KERNEL DENSITY ESTIMATION AND METROPOLIS-HASTINGS SAMPLING IN PROCESS CAPABILITY ANALYSIS OF UNKNOWN DISTRIBUTIONS

摘要

Strong normality assumption is associated with widely used process capability indices such as c_p, c_(pk). Violation of the assumption will mislead the interpretation in applications. A nonparametric method is proposed for density estimation of any unknown distribution. Kernels are used for density estimation and metropolis-hastings (M-H) algorithm is adopted to generate samples from the density. M-H sampling provides a tool to accommodate different kernel functions and flexibility of future extension to multivariate cases. Conformity (yield) based indices (y_p, y) are adopted to replace c_p, c_(pk). These indices can be conveniently assessed by the proposed kernel density based M-H algorithm (K-M-H). The method is validated by several simulation case studies.