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Stability Index of Stochastic Processes: The Statistical Process Control Approach

Abstract The article addresses the stability index of stochastic processes (time series) based on the statistical process control approach. The proposed stability index reveals the relation between assignable and common variabilities: the higher the proportion of the assignable variability, the lower the stability. It is calculated as a ratio of the average moving range to the maximum range between the time series mean and the means of the samples with the fixed end. To address sensitivity of the stability index to process changes such as mean and variance shifts, trends, seasonality, autocorrelation, and sudden changes (outliers), hundred of thousands of simulated time series are analyzed. Considering the impact of sample size, amplitude of process change, moment of process change, and type of distribution, the full factorial design of experiment has been applied. The proposed calculation of the stability index and suggested target levels serve as a guide for interpreting stability of the stochastic processes by index. A combination of stability and capability indexes emphasizes dynamic aspects of the process ability regarding specifications and are presented as a dynamic capability index.