Cumulative probability control charts for geometric and exponential process characteristics

Abstract

A statistical process control chart called the cumulative probability control chart (CPC-chart) is proposed. The CPC-chart is motivated from two existing statistical control charts, the cumulative count control chart (CCC-chart) and the cumulative quantity control chart (CQC-chart). The CCC- and CQC-charts are effective in monitoring production processes when the defect rate is low and the traditional p- and c-charts do not perform well. In a CPC-chart, the cumulative probability of the geometric or exponential random variable is plotted against the sample number, and hence the actual cumulative probability is indicated on the charts, Apart from maintaining all the favorable features of the CCC- and CQC-charts, the CPC-chart is more flexible and it can resolve a technical plotting inconvenience of the CCC- and CQC-charts.