Improved Curtailed Sampling Plans for np Control Charts

Abstract

The use of fully curtailed sampling in monitoring the proportion of nonconforming items is considered. In the usual np control chart with an upper control limit, complete sampling is used; that is, every item in a sample of size n is inspected and the process is declared to be out of control if m or more nonconforming items are found. Under full curtailment, it may not be necessary to sample and inspect all n items; sampling and inspection are halted if either m nonconforming or n – m + 1 conforming items are found. In the former case, the process is declared to be out of control; in the latter it is declared to be in control. In this article, economic criteria are used to select the values of n, m, and k (the inter-sample interval) that minimize the total expected cost of a given control procedure. Fully curtailed sampling is compared to both semi-curtailed (in which out-of-control is declared as soon as m nonconforming items are found) and complete sampling for over 175 combinations of cost coefficients and process parameters. The results indicate that full curtailment can yield substantial improvement in expected cost over both of the other sampling policies, especially when one considers the expected savings in absolute cost over an extended period of time.

• Average Sample Number
• Complete Sampling
• Control Limits
• Economic Design
• Expected Cost Model
• Nonconforming Product

Additional information

Notes on contributors

William W. Williams

Dr. Williams is an Associate Professor of Quantitative Business Analysis and Associate Dean for Graduate Studies. He is an Associate Member of ASQC.

Stephen W. Looney

Dr. Looney is an Associate Professor of Quantitative Business Analysis. He is an Associate Member of ASQC.

Michael H. Peters

Dr. Peters is a Professor of Quantitative Business Analysis. He is an Associate Member of ASQC.