The coefficient of variation (CV) is used in process monitoring when the process mean and standard deviation are proportional to each other. In this work, a side‐sensitive modified group runs CV (SSMGR CV) chart is proposed for monitoring the process CV. The run length performance of the SSMGR CV chart is compared to those of the existing CV charts in terms of the average and standard deviation of the run length criteria. The SSMGR CV chart is found to outperform the existing CV charts. In addition, the run length performance of the SSMGR CV chart is also evaluated in the presence of measurement errors, as these errors are not only unavoidable in practice but they also affect the sensitivity of a control chart in detecting an out‐of‐control situation. The results obtained show that the accuracy and precision errors affect the performance of the SSMGR CV chart in detecting an out‐of‐control situation.
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The run sum
trueX¯ control chart is usually investigated under the assumption of known process parameters. In practice, process parameters are rarely known and they need to be estimated from an in‐control Phase I dataset. However, different practitioners use different numbers of Phase I samples to estimate the process parameters. As a result, the commonly used performance measure, ie, the average run length becomes a random variable. In this study, we present a run sum
trueX¯ control chart with estimated process parameters and use the standard deviation of the average run length to evaluate the average of the average run length performance of the run sum
trueX¯ chart when process parameters are estimated. Based on the standard deviation of the average run length criterion, the number of Phase I samples required by the estimated process parameter–based run sum
trueX¯ chart to have an average of the average run length performance close to that obtained under the assumption of known process parameters is recommended.
In recent years, the suitable use of auxiliary information technique in control charts has shown an improved run length performance compared to control charts that do not have this feature. This article proposes a combined variable sampling interval (VSI) and double sampling (DS) chart using the auxiliary information (AI) technique (called VSIDS-AI chart, hereafter). The plotting-statistic of the VSIDS-AI chart requires information from both the study and auxiliary variables to efficiently detect process mean shifts. The charting statistics, optimal design and performance assessment of the VSIDS-AI chart are discussed. The steady-state average time to signal (ssATS) and steady-state expected average time to signal (ssEATS) are considered as the performance measures. The ssATS and ssEATS results of the VSIDS-AI chart are compared with those of the DS AI, variable sample size and sampling interval AI, exponentially weighted moving average AI (EWMA-AI) and run sum AI (RS-AI) charts. The results of comparison show that the VSIDS-AI chart outperforms the charts under comparison for all shift sizes, except the EWMA-AI and RS-AI charts for small shift sizes. An illustrative example is provided to demonstrate the implementation of the VSIDS-AI chart.
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