Directionally sensitive weighted adaptive multivariate CUSUM mean charts

Abstract

In many service and manufacturing industries, process monitoring involves multivariate data, instead of univariate data. In these situations, multivariate charts are employed for process monitoring. Very often when the mean vector shifts to an out-of-control situation, the exact shift size is unknown; hence, multivariate charts for monitoring a range of the mean shift sizes in the mean vector are adopted. In this paper, directionally sensitive weighted adaptive multivariate CUSUM charts are developed for monitoring a range of the mean shift sizes.Directionally sensitive charts are useful in situations where the aim lies in monitoring either an increasing or a decreasing shift in the mean vector of the quality characteristics of interest. The Monte Carlo simulation is used to compute the run length characteristics in comparing the sensitivities of the proposed and existing multivariate CUSUM charts. In general, the directionally sensitive and weighted adaptive features enhance the sensitivities of the proposed multivariate CUSUM charts in comparison with the existing multivariate CUSUM charts without the adaptive feature or those that are directionally invariant. It is also found that the variable sampling interval feature enhances the sensitivities of the proposed and existing charts as compared to their fixed sampling interval counterparts. The implementation of the proposed charts in detecting upward and downward shifts in the in-control process mean vector is demonstrated using two different datasets. K E Y W O R D Saverage run length, directionally sensitive, Monte Carlo simulation, process mean vector, statistical process control INTRODUCTIONStatistical process control (SPC) contains a set of problem-solving tools that play a vital role in establishing a controlled production environment by reducing the assignable cause of variation that arises due to assignable causes. A statistical quality control chart is an important tool in the SPC toolkit as it is very sensitive to the process variation that occurs due to the presence of assignable causes. This is the main reason why control charts are mostly used in many service and process industries to monitor production or manufacturing processes. Take an example of the pharmaceutical industry that employs batch processing with laboratory assays, namely, hardness, moisture, homogeneity, and dissolution testing, to name a few, which are to be carried out on final products to meet the standards of quality control. The multivariate 2970

Directionally sensitive adaptive MEWMA charts with fixed and variable sampling rates

“…Haq 19 recent work has suggested a new 1ME chart, with a new transformation that truncates observations either above or below the process mean, thus increasing its directional sensitivity. Haq et al 20 . proposed directionally sensitive weighted AMC charts which are useful in monitoring either an increasing or a decreasing shift in the mean vector, for a range of mean shift sizes.…”