Abstract
A popular capability index C pm is defined by C pm = USL − LSL 6γ , where USL and LSL are the upper specification limit and the lower specification limit on the characteristic X of each item from the process, respectively. γ 2 = E( X − T) 2 = σ 2 + ( μ − T) 2. T is a given target value. μ and σ 2 are the mean and the process variance of X, respectively. γ 2 expresses the deviation of X from the target T by σ 2 and the process centering ( μ − T) (Boyles, J. Quality Technology 23 (1991) 17–26). In the situation of the manufacturing process being under control, we assume that X is normally distributed. Besides, USL and LSL are usually fixed and determined in advance. Under the circumstance, to search the largest C pm which are used to provide unitless measure of the process performance is equivalent to looking for the smallest γ 2. The main purpose of the present paper is to select a subset containing the process associated with the smallest γ 2 from k given independent processes (populations). The results are also related to usual selection problems in analysis of variance.
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