PROCESS CAPABILITY INDEX (Cpk). You are the process improvement manager and have developed a new machine to cut insoles for the company’s top-of-the-line running shoes. You are excited because the company’s goal is no more than 3.4 defects per million, and this machine may be the innovation you

Question

PROCESS CAPABILITY INDEX ([latex]C_{pk}[/latex]). You are the process improvement manager and have developed a new machine to cut insoles for the company’s top-of-the-line running shoes. You are excited because the company’s goal is no more than 3.4 defects per million, and this machine may be the innovation you need. The insoles cannot be more than ±.001 of an inch from the required thickness of .250″. You want to know if you should replace the existing machine, which has a [latex]C_{pk}[/latex] of 1.0.

Mean of the new process [latex]\bar{X}[/latex] = .250 inches.
Standard deviation of the new process = σ = .0005 inches.
APPROACH [latex]\blacktriangleright[/latex] You decide to determine the [latex]C_{pk}[/latex], using Equation (S6-14), for the new machine and make a decision on that basis.

[latex]C_{pk} = Minimum of \left[\frac{Upper specification limit - \bar{X}}{3\sigma}, \frac{\bar{X} - Lower specification limit}{3\sigma}\right][/latex] (S6-14)

Accepted Answer

SOLUTION [latex]\blacktriangleright[/latex] Upper specification limit = .251 inches
Lower specification limit = .249 inches

[latex]C_{pk} = Minimum of \left[\frac{Upper specification limit - \bar{X}}{3\sigma}, \frac{\bar{X} - Lower specification limit}{3\sigma}\right][/latex]

[latex]C_{pk} = Minimum of \left[\frac{.251 - .250}{(3).0005}, \frac{.250 - .249}{(3).0005}\right][/latex]

Both calculations result in: [latex]\frac{.001}{.0015} = .67[/latex].

INSIGHT [latex]\blacktriangleright[/latex] Because the new machine has a [latex]C_{pk}[/latex] of only 0.67, the new machine should not replace the existing machine.

LEARNING EXERCISE [latex]\blacktriangleright[/latex] If the insoles can be ±.002″ (instead of .001″) from the required .250″, what is the new [latex]C_{pk}[/latex]? [Answer: 1.33 and the new machine should replace the existing one.]

RELATED PROBLEMS [latex]\blacktriangleright[/latex] S6.41–S6.45 (S6.46–S6.49 are available in MyOMLab)
ACTIVE MODEL S6.2 This example is further illustrated in Active Model S6.2 in MyOMLab.
EXCEL OM Data File Ch06SExS7.xls can be found in MyOMLab.

Question 6.S7: PROCESS CAPABILITY INDEX (Cpk). You are the process improvem...

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