Capability measure for asymmetric tolerance non-normal processes applied to speaker driver manufacturing

Abstract

Process capability indices, C-p(u, v), including Cp, C-pk, C-pm, and C-pmk, have been proposed in the manufacturing industry to provide numerical measures on process potential and performance for normal processes. Earlier studies considered a class of flexible capability indices, called C-Np(u, v), for processes with non-normal distributions where the tolerances are symmetric. In this paper we consider an extension of C-Np(u, v), called C-Np''(u, v), to handle non-normal processes with asymmetric tolerances. The extension takes into account the important property of the asymmetric loss function, which is shown to be more sensitive to process shift and more accurate than C-Np(u, v) in measuring process capability, hence provides better manufacturing quality assurance. Comparisons between C-Np(u, v) and the extension C-NP''(u, v) are provided. We propose a sample percentile estimator, and apply the bootstrap method to find the lower confidence bound for testing manufacturing capability. We also develop an integrated S-PLUS program to calculate the percentile estimator and the corresponding lower confidence bound. As an illustration, the proposed approach is applied to capability testing of home-theater speaker systems.