关键词: ARMA控制图, 马尔科夫链, 可变抽样区间, 经济设计

Abstract: To improve the sensitivity of statistical process control reducing costs for process monitoring at the same time, the economic design of autoregressive moving average control chart with variable sampling interval (VSI ARMA) was discussed. The economic model of autoregressive moving average control chart with variable sampling interval (VSI ARMA) was established based on Lorenzen and Vance’s model, in which Markov chain was used to calculate the average time to signal (ATS) through constructing a three dimensional random vector. Using genetic algorithm to search for the optimal combination of seven parameters of VSI ARMA model made the cost of economic model at unit time to be minimum at the same time. Meanwhile, FSI ARMA control chart was used to monitor the same process, and the economic design of FSI ARMA control chart is also carried out. The results of the two models are compared, which indicates that the loss cost of VSI ARMA control charts is consistently lower than that of the FSI scheme when the design parameter is identical.

Key words: ARMA control chart, Markov chain, variable sampling interval, economic design