SHORT RUNS MULTIVARIATE CONTROL CHART FOR PROCESS DISPERSION

Abstract

The multivariate Hotelling's T2 control chart is designed to be used in a mass production for processes where data to estimate the mean vector and covariance matrix as well as the computation of control limits are available before a production run. Recent years have seen a trend in manufacturing industries to produce smaller lot sizes, a.k.a., low volume production which is a result of increased importance given to just-in-time (JIT) manufacturing techniques, synchronous manufacturing and the reduction of in-process inventory and costs. This new manufacturing environment is also referred to as short runs production or short runs. In a short runs environment, it is difficult or perhaps impossible to establish a reliable historical data set in setting valid control limits and in estimating process parameters due to the availability of insufficient data for a particular process because production runs are usually short and change frequently from one process to another. There is also a need to start charting at or very near the beginning of the run in such a case. Another problem encountered in a short runs production such as in job shops is that there are many different types of measurements so that many different control charts are needed. Standardized control charts that allow different statistics to be plotted on the same chart are extremely useful in short runs. Control charts with standard scale simplify the control charting process in a short runs environment. In this paper, we address the multivariate short runs problems for process dispersion based on individual measurements by presenting the required formulas so that the chart can be used from the start of production, whether or not prior information for estimating the chart's limit and its parameter is available. The proposed chart plots standardized statistics for multiple parts on the same chart. This paper extends the work of the authors in Ref. 13.