Monitoring Bernoulli processes considering measurement errors and learning effect

Abstract

Abstract This paper presents the effect of measurement errors and learning on monitoring processes with individual Bernoulli observations. A cumulative sum control chart is considered to evaluate the possible impacts of measurement errors and learning. We propose a time‐dependent learning effect model along with measurement errors and incorporate them into the Bernoulli CUSUM control chart statistic. The performance of the Bernoulli CUSUM control chart is then merely assessed by comparing the average number of observations to signal (ANOS) under two proposed conditions with the condition of no possible errors. Thus, the ANOS values are obtained under different proportions of non‐conforming items, once considering errors due to measurement by inspectors, and once considering both errors and learning effect together. The experimental results show that the efficiency of the control chart to detect assignable causes deteriorates in the presence of measurement errors and enhances when learning affects operators' performance. The proposed approach has a potential to be used in monitoring high‐quality Bernoulli processes as well as disease diagnosis, and other health care applications with Bernoulli observations.

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