Directionally sensitive MCUSUM mean charts

Abstract

In the context of a disease outbreak detection, a prime interest is to only detect increases in the process mean. It is thus desirable to have a directionally sensitive multivariate chart that can effectively detect either increases or decreases in the process mean vector. In this paper, with a suitable transformation that truncates multivariate observations either above or below the process mean vector, we propose one‐sided and two one‐sided MCUSUM charts for monitoring the mean of a multivariate normal process. Among the proposed charts, the one‐sided MCUSUM charts are directionally sensitive, while the two one‐sided MCUSUM charts are directionally insensitive. In addition, the fast initial response feature is also incorporated into the proposed charts to enhance their sensitivities against initial process shifts. The run length characteristics of these control charts are computed with the Monte Carlo simulation. Based on the run length comparisons, it is found that the proposed charts are more sensitive than the existing charts when detecting moderate‐to‐large shifts in the process mean. The proposed charts are also applied on real datasets to support the theory.

Directionally sensitive weighted adaptive multivariate CUSUM mean charts

“…The OWC, OWP, TOWC, and TOWP charts are weighted adaptive extensions of the existing OC, OP, TOC, and TOP charts, respectively, proposed by Haq and Sohrab. 25 Being nonadaptive charts, the existing OC, OP, TOC, and TOP charts are only useful when the mean shift size where a protection is needed is known in advance, as these charts do not provide optimal performances in the detection of a range of the mean shift sizes. To offset this limitation, the OWC, OWP, TOWC, and TOWP charts have been developed in this paper, as they provide uniformly better protection in the detection of a range of mean shift sizes.…”

“…Then, it can be shown that = −1∕2 ( − ) follows a standard multivariate normal distribution when the underlying process is in an in-control state, i.e., ∼  ( , ) when ≤ , where is a zero vector of dimension × 1, and is an identity matrix of dimension × . To construct C and P charts, Haq and Sohrab 25 considered the following transformations on :…”

“…The next step is to simply devise existing C and P charts based on + and − for monitoring increases and decreases in the PMV, respectively. On the lines of Haq, 9 recently Haq and Sohrab 25 suggested OC/OP and TOC/TOP charts, where the former are directionally sensitive as they target increases or decreases, whereas the latter target changes in the PMV.…”

“…On the lines of Crosier, 2 and based on the sequences, { + } and { − }, the upward and downward OC charts, as suggested by Haq and Sohrab, 25 require the following statistics:…”

“…On the lines of Pignatiello and Runger, 3 using the sequences, { + } and { − }, the OP charts, as suggested by Haq and Sohrab, 25 require the following upward and downward statistics:…”