Economic and economic–statistical designs of VSI Bayesian control chart using Monte Carlo method and ABC algorithm

ABSTRACT

The usual practice in using a Bayesian control chart to monitor a process is done by taking samples from the process with fixed sampling intervals. Recent studies on traditional control charts have shown that variable sampling interval (VSI) scheme compared to classical scheme (fixed ratio sampling, FRS) helps practitioners to detect process shifts more quickly. In this paper, the effectiveness of VSI scheme on performance of Bayesian control chart has been studied, based on economic (ED) and economic–statistical designs (ESD). Monte Carlo method and artificial bee colony algorithm have been utilized to obtain optimal design parameters of Bayesian control chart (sample size, sampling intervals, warning limit and control limit) since the statistic of this approach does not have any specified distribution. Finally, VSI Bayesian control chart has been compared to FRS Bayesian and VSI X-bar approaches based on ED and ESD, separately. According to the results, it has been found that the performance of VSI Bayesian scheme is better than FRS Bayesian and VSI X-bar approaches.

KEYWORDS:

• Bayesian control chart
• economic design (ED)
• economic–statistical design (ESD)
• Monte Carlo method
• variable sampling interval (VSI)
• fixed ratio sampling (FRS)
• artificial bee colony (ABC) algorithm

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

The authors advise no direct funding is associated with the research reported in this article.