Maximum hybrid exponentially weighted moving average control chart in the presence of measurement error by using auxiliary information

Hybrid control charts have become part of statistical process control (SPC) but still, need more emphasis. Researchers are developing charts for joint monitoring of process mean and variance shifts just like Max-EWMA and their hybrid version using auxiliary information but are ignoring the effect of measurement error on the efficiency of charts. We propose maximum hybrid exponentially weighted moving average with measurement error using auxiliary information and name it Max-HEWMAMEAI control chart. The efficiency of this chart is proved through calculations of average run lengths ($ARLs$) and standard deviations of run lengths (SDRLs) using the Monte Carlo simulations method whereas, $ARLs$ and $\text{◂⋅▸}SDRLs$ are shown in tabular form. The effect of measurement error on the efficiency of the chart has been analyzed and the impact of multiple measurements to reduce the error effect has been studied using the covariate model. Real-life application is also part of this article to support the simulation results.     

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

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 $(MRL)$ metric is argued to evaluate the properties of different control charts. In this paper, the $MRL$ is used as a measure of the synthetic $\overline{X}$ chart's performance, and the conditional $MRL$ properties of the synthetic $\overline{X}$ chart with unknown process parameters are investigated. Both the average $MRL$ ( $AMRL$) and the standard deviation of $MRL$ ( $\text{◂⋅▸}SDMRL$) 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 $\overline{X}$ chart and to further prevent many unwanted lower in-control $MRL$ values.     

Practitioners guide on parametric,nonparametric, and semiparametric profile monitoring

Profile monitoring is one of the methods used in statistical process control ($SPC$) to understand the functional relationship between response and explanatory variables by tracking this relationship and estimating parameters. SPC is done in two phases: In Phase $I$, a statistical model is created and its parameters estimated using historical data. Phase $II$ implements the statistical model and monitors the live ongoing process. Control charts are graphical tools used to monitor these functional relationships over time in both Phase $I$ and Phase $II$. This study provides a step-by-step application for parametric, nonparametric, and semiparametric methods in profile monitoring and creates an in-depth guideline with comparative analysis studies for novice practitioners. A comparative analysis under each distributional assumption is conducted for various control charts.     

A hybrid homogeneously weighted moving average control chart for process monitoring: Discussion

The sensitivity of a monitoring scheme depends on many factors including the variance of the charting statistic which is very important in the computation of the control limits. This paper discusses the computation of the variance of the recently proposed hybrid homogeneously weighted moving average (HHWMA) $\overline{X}$ scheme which was based on an incorrect assumption. The correct variance is used to evaluate the run-length characteristics of the HHWMA $\overline{X}$ scheme. It is observed that the incorrect variance has a significant impact on the sensitivity (or performance) of the HHWMA $\overline{X}$ scheme.