Shahed University
DESIGNING A RUN SUM CONTROL CHART FOR MONITORING MULTIVARIATE COEFFICIENT OF VARIATION IN THE PRESENCE OF MEASUREMENT ERRORS
Amirhossein Amiri | Hemmati M. | jalilibal Z.
URL :
http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=169863
Date :
2022/10/09
Publish in :
مهندسي صنايع و مديريت شريف - شريف سابق
Link :
http://sjie.journals.sharif.edu/article_22722.html?lang=fa
Keywords :
Control chart; monitoring coefficient of variation; measurement errors; multivariate coefficient of variation; markov chain
Abstract :
Most Shewhart control charts are designed to monitor changes in the mean or variance of the process. There are some situations when the process mean fluctuates from time to time, but is still considered as in-control and the process standard deviation is a linear function of the process mean. In addition, in some cases, the mean and the variance of the process are actually dependent on each other. Also, in many processes, monitoring the mean or variance of the process is unreasonable due to the nature of the process, and it is recommended that the coefficient of variation be used to monitor the process. Although monitoring multivariate coefficient of variation was studied at both Phases I and II, the design of chart for monitoring multivariate CV considering measurement errors was not thoroughly studied in previous studies; hence, it has been considered in this research. In this paper, a run sum control chart is developed for monitoring multivariate coefficient of variation in the presence of measurement errors at Phase II and the performance of the proposed chart with and without the assumption of measurement errors was compared through Average Run Length (ARL) criterion based on Markov chain approach. The results show that the presence of measurement errors has a negative effect on the performance of the run sum control chart. In other words, ARL of the run sum chart in the presence of measurement errors gets far away from the corresponding value without measurement errors as the magnitude of measurement errors increases. This research considers multiple measurements approach to reduce the effect of measurement errors on the performance of control charts in monitoring the multivariate coefficient of variation at Phase II. The results of the proposed charts performance show that ARL decreases in the presence of measurement errors due to increasing the effect of measurement errors on the performance of control chart. The results show that by using the multiple measurements approach, the results become closer to the case without measurement errors.
Authors' Home page
Amirhossein Amiri