Adaptive charting schemes based on double sequential probability ratio tests

Abstract

Sequential probability ratio test (SPRT) control charts are shown to be able to detect most shifts in the mean or proportion substantially faster than conventional charts such as CUSUM charts. However, they are limited in applications because of the absence of the upper bound on the sample size and possibly large sample numbers during implementation. The double SPRT (2-SPRT) control chart, which applies a 2-SPRT at each sampling point, is proposed in this paper to solve some of the limitations of SPRT charts. Approximate performance measures of the 2-SPRT control chart are obtained by the backward method with the Gaussian quadrature in a computer program. On the basis of two industrial examples and simulation comparisons, we conclude that the 2-SPRT chart is competitive in that it is more sensitive and economical for small shifts and has advantages in administration because of fixed sampling points and a proper upper bound on the sample size.

A rational sequential probability ratio test control chart for monitoring process shifts in mean and variance

“…Stoumbos and Reynolds [18] proposed the SPRT fixed-times chart, in which each individual observation is too long to be neglected and observations in group are considered. Li et al [19] studied the double SPRT chart, which applies a 2-SPRT at each sampling point. Ou et al [20] carried out the optimization design of an SPRT chart for monitoring process mean.…”

An economically designed Sequential Probability Ratio Test control chart for short-run production

“…Subsequently, several researches started to focus on the design of control charts based on SPRT. Li, Pu, and Tsung (2009) studied the double SPRT chart which applies a 2-SPRT at each sampling point. Ou, Wu, Chen, and Lee (2010) proposed a design algorithm for an SPRT chart in which the reference value is optimized.…”

Asymptotic Optimality of Combined Double Sequential Weighted Probability Ratio Test for Three Composite Hypotheses

“…For example, in clinical trial applications, in order to compare the effects of two drugs (Goeman et al [1]), the equivalence trial 0 : |Δ| > Δ 1 versus 1 : |Δ| < Δ 0 (0 < Δ 0 < Δ 1 ) would be more realistically stated as 1 : Δ < −Δ 1 (inferiority), 2 : −Δ 0 < Δ < Δ 0 (equivalence), and 3 : Δ > Δ 1 (superiority), where Δ is the difference of effect between two drugs. The sequential testing of three or more hypotheses has been applied to a variety of engineering problems such as pattern recognition (Fu [2]; McMillen and Holmes [3]), multiple-resolution radar detection (Bussgang [4]), products comparisons (Anderson [5]), and others (Li et al [6]). Published work on this problem has taken two main approaches.…”