DESIGN OF THE c AND np CHARTS WHEN THE PARAMETERS ARE ESTIMATED

Abstract

The performance of attribute control charts is usually evaluated under the assumption of known process parameters (i.e., the nominal proportion of nonconforming units or the nominal number of nonconformities). However, in practice, these process parameters are rarely known and have to be estimated from an in-control historical Phase I data set. In this paper, we investigate the number m of Phase I samples that would be necessary for the c and p charts with estimated parameters in order to obtain similar in-control ARL's as in the known parameters case. We also propose new specific chart parameters that allow the c and np charts with estimated parameters to have approximately the same in-control ARL's as the ones obtained in the known parameter case.