Control Charts for Multivariate Processes Based on Influence Functions

Abstract

Every product possesses a number of elements that jointly describes its fitness for use. These parameters are called quality characteristics and generally p quality characteristics are necessary for an adequate description of each item quality. Because of the inherent variability of a process, these quality characteristics are random variables. There are many causes of variability, but in statistical process control is useful to think of variability as arising from two sources. First, there are random causes and second there are assignables causes. When assignable causes are present in a multivariate process they may affect different process parameters: the process mean, and/or orientation and/or variability. Special causes that affect one of these parameters do not necessarily effect the others. Therefore control charts for different situations are necessary. This paper deals with on-line methods for quality improvement where the influence function is used to build up control charts to monitor process variability and orientation. Our aim is to quickly detect the time when special causes are present in a manufacturing process, so investigation of the process and corrective actions may be undertaken before very many noconforming units are produced. Our idea is, that subgroups taken when special causes are present in the process, tend to have an unduly large influence on process parameter estimators. Therefore the influence function can be used to tailor control charts for different parameters. In section 2 we derive the influence measures to monitor process dispersion and orientation. Shewhart control charts for process variability and process orientation are given in section 3. In section 4 we give a numerical example to illustrate our control charts.