Calculate the average values of the Cp and Cpk capability indices for the photolithography thickness data in Example 21.2. Omit the two outliers (samples #5 and #15), and assume that the upper and lower specification limits for the photoresist thickness are USL = 235 Å and LSL = 185 Å.

Question

Accepted Answer

After samples #5 and #15 are omitted, the grand mean is [latex]\bar{\bar{x}} = 199 Å[/latex], and the standard deviation of [latex]\bar{x}[/latex] (estimated from Eq. 21-13 with [latex]c_{4} = 0.8862[/latex]) is

[latex]\hat{\sigma }_{ \bar{x}} = \frac{1}{c_{4}\sqrt{n} }\bar{s}[/latex] (21-13)

[latex]\hat{ \sigma }_{\bar{x}} =\frac{\bar{s} }{c_{4} \sqrt{n} } =\frac{8.83}{0.8862\sqrt{3} } =5.75 Å[/latex]

From Eqs. 21-25 and 21-26,

[latex]C_{p} ≜ \frac{USL-LSL}{6\sigma }[/latex] (21-25)

[latex]C_{pk}≜ \frac{min \left[\bar{x} -LSL, USL -\bar{x} \right] }{3\sigma }[/latex] (21-26)

[latex]C_{p} = \frac{235-185}{6(5.75)}=1.45[/latex]

[latex]C_{pk} = \frac{min\left[199.5-185, 235-199.5\right] }{3(5.75)} =0.84[/latex]

Note that [latex]C_{pk}[/latex] is much smaller than the[latex]C_{p}[/latex], because [latex]\bar{\bar{x}}[/latex] is closer to the LSL than the USL.

Question 21.4: Calculate the average values of the Cp and Cpk capability in...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions