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Diagnostic errors and repetitive sequential classifications in on-line process control by attributes

Author

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  • Costa Quinino, Roberto da
  • Colin, Emerson C.
  • Ho, Linda Lee

Abstract

The procedure of on-line process control by attributes, known as Taguchi's on-line process control, consists of inspecting the mth item (a single item) at every m produced items and deciding, at each inspection, whether the fraction of conforming items was reduced or not. If the inspected item is non-conforming, the production is stopped for adjustment. As the inspection system can be subject to diagnosis errors, one develops a probabilistic model that classifies repeatedly the examined item until a conforming or b non-conforming classification is observed. The first event that occurs (a conforming classifications or b non-conforming classifications) determines the final classification of the examined item. Proprieties of an ergodic Markov chain were used to get the expression of average cost of the system of control, which can be optimized by three parameters: the sampling interval of the inspections (m); the number of repeated conforming classifications (a); and the number of repeated non-conforming classifications (b). The optimum design is compared with two alternative approaches: the first one consists of a simple preventive policy. The production system is adjusted at every n produced items (no inspection is performed). The second classifies the examined item repeatedly r (fixed) times and considers it conforming if most classification results are conforming. Results indicate that the current proposal performs better than the procedure that fixes the number of repeated classifications and classifies the examined item as conforming if most classifications were conforming. On the other hand, the preventive policy can be averagely the most economical alternative rather than those ones that require inspection depending on the degree of errors and costs. A numerical example illustrates the proposed procedure.

Suggested Citation

  • Costa Quinino, Roberto da & Colin, Emerson C. & Ho, Linda Lee, 2010. "Diagnostic errors and repetitive sequential classifications in on-line process control by attributes," European Journal of Operational Research, Elsevier, vol. 201(1), pages 231-238, February.
  • Handle: RePEc:eee:ejores:v:201:y:2010:i:1:p:231-238
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    References listed on IDEAS

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    1. Bersimis, Sotiris & Koutras, Markos V. & Maravelakis, Petros E., 2014. "A compound control chart for monitoring and controlling high quality processes," European Journal of Operational Research, Elsevier, vol. 233(3), pages 595-603.
    2. Ho, Linda Lee & Quinino, Roberto C., 2012. "Integrating on-line process control and imperfect corrective maintenance: An economical design," European Journal of Operational Research, Elsevier, vol. 222(2), pages 253-262.
    3. L Bessegato & R Quinino & L L Ho & L Duczmal, 2011. "Variable interval sampling in economical designs for online process control of attributes with misclassification errors," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1365-1375, July.

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