Interval estimation of capability index Cpmk for manufacturing processes with asymmetric tolerances

• Authors: Y. C. Chang
• Venue: Computers and Industrial Engineering
• Year: 2009

The index C"p"m"k combines the merits of the three earlier indices C"p, C"p"k, C"p"m and alerts the user if the process variance increases and/or the process mean deviates from its target value. In practice, treat the calculated estimate C@?"p"m"k as true value and ignore the effect on asymmetric tolerances may lead to misinterpretation of process capability. Pearn et al. [Pearn, W. L., Chen, K. S. & Lin, P. C. (1999). On the generalizations of the capability index C"p"m"k for asymmetric tolerances. Far East Journal of Theoretical Statistics, 3(1), 47-66.] introduced a generalization of C"p"m"k, which referred to as C"p"m"k^'', to handle processes with asymmetric tolerances. However, the sampling distribution of the estimator C@?"p"m"k^'' is exceedingly complex and the derivation of an interval estimation of C@?"p"m"k^'' is mathematically intractable. In this paper, we reformulate the explicit formulas and propose a heuristic algorithm to compute a lower confidence bound on C"p"m"k^'', which presents a measure on the minimum capability of the process, to enhance the applicability of the theoretical results. Tables are provided to assist the practitioners for a wide range of real world situation involving processes capability analysis. Equations and tables to estimate approximate sample size necessary to achieve a desired confidence limit with a specified confidence level are also developed. An application example on the trench capacitor etch process is also presented for illustrating the applicability of the generalization.