Optimal designs of the omnibus SPRT control chart for joint monitoring of process mean and dispersion
本文开发了一种结合均值和方差信息的综合SPRT控制图，通过马尔可夫链推导运行长度性质，并基于两种指标提出最优设计，相比经典控制图表现更优，且平均采样数更少。
The vast majority of control schemes related to the sequential probability ratio test (SPRT) are designed for the purpose of monitoring only the process mean. Nonetheless, most manufacturing processes are vulnerable to external factors that cause the process mean and variability to change simultaneously. It is, therefore, crucial to consider a joint scheme for monitoring both the location and scale parameters of a production process. In this article, we develop a scheme that combines both mean and variance information in a single SPRT, known as the omnibus SPRT (OSPRT) chart. Expressions for the run-length properties of the OSPRT chart are derived by means of the Markov chain approach. We also propose optimal designs for the OSPRT chart based on two different metrics, i.e. by minimising the average time to signal and the average extra quadratic loss. Through a comprehensive analysis, this article reveals that the optimal OSPRT chart outperforms the classical X¯-S, weighted-loss cumulative sum, absolute-value SPRT, and two maximum weighted-moving-average-type charts. The optimal OSPRT chart also has the advantage of collecting a small number of samples on average before producing a decision. Finally, the implementation of the OSPRT chart is presented with a wire bonding industrial dataset.