An evaluation of the multivariate dispersion charts with estimated parameters under non‐normality

Abstract

Various charts such as |S|, W, and G are used for monitoring process dispersion. Most of these charts are based on the normality assumption, while exact distribution of the control statistic is unknown, and thus limiting distribution of control statistic is employed which is applicable for large sample sizes. In practice, the normality assumption of distribution might be violated, while it is not always possible to collect large sample size. Furthermore, to use control charts in practice, the in‐control state usually has to be estimated. Such estimation has a negative effect on the performance of control chart. Non‐parametric bootstrap control charts can be considered as an alternative when the distribution is unknown or a collection of large sample size is not possible or the process parameters are estimated from a Phase I data set. In this paper, non‐parametric bootstrap multivariate control charts |S|, W, and G are introduced, and their performances are compared against Shewhart‐type control charts. The proposed method is based on bootstrapping the data used for estimating the in‐control state. Simulation results show satisfactory performance for the bootstrap control charts. Ultimately, the proposed control charts are applied to a real case study.

Bivariate modified hotelling’s T2 charts using bootstrap data

“…Besides that, in general, estimation to the in-control state of the control charts has to be carried out, but this will have adverse impact on the performance of the control chart. As indicated in Mostajeran et al in [7], non-parametric bootstrap control charts are appropriate for an unidentified distribution or when making estimation on the process parameters from Phase I dataset or when it is impractical to gather sample of large size.…”

“…In Mostajeran et al [7], the authors presented the use of non-parametric bootstrap multivariate control charts |S|, W, and G, and this method is grounded upon the use of bootstrapped data in the estimation of the in-control state. In this study, the authors succeeded in obtaining satisfactory performance of bootstrap [12] demonstrated the application of a bootstrap multivariate control chart and compared it with a Hotelling's T 2 parametric multivariate control chart, a multivariate sign control chart, and a multivariate Wilcoxon control chart.…”