Ettlie Engineering has a new catalyst injection system for your countertop production line. Your process engineering department has conducted experiments and determined that the mean is 8.01 grams with a standard deviation of .03. Your specifications are: µ = 8.0 and σ = .04, which means an upper specification limit of 8.12[= 8.0 + 3(.04)] and a lower specification limit of 7.88[= 8.0 – 3(.04)].

What is the $C_{pk}$ performance of the injection system?

Question

Ettlie Engineering has a new catalyst injection system for your countertop production line. Your process engineering department has conducted experiments and determined that the mean is 8.01 grams with a standard deviation of .03. Your specifications are: µ = 8.0 and σ = .04, which means an upper specification limit of 8.12[= 8.0 + 3(.04)] and a lower specification limit of 7.88[= 8.0 – 3(.04)].

What is the $C_{pk}$ performance of the injection system?

What is the [latex]C_{pk}[/latex] performance of the injection system?

Accepted Answer

Using Equation (S6-14):

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

where
[latex]\bar{X}[/latex] = process mean
σ = standard deviation of the process population

[latex]C_{pk} = Minimum of \left[\frac{8.12 - 8.01}{(3) (.03)}, \frac{8.01 - 7.88}{(3) (.03)}\right][/latex]

[latex]\left[\frac{.11}{.09} = 1.22, \frac{.13}{.09} = 1.44\right][/latex]

The minimum is 1.22, so the [latex]C_{pk}[/latex] is within specifications and has an implied error rate of less than 2,700 defects per million.

Question 6.S6.4: Ettlie Engineering has a new catalyst injection system for y...

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