A variable sample size side-sensitive synthetic coefficient of variation chart

Abstract

A major challenge for control charts monitoring the coefficient of variation is to quickly detect shifts in this parameter, so that assignable cause(s) can be quickly removed and the process can operate in an in-control state with a stable coefficient of variation. This is especially so when there are constraints in the sample size. One proposed strategy is to vary the sample size according to the most recent information. However, a side-sensitive synthetic chart monitoring the coefficient of variation with variable sample size is not available. This paper contributes to the literature by developing a variable sample size side-sensitive synthetic chart for the coefficient of variation. The main contributions are in terms of illustrating the operations of the chart, deriving the formulae to evaluate its performance and developing the algorithms to optimize its performance. Comparisons with current charts show that the proposed chart outperforms all existing synthetic-type charts monitoring the coefficient of variation. The proposed chart also outperforms the variable sample size coefficient of variation chart for all shift sizes. In addition, it outperforms the variable sample size run sum and variable sample size Exponentially Weighted Moving Average charts monitoring the coefficient of variation for moderate and large shift sizes.