A new adaptive control chart for the simultaneous monitoring of the mean and variability of multivariate normal processes

Abstract

This paper considers adaptive schemes for the simultaneous monitoring of the mean and variability of a multivariate normal quality characteristic. At first, we extend an already existing bivariate nonadaptive simultaneous control chart to a multivariate one. Then, we develop several adaptive schemes, which will cover both previously bivariate and newly multivariate charts. After having designed adaptive schemes for the multivariate chart, eight performance measures are computed based on the run length, time to signal, number of observations to signal and number of switches to signal and evaluated using a new Markov chain model. With the developed performance measures, non-adaptive and adaptive schemes under different mean, variability, simultaneous shift sizes, and different number of quality characteristics are compared. Our scheme is also compared to one of the best methods available in the literature. A numerical example is also provided in order to demonstrate how the adaptive scheme can be implemented in practice.

A literature review on joint control schemes in statistical process monitoring

“…According to the results, most of the efforts used nonadaptive (FP) control charts and only a few papers involve adaptive control charts. Nenes and Panagiotidou, 46 Wang et al, 50 Salmasnia et al, 70 Tasias and Nenes, 74 Sabahno et al, 82 Sabahno et al 83 and Sabahno et al 33 are the seven articles that considered adaptive control charts in joint monitoring.…”

Optimal design of an improved X¯ and R control chart for joint monitoring of process location and dispersion

“…, of X : 2=4 chart can be calculated out by substituting the value of δ > 0 into equations (23)(24)(25)(26)(27)(28), while the in-control ARL, ARL X : 2=4 0 , can be calculated out by substituting δ = 0 into equations (23)(24)(25)(26)(27)(28).…”

“…Meta-heuristic algorithms, especially genetic algorithm (GA), have been proven to be suitable for optimizing such problems and it has a high probability of finding a global optimum solution on most occasions. 27 Successful applications of GA in the optimization design of control charts can be seen in Sabahno et al, 28 Wang and Li, 29 Wan 30 and so on. Due to the flexibility and adaptive nature of GA in solving this kind of optimization problems, a GA will be developed to optimize the minimization problem for statistical design of the joint X ¯ / R : r / m chart.…”

A variable parameters multivariate control chart for simultaneous monitoring of the process mean and variability with measurement errors

“…There are very few researchers who added adaptive features to such charts. Reynolds and Kim and Reynolds and Cho did it for multivariate double‐chart schemes and Sabahno et al for a multivariate single‐chart scheme. The latter, considered VP, VSSI, VSI, and VSS adaptive features on a max‐type multivariate single‐chart, which was extended itself from Khoo's bivariate chart.…”

“…In this paper, we consider the effect of measurement errors on the adaptive simultaneous control chart introduced by Sabahno et al which includes Khoo's bivariate control chart too. Since they concluded that the best adaptive feature for their scheme is the VP one, therefore, we only consider the VP feature in this current paper.…”