A new approach for designing the Shewhart-type control charts with generalized sensitizing rules

Abstract

Two commonly used approaches for developing a Shewhart-type control chart with sensitizing rules are; the Markov Chain approach (MCA) and the single polynomial approach (SPA). The MCA for designing a control chart involves linear equations based on the choice of sensitizing rules. The MCA often becomes complex as the system of linear equations increases in size. The existing SPA for designing a control chart with sensitizing rules results in inconsistent in-control run length properties (RLP). To overcome the limitations of existing approaches, we present a new SPA for designing the Shewhart-type control charts with sensitizing rules. Furthermore, the new SPA has an interesting relationship with classical geometric distribution, generalized geometric distribution, and MCA. To show the significance of the new SPA, we have implemented it in designing the two-sided and one-sided mean control charts with sensitizing rules. The performance of the proposed and existing control charts is evaluated and compared using various RLP. The results reveal that the in-control RLP of the new SPA based mean control charts are sustained at their desired level. The out-of-control RLP is elaborated to highlight an optimal choice of sensitizing rules and other factors. Extensive comparative analysis shows that the new SPA based mean control charts have advantages over sustained behavior and computational reduction. Lastly, a real-life example of proposed methods is included using data on turnaround time of complete blood count (CBC) test results.