Procedures for testing manufacturing precision Cpbased on ( $\bar{x}$ ,R) or ( $\bar{x}$ ,S) control chart samples

Abstract

Process precision index C p has been widely used in the manufacturing industry for measuring process potential and precision. Estimating and testing process precision based on one single sample have been investigated extensively. In this paper, we consider the problem of estimating and testing process precision based on multiple samples taken from (X, R)or (X, S )control chart. We first investigate the statistical properties of the natural estimator of C p and implement the hypothesis testing procedure. We then develop efficient MAPLE programs to calculate the lower confidence bounds, critical values, and p-values based on m samples of size n. Based on the test, we develop a step-by-step procedure for practitioners to use in determining whether their manufacturing processes are capable of reproducing products satisfying the preset precision requirement.