Control charts for monitoring the coefficient of variation (γ) are useful for processes with an inconsistent mean (μ) and a standard deviation (σ) which changes with μ, by monitoring the consistency in the ratio σ over μ. The synthetic‐γ chart is one of the charts proposed to monitor γ, and its attractiveness lie in waiting until a second point to fall outside the control limits before a decision is made. However, existing synthetic‐γ charts do not differentiate between the points falling outside the upper control limit (UCL) and lower control limit (LCL). Hence, this paper proposes a side‐sensitive synthetic‐γ chart, where successive nonconforming samples must either fall above the UCL or below the LCL. Formulae to compute the average run length (ARL), the standard deviation of the run length (SDRL) and expected average run length (EARL) are derived using the Markov chain approach, and the algorithms to obtain the optimal charting parameters are proposed. Subsequently, the optimal charting parameters, ARL, SDRL and EARL values for various numerical examples are shown. Comparisons show that the side‐sensitive synthetic‐γ chart consistently outperforms the existing synthetic‐γ chart, especially for small shifts. The proposed chart also consistently outperforms the Shewhart‐γ chart, while showing comparable or better performance than the Exponentially Weighted Moving Average (EWMA) chart for most shift sizes, except for very small shifts. Finally, this paper shows the implementation of the proposed chart on an industrial example.

The side sensitive synthetic chart was proposed to improve the performance of the synthetic chart to monitor shifts in the coefficient of variation (γ), by incorporating the side sensitivity feature where successive non-conforming samples must fall on the same side of the control limits. The existing side sensitive synthetic- γ chart is only evaluated in terms of the average run length (ARL) and expected average run length (EARL). However, the run length distribution is skewed to the right, hence the actual performance of the chart may be frequently different from what is shown by the ARL and EARL. This paper evaluates the entire run length distribution by studying the percentiles of the run length distribution. It is shown that false alarms frequently happen much earlier than the in-control ARL (ARL0), and small shifts are often detected earlier compared to the ARL1. Subsequently, this paper proposes an alternative design based on the median run length (MRL) and expected median run length (EMRL). The optimal design based on the MRL shows smaller out-of-control MRL (MRL1), which shows a quicker detection of the out-of-control condition, compared to the existing design, while the results from the optimal design based on the EMRL is similar to that of the existing designs. Comparisons with the synthetic-γ chart without side sensitivity shows that side sensitivity reduces the median number of samples required to detect a shift and reduces the variability in the run length. Finally, the proposed designs are implemented on an actual industrial example.