Improving the Performance of Bi-Variate EWMA Control Charts Using Bayesian Approach

In many situations, the quality of a process can be characterized by a single continuous random variable, which is usually assumed to follow a normal distribution. However, it is increasingly common for processes to be characterized by several, usually correlated, variables. (Kim and Reynolds 2005)Multivariate control charts are widely used to monitor industrial processes (Mason, et al. 1995). As the objective of performing multivariate statistical process control is to monitor the process over time, in order to detect any unusual events allowing quality and process improvement, it is essential to track the cause of an out-of-control signal. However, as opposed to univariate control charts, the complexity of multivariate control charts and the cross-correlation among variables make it difficult for analysis of assignable causes to the out-of-control signal. This is the basis for extensive research performed in the field of multivariate control chart since the 1940’s, when Hotteling (1947) recognized that the quality of a product might depend on several correlated characteristics. However, because of computational complexity, researchers and practitioners did not pursue the multivariate quality control at that time. Now that the development of high-speed computers, the technological advances in industrial control procedures, and the availability of modern data-acquisition equipments have alleviated this problem, many researchers have proposed several multivariate control charts, where each has advantages as well as disadvantages (Montgomery 2005). Most work on multivariate control charts has concentrated on the problem of monitoring the process mean µ. Multivariate control charts of the Shewhart type were first developed by Hotelling (1947). Multivariate Exponential Weighted Moving Average (MEWMA) Charts have been also discussed by Mohebbi and Lakhbir 1989, Ryan 2000, Wade and Woodall 1993, Crowder 1989, Lowry et al. 1992, Lucas and Saccucci 1990, Prabhu and Runger 1997, Doganaksoy et al. 1991, and Marion and Young 2006.