This set of Statistical Quality Control Problems focuses on “Process Capability Ratios – 5”.
Explanation: The value of τ in the expression of Cpm 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?
Explanation: The value of squared value of τ,
Explanation: The estimate of Cpm, when the standard values of σ, μ are not given, is calculated by expression,
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 Cpm when the value |μ-T|→∞ ?
Explanation: The value of Cpm approaches to zero asymptotically as the value |μ-T|→∞. This is because,
8. What is the value of Cpm when the value μ=T?
11. Cpkm is also called _____ generation process capability ratio.
Explanation: Cpkm is sometimes called third generation process capability ratio since it is constructed from the second generation PCR Cpm and Cpk.
12. Cp is called the ____ generation PCR.
Explanation: Cp is called the first generation process capability ratio as it was designed before any other process capability ratio like Cpk or Cpm.
13. Which of these is one of the first generation process capability ratios?
Explanation: As we know, the first Process capability ratios, that were designed, were Cp, Cpu, Cpl. So they are called the first generation process capability ratios.
14. Cpm is the second generation process capability ratio.
Explanation: Cpk and Cpm 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.
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/d2 in the confidence intervals indicate?
b) Process must be in control
c) Process may be in the out-of-control state
Explanation: 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. Pp is a ___
a) Process capability ratio
b) Process stability ratio
c) Process prediction index
d) Process performance index
Explanation: AIAG has recommended using the process performance indices to be used instead of the process capability ratios when process is not in control. Pp is one of them.
Sanfoundry Global Education & Learning Series – Statistical Quality Control.
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