The Probability of a Type I Error and the Power to Detect a Single Slippage for the Upper Limit Control Chart for Number of Defects

Abstract

A procedure for testing an industrial process for control with respect to defects-per-unit is to compare the number of defects observed in each of k samples with an upper control limit. The control limit is calculated using a multiplier of the standard deviation which may be different than the multiplier three, which is usually used for control charts. Using the variation in the probability of a type I error and power for different values of the multiplier and k, procedures are described to increase the effectiveness of the control chart for number of defects.

• a-Sigma Limit Control Chart
• Single Slippage Probabilities
• Upper Bounds for Type I Error
• Upper Limit Control Chart

Additional information

Notes on contributors

Edmund B. McCue

Edmund B. McCue is Associate Professor in the Department of Mathematics, Statistics and Computer Science at The American University, Washington, D.C.