A side-sensitive double sampling X¯ monitoring scheme with estimated process parameters. Issue 7 (3rd July 2022) - Motsepa, Collen M.; Malela-Majika, Jean-Claude; Castagliola, Philippe; Shongwe, Sandile C.
Abstract: In statistical process monitoring (SPM), most of the monitoring schemes are designed assuming that the process parameters for the underlying distribution are known (i.e., Case K). In a variety of contexts, it has been shown that when the parameters used to design the control limits are unknown (i.e., Case U), this greatly affects the monitoring schemes properties. Hence, in this paper, we study the parameter estimation effect of the side-sensitive double sampling (SSDS) X ¯ monitoring scheme for detecting changes in the process mean when distribution design parameters are estimated from an in-control retrospective sample. A thorough investigation is conducted using the unconditional run-length properties (i.e., average, standard deviation and percentiles), average sample size ( ASS ) and average number of observations to signal ( ANOS ) through exact integral formulas and simulations. In addition, the average extra quadratic loss ( AEQL ), average ratio of the average run-length ( ARARL ) and performance comparison index ( PCI ) are used to quantify the run-length of the SSDS scheme from an overall performance perspective. Comparisons with other established monitoring schemes when parameters are unknown indicate that the SSDS scheme has a better overall performance. An illustrative example is also given to facilitate the design and implementation of the new scheme. An additional section briefly discussing the synthetic version of the SSDS scheme is also provided.