Abstract
Due to the proper performance of Bayesian control chart in detecting process shifts, it recently has become the subject of interest. It has been proved that on Bayesian and traditional control charts, the economic and statistical performances of the variable sampling interval (VSI) scheme are superior to those of the fixed ratio sampling (FRS) strategy in detecting small to moderate shifts. This paper studies the VSI multivariate Bayesian control chart based on economic and economic-statistical designs. Since finding the distribution of Bayesian statistic is t complicated, we apply Monte Carlo method and we employ artificial bee colony (ABC) algorithm to obtain the optimal design parameters (sample size, sampling intervals, warning limit and control limit). In the end, this case study is compared with VSI Hotelling’s T2 control chart and it is shown that this approach is more desirable statistically and economically.
Highlights
The source of shifts in process means are random and assignable causes
The optimal values of economic and statistical properties of variable sampling interval (VSI) multivariate Bayesian control chart based on economicstatistical design (ESD) and economic designs (ED) show that this scheme compered to VSI Hotelling’s T2 control chart based on ED and ESD has a more favorable performance in all cases and conditions of process shifts, costs and times
These results proved our hypothesis about the features of ESDs and the weakness of EDs
Summary
The source of shifts in process means are random and assignable causes. Control charts are used to monitor a process in order to detect assignable causes. Tagaras and Nikolaidis (2002) evaluated the economic performance of various adaptive control schemes to derive conclusions about their relative effectiveness They used the analysis that concentrated on Bayesian control charts for monitoring the process mean in finite production run. He included the statistical constraints upon the ED and showed that its economic properties are as good efficient as EDs, and its statistical properties are acceptable These constraints due to the designer needs, can be Type I error, power of the chart, adjusted average time to signal (AATS) and average number of false alarm (ANF). We proposed VSI multivariate Bayesian control chart and According to this sampling method, the performance of considered control improved.
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