Optimal designs of the side sensitive synthetic chart for the coefficient of variation based on the median run length and expected median run length

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.

A Comparative Analysis of Control Charts for Monitoring Process Mean

Control charts serve as an effective tool for controlling and monitoring process quality in industries of production and service. The Shewhart chart is the first control chart that was used to detect large mean shifts in a process. Since then, to increase the Shewhart chart’s sensitivity, synthetic type control charts, such as synthetic control chart, side sensitive group runs (SSGR) control chart, have been proposed. SSGR chart ismore efficient compared to the Shewhart chart and synthetic chart,primarily due to the side sensitive feature in SSGR chart. Meanwhile, exponentially weighted moving average (EWMA) chart isoften used to detect small process changes. In practice, the evaluation of a control chart’s performance is vital. Nevertheless, the cost of implementing a control chart is an important factor that influences the choice of a control chart. The cost of repairs, sampling, nonconforming products from a failure in detecting out-of-control status, and investigating false alarms, can be significantly high. Therefore, the aim of this paper is to compare the implementation cost of synthetic, SSGR and EWMA charts, so that quality practitioners can identify the most cost-effective chart to implement. Here, the cost function was adopted to compute the implementation cost of the control chart. According to the findings, quality practitioners are recommended to adopt the SSGR chart,since it is more economical compared to the synthetic chart. However, the cost to implement anEWMA chart is higher than the synthetic and SSGR charts. In light of this, this study allows for quality practitioners to have a better idea on the selection of the control chart to implement, with respect to its cost.

An Optimal Design of the Synthetic Coefficient of Variation Chart Based on the Median Run Length

The synthetic coefficient of variation (CV) chart is currently evaluated based only on the average run length (ARL), but this paper evaluates the chart based on different percentiles of the run length, which shows that false alarms frequently happen earlier than that shown by the in-control ARL (ARL[Formula: see text], and for small sample sizes and shift sizes, the out-of-control condition is frequently detected before what is shown by the out-of-control ARL (ARL[Formula: see text]. Furthermore, the run lengths show large variations. Hence, the chart’s performance could not be interpreted only in terms of the ARL. This paper proposes the median run length (MRL)-based design for the synthetic CV chart, which is not available in the literature. The MRL-based design shows larger MRL0 and ARL0, smaller MRL1 and ARL1, and less variation in the out-of-control run lengths compared to existing ARL-based designs. However, the in-control run lengths show more variation. Comparisons show that the synthetic chart outperforms the VSS and Shewhart charts, while comparison with the Exponentially Weighted Moving Average (EWMA) chart shows that although it outperforms the synthetic chart based on the ARL for small shift sizes, the synthetic chart shows better performance in terms of the MRL. The MRL-based synthetic chart is then implemented on an industrial example.

A Combined Upper-Sided Synthetic S2 Chart for Monitoring the Process Variance

In order to monitor the process variance, this paper proposes a combined upper-sided synthetic S2 chart for monitoring the process standard deviation of a normally distributed process. This combined upper-sided synthetic S2 chart comprises a synthetic chart and an upper-sided S2 chart. The design and performance of the proposed chart are presented, and the steady-state average run length comparisons show that the combined upper-sided synthetic S2 chart outperforms the standard synthetic S2 chart as well as several run rules S2 charts, especially for larger shifts in the process variance.