250+ TOP MCQs on Process Capability Ratios – 5 and Answers

Statistical Quality Control Problems on “Process Capability Ratios – 5”.

1. What is the value of τ in the expression of C_pm process capability ratio?
a) (τ=sqrt{[Ebig{x-T)^2]})
b) (τ=sqrt{E[{x+T}^2]})
c) (τ=sqrt{E[(x-T)^2]})
d) (τ=sqrt{E[(x+T)^2]})
Answer: a
Clarification: The value of τ in the expression of C_pm is the square root of expected squared deviation from target T, i.e.
(τ=sqrt{[Ebig{x-T)^2]})

2. Which of these is equal to the squared value of τ?
a) σ²-(μ+T)²
b) σ²+(μ-T)²
c) σ²-(μ-T)²
d) σ²+(μ+T)²
Answer: b
Clarification: The value of squared value of τ,
τ²=E[(x-T)²]=E[(x-μ)² ]+(μ-T)²=σ²+(μ-T)².

3. Which of these is having same value as C_pm?
a) (frac{USL-LSL}{6sqrt{σ^2-(μ-T)^2}})
b) (frac{USL+LSL}{6sqrt{σ^2-(μ-T)^2}})
c) (frac{USL-LSL}{6sqrt{σ^2+(μ-T)^2}})
d) (frac{USL+LSL}{6sqrt{σ^2+(μ-T)^2}})
Answer: c
Clarification: As we know,
τ²=σ²+(μ-T)²
We may write,
C_pm = (frac{USL-LSL}{6sqrt{σ^2+(μ-T)^2}})

4. What is value of ξ in the expression for C_pm Process Capability Ratio?
a) (frac{μ+T}{3σ})
b) (frac{μ-T}{6σ})
c) (frac{μ+T}{σ})
d) (frac{μ-T}{σ})
Answer: d
Clarification: The value of ξ in the expression of C_pm is given by,
ξ = (frac{μ-T}{σ})

5. If standard values are not given, the value of C_pm is estimated by expression _____
a) (widehat{C_{pm}}=frac{C_p}{sqrt{1+V^2}})
b) (widehat{C_{pm}}=frac{C_p}{sqrt{1-V}})
c) (widehat{C_{pm}}=frac{C_p}{sqrt{1+V}})
d) (widehat{C_{pm}}=frac{C_p}{sqrt{1-V^2}})
Answer: a
Clarification: The estimate of C_pm, when the standard values of σ, μ are not given, is calculated by expression,
(widehat{C_{pm}}=frac{C_p}{sqrt{1+V^2}})

6. What is the value of V in the expression of the estimate of C_pm Process Capability Ratio?
a) (frac{bar{x}-T}{s})
b) (frac{bar{x}+T}{s})
c) (frac{bar{x}-T}{s^2})
d) (frac{bar{x}-T}{σ})
Answer: a
Clarification: 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,
V = (frac{bar{x}-T}{s})

7. What is the value of C_pm when the value |μ-T|→∞ ?
a) 1
b) 0
c) ∞
d) -∞
Answer: b
Clarification: The value of C_pm approaches to zero asymptotically as the value |μ-T|→∞. This is because,
C_pm = (frac{USL-LSL}{6sqrt{σ^2+(μ-T)^2}})

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_pmp
Answer: c
Clarification: As we know,
C_pm = (frac{USL-LSL}{6sqrt{σ^2+(μ-T)^2}})
When, μ=T we get C_pm=C_p.

9. What is the value of C_pkm process capability ratio?
a) (C_{pkm}=frac{C_{pk}}{sqrt{1-ξ}})
b) (C_{pkm}=frac{C_{pk}}{sqrt{1+ξ^2}})
c) (C_{pkm}=frac{C_{pk}}{sqrt{1+ξ}})
d) (C_{pkm}=frac{C_{pk}}{sqrt{1-ξ^2}})
Answer: b
Clarification: The value of PCR C_pkm is given by
(C_{pkm}=frac{C_{pk}}{sqrt{1+ξ^2}})

10. What is the value of ξ in the expression for C_pkm PCR?
a) (frac{μ-T}{6σ})
b) (frac{μ-T}{σ})
c) (frac{μ+2T}{3σ})
d) (frac{μ+T}{6σ})
Answer: b
Clarification: The value of ξ in the expression of C_pkm is given by,
ξ = (frac{μ-T}{σ})

11. C_pkm is also called _________ generation process capability ratio.
a) Third
b) Fourth
c) Second
d) First
Answer: a
Clarification: 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
Answer: a
Clarification: 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
Answer: d
Clarification: 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
Answer: a
Clarification: 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 (widehat{C_{pkm}}).
a) True
b) False
Answer: b
Clarification: 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 (widehat{C_{pkm}}).

16. What does usage of s instead of R/d₂ 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) d₂<1
Answer: b
Clarification: When process is not in control, the value of s has a big difference with the value of R/d₂. 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
Answer: d
Clarification: 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)?
a) (frac{USL-LSL}{4s})
b) (frac{USL+LSL}{4s})
c) (frac{USL-LSL}{6σ})
d) (frac{USL-LSL}{6s})
Answer: d
Clarification: The estimate of process performance index P_p has the value,
P_p = (frac{USL-LSL}{6s})

Statistical Quality Control Problems,