Statistical Control Charts Based on a Geometric Distribution

TLDR

Certain events in production and administrative processes follow a geometric distribution. The authors develop control charts for total and average event counts and use simulations to show the impact of applying standard c‑ or u‑charts under a geometric model. Simulations show that a geometric‑distribution control chart cuts the false‑alarm rate from 9.6 % to 0.9 %, and two practical examples demonstrate its applicability.

Abstract

In some production processes and administrative processes, the occurrence of certain events is best described by a geometric distribution. Control charts are developed for the total number of events and for the average number of events in a fixed number of units. Computer simulation is used to demonstrate the consequences of applying a standard c-chart or u-chart when the geometric model is appropriate. In a simulated example, construction of a control chart based upon a geometric distribution reduces the false alarm rate from 9.6% to 0.9%. In conclusion, two examples illustrating the applicability of these charts are presented.