As we understand it, Process Capability indices are intended to provide single-number assessments of ability to meet specification limits on quality characteristics of interest. As a consequence of the varied ways in which PCIs are used, there have been two natural lines of research work: ① studies on the properties of PCIs and their estimators in many different environments; ② construction of new PCIs purporting to have better properties in certain circumstances. The most of existing process capability indices are concerned with the single variable. But, in many cases, a quality characteristic is composed with several factors. In that case, we want to know the integrated process capability of a quality characteristic not those of each factor. In this paper, we proposed a new multivariate system process capability index called MSPCI:SCpsk which is the geometric mean of performance measure Cpsk'S, and will be used as the criterion to assess multiple response process designs. Numerical illustration is done for SCpsk, Cp(f), Cp, Cpk, Cpm, and Cpsk.

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