Dynamic probability control limits for CUSUM charts for monitoring proportions with time‐varying sample sizes

Abstract

We consider the problem of monitoring a proportion with time‐varying sample sizes. Control charts are generally designed by assuming a fixed sample size or a priori knowledge of a sample size probability distribution. Sometimes, it is not possible to know, or accurately estimate, a sample size distribution or the distribution may change over time. An improper assumption for the sample size distribution could lead to undesirable performance of the control chart. To handle this problem, we propose the use of dynamic probability control limits (DPCLs) which are determined successively as the sample sizes become known. The method is based on keeping the conditional probability of a false alarm at a predetermined level given that there has not been any earlier false alarm. The control limits dynamically change, and the in‐control performance of the chart can be controlled at the desired level for any sequence of sample sizes. The simulation results support this result showing that there is no need for any assumption of a sample size distribution with the use of this proposed approach.

Transition Activity Recognition System Based on Standard Deviation Trend Analysis

“…Moreover, we introduce the CUSUM chart (cumulative sum control chart) as another state-of-the-art algorithm in this experiment. CUSUM has excellent performance in change point detection issues [35,36], which are similar with our problem. We use a similar strategy using SVM as the basic classifier and CUSUM as the transition activity recognition method.…”

Design of adaptive EWMA control charts using the conditional false alarm rate

“…Using simulation or other numerical methods to control the conditional false alarm rate (CFAR) has proven very useful in designing control charts, especially when a covariate varies over time. Recent examples accounting for varying sample sizes include Aytaçoğlu and Woodall, 1 who used the CFAR to determine control limits for the cumulative sum (CUSUM) chart for monitoring proportions, and Aytaçoğlu et al 2 . who used this dynamic control limit approach to design the multivariate exponentially weighted moving average (MEWMA) chart.…”

Effect of estimation error on the conditional false alarm rate design of the EWMA chart

“…The CFAR at a given time is the probability of a false alarm given no previous false alarm. Recent studies by Aytaçoğlu and Woodall, 1 Aytaçoğlu et al, 2 and Aytaçoğlu et al 3 have demonstrated the effectiveness of this approach in designing the binomial cumulative sum, the multivariate exponentially weighted moving average (EWMA), and the adaptive EWMA charts, respectively, while accommodating varying sample sizes. More related works in this direction are Shen et al, 4 Zhang and Woodall, 5 Huang et al, 6 Zhang and Woodall, 7 and Driscoll et al, 8 to name a few.…”