On the distributional properties of the estimated process accuracy index C-a

Abstract

Pearn et al. (1998) introduced the process accuracy index C-a to measure the degree of process centering (the ability to cluster around the center). Assuming that the process runs under uniform process condition, so that the process mean may be assumed as an unknown constant, the distributional and inferential properties of the estimator of Ca are investigated for normal processes. In this paper, the distributional properties of an estimator are investigated under a different but practical condition for stable normal processes, in which the knowledge P{mu greater than or equal to m} = p epsilon [0, 1] is available. The sampling distribution of the new estimator is derived. It is shown that the proposed estimator under the new process condition investigated, follows the normal distribution. Consequently, process accuracy testing based on the ability to cluster around the center, can be easily performed. The expected value and the mean square error of the new estimator are also calculated for various values of two commonly-used process characteristic parameters, (mu - m)/sigma = 0.0(0.5)2.0, and d/sigma = 2(1)6. Significance: The sampling distribution of the proposed new estimator is derived. Consequently, process accuracy testing based on the ability to cluster around the center, can be easily performed, and decisions therefore can be made on whether actions should be taken to improve the process quality.