A Quantitative Approach for Detection of Unstable Processes Using a Run Chart

Abstract

Nearly all process data have a time variable, representing the time each data point is measured. A process can be said stable if the parameter(s) of the distribution of a process/product characteristic remain constant over time and there is no autocorrelation. Only a stable process has the ability to perform in a predictable manner over time. Statistical analysis of process data usually assume that these data are obtained from stable processes. In the absence of control charts, the hypothesis of process stability is usually assessed by visually examining the pattern in the run chart. In this paper, a measure for process stability called process stability indicator (PSI) is proposed based on two shape features of run chart pattern, using which an unstable process can be detected objectively from the run chart of considerably shorter length. Important properties of PSI are derived and cutoff values of PSI for run charts of different lengths are determined. The effectiveness of the proposed approach is evaluated and compared with the existing quantitative approaches using simulated data. The results show that the proposed PSI method, in general, results in much better performance than the other approaches. But it is relatively less effective in detection of the unstable process conditions that leads to cyclic pattern.