A VARIABLE SAMPLE SIZE SYNTHETIC CHART FOR THE COEFFICIENT OF VARIATION

Abstract

A variable sample size (VSS) synthetic chart to monitor the coefficient of variation  is proposed in this paper to improve the performance of the existing synthetic  chart. A description of how the chart operates, as well as the formulae for various performance measures (i.e., the average run length (ARL), standard deviation of the run length (SDRL), average sample size (ASS), and expected average run length (EARL)) are proposed. The algorithms that optimise the out-of-control ARL (ARL₁) and EARL (EARL₁), subject to the constraints in the in-control ARL (ARL₀) and ASS (ASS₀), are also proposed. Subsequently, optimal charting parameters for various numerical examples are obtained. The proposed chart shows a significant improvement over the existing synthetic -chart. Comparisons with other -charts also show that the proposed chart performs better than the Shewhart-  and VSS-  charts under all cases, while showing better performance than the exponentially weighted moving average (EWMA) and VSS EWMA-  charts for moderate and large shift sizes. Finally, this paper shows the implementation of the proposed chart on an actual industrial example.