Shewhart control charts for dispersion adjusted for parameter estimation

Self Cite

Research on the performance evaluation and the design of the Phase II EWMA control chart for monitoring the mean, when parameters are estimated, have mainly focused on the marginal in‐control average run‐length (ARLIN). Recent research has highlighted the high variability in the in‐control performance of these charts. This has led to the recommendation of studying of the conditional in‐control average run‐length (CARLIN) distribution. We study the performance and the design of the Phase II EWMA chart for the mean, using the CARLIN distribution and the exceedance probability criterion (EPC). The CARLIN distribution is approximated by the Markov Chain method and Monte Carlo simulations. Our results show that in‐order to design charts that guarantee a specified EPC, more Phase I data are needed than previously recommended in the literature. A method for adjusting the Phase II EWMA control chart limits, to achieve a specified EPC, for the available amount of data at hand, is presented. This method does not involve bootstrapping and produces results that are about the same as some existing results. Tables and graphs of the adjusted constants are provided. An in‐control and out‐of‐control performance evaluation of the adjusted limits EWMA chart is presented. Results show that, for moderate to large shifts, the performance of the adjusted limits EWMA chart is quite satisfactory. For small shifts, an in‐control and out‐of‐control performance tradeoff can be made to improve performance.

Section: Discussionmentioning

confidence: 63%

Section: Adjustment Of the Standard Phase II Ewma Chart Limits For Gumentioning

confidence: 91%

Guaranteed in‐control performance of the EWMA chart for monitoring the mean

Diko

Chakraborti

Does

2019

Self Cite

“…The utilization of auxiliary information at estimation stage and imposing the restrictive assumptions of known process parameters do not seem realistic practically. The drawbacks of the assumption of known process parameters can be viewed in the studies of Schoonhoven et al, Schoonhoven and Does, Diko et al, Goedhart et al, Haridy et al, and Jensen et al…”

Section: Introductionmentioning

confidence: 99%

On a class of mixed EWMA‐CUSUM median control charts for process monitoring

Hussain

Wang

Ahmad

et al. 2020

Monitoring of any manufacturing, production, or industrial process can be controlled and improved by removing these special cause of variations using control charts. Shewhart‐type control charts are effective to control a large amount of special variations, whereas, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts detect small and moderate variations efficiently in the process parameters. Monitoring of location parameter can be done with mean control charts under the assumption that the parameters are known or correctly estimated from in‐control samples and data are free from outliers (but in practice data occasionally have outliers). In this study, we have proposed generalized mixed EWMA‐CUSUM median control charts structures for known and unknown parameters based on auxiliary variables for detecting shifts in process location parameter. The proposed charts are compared with the corresponding charts for the mean, based on contaminated and uncontaminated data. Different performance measures are used to evaluate the performance of proposed control charts and revealed through results that the median‐based charts are more sensitive to detect a shift in process location parameter in the presence of outliers. An illustrative example using real data is also shown for practical consideration.

“…The results have shown that the analytical and the bootstrap approaches get similar performance by efficiently adjusting the control limits of the chart. To monitor the process variance, some studies were also conducted on the Shewhart

S^{2}

chart; readers may refer to Faraz et al and Goedhart et al All the above studies focused on the conditional properties of control charts with unknown process parameters. General results showed that an impractically large number of phase I data is needed when a practitioner wants to have his(her) own chart's in‐control properties close to the desired one.…”

Section: Introductionmentioning

confidence: 99%

Conditional median run length performance of the synthetic X¯ chart with unknown process parameters

Castagliola

Tang

et al. 2020

Synthetic‐type charts are efficient tools for process monitoring. They are easy to design and implement in practice. The properties of these charts are usually evaluated under the assumption of known process parameters. This assumption is sometimes violated in practice, and process parameters have to be estimated from different phase I data sets collected by different practitioners. This fact causes the between‐practitioners variability among the properties of the synthetic‐type charts designed for each practitioner. In fact, the shape of the run length distribution of the synthetic‐type charts changes with the mean shift size. As a good alternative, the median run length false(MRLfalse) metric is argued to evaluate the properties of different control charts. In this paper, the MRL is used as a measure of the synthetic trueX¯ chart's performance, and the conditional MRL properties of the synthetic trueX¯ chart with unknown process parameters are investigated. Both the average MRL ( AMRL) and the standard deviation of MRL ( SDMRL) are used together to investigate the chart's properties when the process parameters are unknown. If the available number of phase I samples is not large enough to reduce the variability of the in‐control MRL values to an acceptable level, a bootstrap‐type approach is suggested to adjust the control limits of the synthetic trueX¯ chart and to further prevent many unwanted lower in‐control MRL values.