Statistical Quality Control Charts Based on Hyper-Geometrically Distributed Data

Abstract

In some production and administrative processes, the occurrence of certain events is best described by a hyper-geometric distribution, which in turn should be pictorially depicted by what should be called a “hyper-geometric chart (Hg-chart)” in the field of Statistical Quality Control (SQC). However, this has never been the practice, since the existence of such a chart is absent; as such, prompting administrators and process engineers to make use of already existing charts for approximately depicting hyper-geometric processes. In this article, an SQC chart for any hyper-geometric process has been developed for the total number of events in a fixed number of units. This chart has been referred to as the Hg-chart. The center line (CC), lower control limit (LCL) and the upper control limit (UCL) have been obtained for the proposed chart with a sketch of how the proposed chart should be if used for simulation. It has been recommended that simulation should be used to test the proposed chart as this could prove to be more efficient and appropriate for describing hyper-geometric data rather than using an inappropriate chart to be an approximation for solving the problem.