Monitoring the Process Mean and Variance Using Individual Observations and Variable Sampling Intervals

TLDR

The study investigates control chart strategies for detecting and diagnosing mean and variance shifts in a process using individual observations. The authors compare traditional X and moving‑range charts with EWMA charts of observations and squared deviations, and evaluate a variable‑sampling‑interval feature that adapts the sampling interval to the plotted statistics. EWMA‑based chart combinations detect small and moderate shifts faster and diagnose shift type as effectively as the X/MR pair, while adding the variable‑sampling‑interval feature substantially reduces the expected time to detect parameter shifts.

Abstract

In this paper we investigate control charts for monitoring a process to detect changes in the mean and/or variance of a normal quality variable when an individual observation is taken at each sampling point. The traditional X chart and moving range (MR) chart are evaluated. Also evaluated are the exponentially weighted moving average (EWMA) chart of the observations and the EWMA chart of the squared deviations of the observations from the target. It is shown that the combination of the X and MR charts will not detect small and moderate parameter shifts as fast as combinations involving the EWMA charts. The ability of charts to diagnose the type of parameter shift produced by a special cause is also investigated. It is shown that combinations involving the EWMA charts are just as effective at diagnosing the type of parameter shift as the traditional combination of the X and MR charts. The effect of adding the variable sampling interval (VSI) feature is also evaluated for some of the combinations of charts. The VSI feature allows the sampling interval to be varied as a function of the values of the statistics being plotted. It is shown that adding the VSI feature to the combinations of charts results in very substantial reductions in the expected time required to detect shifts in process parameters.