Distributional and inferential properties of some new multivariate process capability indices for symmetric specification region

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Research Article

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Quality and Reliability Engineering International


Statistical quality control is used to improve performance of processes. Since most of the processes are multivariate in nature, multivariate process capability indices (MPCIs) have been developed by many researchers depending on the context. However, it is generally difficult to understand and calculate MPCIs, compared to their univariate counterparts like (Formula presented.), (Formula presented.), and so on. This paper discusses a relatively new development in MPCIs, namely, (Formula presented.), which is a multivariate analogue of (Formula presented.) —the celebrated superstructure of univariate process capability indices. Some statistical properties of (Formula presented.) are studied, particularly of (Formula presented.), a member MPCI of the superstructure, which measures potential capability of a multivariate process. A threshold value of (Formula presented.) is computed, and this can be considered as a logical cut-off for other member indices of (Formula presented.) as well. The expression for the upper limit of the proportion of nonconformance is derived as a function of (Formula presented.). Density plots of asymptotic distributions of four major member indices of (Formula presented.), namely, (Formula presented.), (Formula presented.), (Formula presented.), and (Formula presented.), are made. Finally, a numerical example is discussed to supplement the theory developed in this paper.

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