Variable sampling size and sampling interval with conforming run length synthetic control chart

We propose a VSSI–CRL (Variable Sampling Size and Sampling Interval–Conforming Run Length) synthetic control chart in order to improve the statistical characteristics of both the VSSI chart and the CRL synthetic chart. The VSSI–CRL chart utilizes VSSI sampling scheme, but it produces a signal only when the CRL is less than a given limit. An algorithm for calculating the ARL (Average Run Length) and ATS (Average Time to Signal) of the VSSI–CRL chart is developed by employing Markov chain method. We present some lemmas for describing the statistical characteristics of the VSSI–CRL chart under in-control state. A procedure for designing the VSSI–CRL chart is proposed based on the lemmas. Extensive comparative studies show that the VSSI–CRL chart is superior to the CRL synthetic chart or the VSSI chart in general, and is comparable to the EWMA chart in ATS performance.