Measurement error is often occurred in statistical process control. The effect of a linearly covariate error model on the exponentially weighted moving average (EWMA) median and cumulative sum (CUSUM) median charts is investigated.The results indicate that the EWMA median and CUSUM median charts are significantly affected in the presence of measurement errors. We compared the performance of the EWMA median and CUSUM median charts by using Markov chain method in the average run length and the standard deviation of the run length. We concluded that the CUSUM median chart for small shifts and the EWMA median chart for larger shifts are recommended. Two examples are provided to illustrate the application of the EWMA and CUSUM median charts with measurement errors.
An adaptive control chart called Shewhart X chart with variable sample size and sampling interval (VSSI) is quicker than Shewhart X chart, X chart with variable sample size (VSS), and X chart with variable sampling interval (VSI) in detecting the mean shifts of a normal process. In practice, the effects of measurement errors on control charts should be included. In this study, we present an VSSI median control chart with estimated parameters in the presence of measurement errors for a normal process. The average time to signal (ATS) is computed by using the Markov chain approach. The results show that the VSSI median control chart performs better than the Shewhart median, VSS median, and VSI median control charts in terms of ATS. The design parameters of the proposed chart are provided. Two examples are used to illustrate the application of the proposed control chart.
In this paper, we propose 3 new control charts for monitoring the lower Weibull percentiles under complete data and Type‐II censoring. In transforming the Weibull distribution to the smallest extreme value distribution, Pascaul et al (2017) presented an exponentially weighted moving average (EWMA) control chart, hereafter referred to as EWMA‐SEV‐Q, based on a pivotal quantity conditioned on ancillary statistics. We extended their concept to construct a cumulative sum (CUSUM) control chart denoted by CUSUM‐SEV‐Q. We provide more insights of the statistical properties of the monitoring statistic. Additionally, in transforming a Weibull distribution to a standard normal distribution, we propose EWMA and CUSUM control charts, denoted as EWMA‐YP and CUSUM‐YP, respectively, based on a pivotal quantity for monitoring the Weibull percentiles with complete data. With complete data, the EWMA‐YP and CUSUM‐YP control charts perform better than the EWMA‐SEV‐Q and CUSUM‐SEV‐Q control charts in terms of average run length. In Type‐II censoring, the EWMA‐SEV‐Q chart is slightly better than the CUSUM‐SEV‐Q chart in terms of average run length. Two numerical examples are used to illustrate the applications of the proposed control charts.
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