On-Line Process Control using Attributes with Misclassification Errors: An Economical Design for Short-Run Production

• Published in: Communications in statistics. Theory and methods Vol. 41; no. 10; pp. 1813 - 1832
• Main Authors: Bessegato, Lupércio F., Quinino, Roberto C., Duczmal, Luiz H., Lee Ho, Linda
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 15.05.2012; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Applications; Combinatorics; Combinatorics. Ordered structures; Control charts; Designs and configurations; Economic design; Exact sciences and technology; Experimental design; General topics; Insurance, economics, finance; Markov analysis; Markov chain; Mathematics; Misclassification errors; On-line process control using attributes; Probability and statistics; Process controls; Sciences and techniques of general use; Short-run production; Statistics; 60J10; 60J20; 62P30; Process control; Control system; Average cost; Misclassification error; Stochastic method; Economic sciences; Markov chain; Statistical method; Integer; Short-run production; On-line process control using attributes; Experimental design; Probabilistic model; 60J05; Economic design; Misclassification errors; Sampling; Econometrics; Production process
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2010.551451

On-line process control consists of inspecting a single item for every m (integer and m ≥ 2) produced items. Based on the results of the inspection, it is decided whether the process is in-control (the fraction of conforming items is p 1 ; State I) or out-of-control (the fraction of conforming items is p 2  < p 1 ; State II). If the inspected item is non conforming, it is determined that the process is out-of-control, and the production process is stopped for an adjustment; otherwise, production continues. As most designs of on-line process control assume a long-run production, this study can be viewed as an extension because it is concerned with short-run production and the decision regarding the process is subject to misclassification errors. The probabilistic model of the control system employs properties of an ergodic Markov chain to obtain the expression of the average cost of the system per unit produced, which can be minimised as a function of the sampling interval, m. The procedure is illustrated by a numerical example.