SUPPLEMENTARY EXERCISES FOR CHAPTER 10235Thereforeσ0 002171.Sinceμis closer toUSLthan toLSL,CpkUSLμ3σ2 303.(b) Yes. SinceCpk1, the process capability is acceptable.3. (a) The capability is maximized when the process mean is equidistant from the specification limits.Therefore the process mean should be set to 0.20.(b)LSL0 18,USL0 22,σ0 002171.Ifμ0 20, thenCpk0 220 203 0 0021713 071.5. (a) Letμbe the optimal setting for the process mean.ThenCpUSLμ3σμLSL3σ, so 1 2USLμ3σμLSL3σ.Solving forLSLandUSLyieldsLSLμ3 6σandUSLμ3 6σ.(b) Thez-scores for the upper and lower specification limits arez3 60.Therefore, using the normal curve, the proportion of units that are non-conformingis the sum of the areas under
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