Waie Chung YeongPing Yin LeeSok Li LimNg Peh SangKhai Wah KhawAlejandro Fernández Villaverde2024-10-212024-10-212021-07-30https://doi.org/10.1371/journal.pone.0255366https://dspace-cris.utar.edu.my/handle/123456789/3933<jats:p>The side sensitive synthetic chart was proposed to improve the performance of the synthetic chart to monitor shifts in the coefficient of variation (<jats:italic>γ</jats:italic>), 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-<jats:italic>γ</jats:italic>chart is only evaluated in terms of the average run length (<jats:italic>ARL</jats:italic>) and expected average run length (<jats:italic>EARL</jats:italic>). 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<jats:italic>ARL</jats:italic>and<jats:italic>EARL</jats:italic>. 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<jats:italic>ARL</jats:italic>(<jats:italic>ARL</jats:italic><jats:sub>0</jats:sub>), and small shifts are often detected earlier compared to the<jats:italic>ARL</jats:italic><jats:sub>1</jats:sub>. Subsequently, this paper proposes an alternative design based on the median run length (<jats:italic>MRL</jats:italic>) and expected median run length (<jats:italic>EMRL</jats:italic>). The optimal design based on the<jats:italic>MRL</jats:italic>shows smaller out-of-control<jats:italic>MRL</jats:italic>(<jats:italic>MRL</jats:italic><jats:sub>1</jats:sub>), 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<jats:italic>EMRL</jats:italic>is similar to that of the existing designs. Comparisons with the synthetic-<jats:italic>γ</jats:italic>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.</jats:p>journal-article