Run rules based phase II c and np charts when process parameters are unknown

Abstract

The performance of attributes control charts is usually evaluated under the assumption of known process parameters (i.e., the nominal proportion of non conforming units or the nominal average number of nonconformities). However, in practice, these process parameters are rarely known and have to be estimated from an in-control Phase I data set. The major contributions of this paper are (a) the derivation of the run length properties of the Run Rules Phase II c and np charts with estimated parameters, particularly focusing on the ARL, SDRL, and 0.05, 0.5, and 0.95 quantiles of the run length distribution; (b) the investigation of the number m of Phase I samples that is needed by these charts in order to obtain similar in-control ARLs to the known parameters case; and (c) the proposition of new specific chart parameters that allow these charts to have approximately the same in-control ARLs as the ones obtained in the known parameters case.