Department of Mathematics, Fu-Jen Catholic University, New Taipei City, 24205, Taiwan, R.O.C.
Department of Mathematics, National Central University, Taoyuan City, Chung-Li, 32054, Taiwan, R.O.C.
Comparison of quality for products (supplies and goods) is extremely important for manufacturers and consumers. Based on correct comparisons, manufacturers and consumers can nd better suppliers to cooperate and better merchandise to purchase, respectively. Quality is often measured and compared by process capability indices, among which Cp is very eective, simple to apply, and particularly useful for the rst round of comparison. In practice, Cp is unknown and should be estimated from observations. Let dCpi denote the maximum likelihood estimator obtained from normal process, Xi, with index value Cpi; i = 1; 2. If dCp1 >dCp2 with high probability when (1 + )Cp2 Cp1. Given 0 dCp2), we demonstrate how to nd the smallest sample size needed to ensure observing dCp1 > dCp2 with probability greater