Variable interval sampling in economical designs for online process control of attributes with misclassification errors

• Published in: The Journal of the Operational Research Society Vol. 62; no. 7; pp. 1365 - 1375
• Main Authors: Bessegato, L, Quinino, R, Ho, L L, Duczmal, L
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 01.07.2011; Palgrave Macmillan; Palgrave Macmillan UK; Taylor & Francis Ltd
• Subjects: Applications; Applied sciences; Average cost; Business and Management; Capital costs; Cost estimates; Economic costs; economical design; Error rates; Exact sciences and technology; Inventory control, production control. Distribution; Management; Markov analysis; Markov chain; Markov chains; Mathematics; Mechanical engineering. Machine design; misclassification errors; Musical intervals; online process control for attributes; Operational research and scientific management; Operational research. Management science; Operations research; Operations Research/Decision Theory; Probability; Probability and statistics; Process control; Process controls; quality control; Random variables; Reliability, life testing, quality control; Sampling; Sciences and techniques of general use; Statistics; Studies; Theoretical Paper; Theoretical Papers; Transition probabilities; variable inspection interval; Markov chain; misclassification errors; quality control; economical design; online process control for attributes; variable inspection interval; Process planning; Process control; Average cost; Sampling design; Interval arithmetic; Optimization; Engineering design; Production management; Design process; Classification; Quality control; Interval matrix; Sampling
• ISSN: 0160-5682; 1476-9360
• DOI: 10.1057/jors.2010.79

Online process control consists of inspecting a single item at every mth items produced, where m is an integer greater than two. Based on the results of the inspection, one decides if the process is in-control (the fraction of conforming item is p 1 -state I) or out-of-control (the fraction of conforming item is p 2 -state II). If the inspected item is non-conforming, the process is designated as out-of-control and production is stopped for possible adjustment; otherwise, production goes on. In this paper, a contribution to online process control is presented, where the inspection system is considered to be subject to classification errors. After every adjustment, the sampling interval is L units (L⩾m), and in the case of non-adjustment, the sampling interval is m units. The expression for the average cost per produced item is calculated, and optimum parameters (the sampling intervals L and m) are obtained by a direct search. The procedure is illustrated by a numerical example.