No abstract

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 e ective, simple to apply, and particularly useful for the rst round of comparison. In practice, C p is unknown and should be estimated from observations. Let d Cpi denote the maximum likelihood estimator obtained from normal process, Xi, with indexCp2 is observed, we will conclude that Cp1 > (<)Cp2 and decide that X 1 is better (worse) than X 2 . Given a small and positive number, , there is no need to make comparison when (1 )C p2 < C p1 < (1+ )C p2 since C p1 is close to C p2 . It is desirable to observe d Cp1 > d Cp2 with high probability when (1 + )Cp2 < Cp1 and with low probability when (1 )C p2 > C p1 . Given 0 < 1 , 2 < 1, based on the table constructed from P ( d Cp1 > d Cp2), we demonstrate how to nd the smallest sample size needed to ensure observing d C p1 > d C p2 with probability greater than 1 1 when (1 + )C p2 < C p1 and smaller than 2 when (1 )C p2 > C p1 .