm}=C_{p}

d) C_{pm}<C_{p}

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9. What is the value of C_{pkm} process capability ratio?

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10. What is the value of ξ in the expression for C_{pkm} PCR?

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11. C_{pkm} is also called _____ generation process capability ratio.

a) Third

b) Fourth

c) Second

d) First

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Explanation: C

_{pkm}is sometimes called third generation process capability ratio since it is constructed from the second generation PCR C

_{pm}and C

_{pk}.

12. C_{p} is called the ____ generation PCR.

a) First

b) Second

c) Third

d) Fourth

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Explanation: C

_{p}is called the first generation process capability ratio as it was designed before any other process capability ratio like C

_{pk}or C

_{pm}.

13. Which of these is one of the first generation process capability ratios?

a) C_{pk}

b) C_{pm}

c) C_{pc }

d) C_{pu}

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Explanation: As we know, the first Process capability ratios, that were designed, were C

_{p}, C

_{pu}, C

_{pl}. So they are called the first generation process capability ratios.

14. C_{pm} is the second generation process capability ratio.

a) True

b) False

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Explanation: C

_{pk}and C

_{pm}were designed after the first generation capability ratios, which were not able to consider the process centering fact into their evaluation. So they are called the second gen. process capability ratios.

15. Confidence intervals are not needed for .

a) True

b) False

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Explanation: All the estimates of the process capability ratios are point estimates. This means there is a strong possibility of error due to statistical fluctuation. So confidence interval is needed also for .

16. What does usage of s instead of R/d_{2} in the confidence intervals indicate?

a) s=1

b) Process must be in control

c) Process may be in the out-of-control state

d) d_{2}<1

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Explanation: When process is not in control, the value of s has a big difference with the value of R/d

_{2}. So for the calculation of confidence interval s is used. This means, for a PCR to have a meaning, the process must be in control.

17. P_{p} is a ___

a) Process capability ratio

b) Process stability ratio

c) Process prediction index

d) Process performance index

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Explanation: AIAG has recommended using the process performance indices to be used instead of the process capability ratios when process is not in control. P

_{p}is one of them.

18. What is the value of process performance index estimate (P_{p} ) ̂?

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

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