Identifying the time of a step change in bivariate binomial processes

Abstract

Control charts are one of the most applicable tools in statistical process control. The time in which the control chart signals an out-of-control alarm is not the actual time in which the change has occurred. In other words, control chart detects the change with some delay. The actual time of the change taking place is referred to as change point. Change point estimation facilitates the identification of cause(s) of change and reduces the corresponding time and cost. There are many processes in which the control of two correlated attributes is necessary. Multiattribute control charts are used in such cases due to correlation between attributes. In this paper, two methods including maximum likelihood estimation (MLE) and clustering are proposed for estimating change point in nonconformity ratio vector of a process with bivariate binomial distribution. Also, the performances of these methods are evaluated and compared by Monte Carlo simulations.

Monitoring bivariate and trivariate mean vectors with a Shewhart chart

“…He, Wang, and Shang considered the EWMA chart based on the likelihood ratio test to control autocorrelated bivariate binomial data; shortly, the LR‐EWMA chart. Amiri, Allahyari, and Sogandi developed 2 change point estimators using the maximum likelihood estimation and clustering approaches to find the real time of a step change in bivariate binomial processes.…”

The S chart with variable charting statistic to control bi and trivariate processes

“…In many production lines, samples are regularly taken from the process with the purpose to obtain information about different quality characteristics of the products, which are used to calculate the plotting statistic of multivariate control charts. Signs of interest in bivariate control charts are acknowledged by numerous publications on this subject (Amiri, Allahyari, & Sogandi, 2015;Bersimis, Sachlas, & Castagliola, 2016;He, Wang, Tsung, & Shang, 2016;Ho & Costa, 2015;Leoni & Costa, 2017;Leoni, Machado, & Costa, 2015Melo, Ho, & Medeiros, 2016;Osei-Aning, Abbasi, & Riaz, 2017;Saghir, 2015;Saghir, Chakraborti, & Ahmad, 2017;Saghir, Khan, & Chakraborti, 2016;Simões, Leoni, Machado, & Costa, 2016;Tran, 2016;Yang, 2016).…”