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Inspection allocation for multistage deteriorating production systems

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IIE Transactions

Abstract

The paper deals with the layout and operation of an inspection system used for detecting malfunctioning processors in a multistage production system. This problem involves three inter-related decisions: (i) the overall inspection capacity; (ii) the assignment of inspection tasks to inspectors; and (iii) the scheduling of the inspector's tasks. These decisions require a trade-off between the cost of inspectors and the loss associated with non-conforming products. A hierarchical heuristic solution procedure is proposed to support these three related decisions. Numerical experiments demonstrate the performance of the heuristic, showing that solution criteria are very close to their lower bounds. Although we use production terminology, the results might be applicable to any organization, which inspects and maintains a variety of characteristics of its branches or activities.

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References

  • Ballou, D.P. and Pazer, H.L. (1982) The impact of inspection fallibility on the inspection policy in serial production systems. Management Science, 28, 387–399.

    Google Scholar 

  • Barad, M. and Braha, D. (1996) Control limits for multi-stage manufacturing processes with binomial yield (single and multiple production runs). Journal of the Operational Research Society, 47(1), 98–112.

    Google Scholar 

  • Barker, T.B. (1986) Quality engineering by design: Taguchi's philosophy. Quality Progress, 32–42.

  • Bazaraa, M.S. and Shetty, C.M. (1979) Nonlinear Programming Theory and Algorithms, John Wiley, New York, NY.

    Google Scholar 

  • Beightler, C.C. and Mitten, L.G. (1964) Design of an optimal sequence of interrelated sampling plans. Journal of the American Statistical Association, 59, 96–104.

    Google Scholar 

  • Britney, R. (1972) Optimal screening plans for nonserial production systems. Management Science, 18, 550–559.

    Google Scholar 

  • Brown, E.C. (1968) Some mathematical models of inspection along a production line. Technical report no. 36, Operations Research Center, MIT, Cambridge, MA.

    Google Scholar 

  • Buzacott, J.A. and Shanthikumar, J.G. (1993) Stochastic Models of Manufacturing Systems, Prentice Hall, New York, NY.

    Google Scholar 

  • Coffman, E.G. Jr., Lueker, G.S. and Rinnooy Kan, A.H.G. (1988) Asymptotic methods in the probabilistic analysis of sequencing and packing heuristics. Management Science, 34, 266–290.

    Google Scholar 

  • Deliman, N.C. and Feldman, R.M. (1996) Optimization of process improvement and inspection location for serial manufacturing. International Journal of Production Research, 34, 395–405.

    Google Scholar 

  • Dietrich, D.L. (1971) A Bayesian quality assurance model for a multistage production process, in ASQC Technical Conference Transactions, pp. 338–348.

  • Do, S.B. and Hyung, J.Y. (1996) Optimal allocation of inspection effort in a serial multi-stage production system. Computers and Industrial Engineering, 30(3), 387–396.

    Google Scholar 

  • Dorris, A.L. and Foote, B.L. (1978) Inspectors errors and statistical quality control: a survey. American Institute of Industrial Engineers Transactions, 10, 148.

    Google Scholar 

  • Eppen, G. and Hurst, E. (1974) Optimal location of inspection stations in multistage production process. Management Science, 20, 1194–1200.

    Google Scholar 

  • Ercan, S.S. (1972) Systems approach to the multistage manufacturing connected unit situation. Naval Research Logistics Quarterly, 19, 493–500.

    Google Scholar 

  • Garey, M.R. (1971) Optimal test point selection for sequential manufacturing processes. Bell System Technical Journal, 51, 291–300.

    Google Scholar 

  • Hurst, E.G. Jr. (1973) Imperfect inspection in multistage production processes. Management Science, 20, 378–384.

    Google Scholar 

  • Lee, H.L. and Rosenblatt, M.J. (1987) Simultaneous determination of production cycle and inspection schedules in a production system.Management Science, 33(9), 1125–1136.

    Google Scholar 

  • Lee, H.L. and Rosenblatt, M.J. (1989) A production and maintenance planning model with restoration cost dependent on detection delay.IIETransactions, 21(4), 368–375.

    Google Scholar 

  • Lee, H.L. and Yano, C.A. (1988) Production control for multi-stage systems with variable yield losses. Operations Research, 36, 269–278.

    Google Scholar 

  • Lee, J.S. and Park, K.S. (1991) Joint determination of production cycle and inspection intervals in a deteriorating production system.Journal of the Operational Research Society, 42(9), 775–783.

    Google Scholar 

  • Lin, T.M., Tseng, S.T. and Liou, M.J. (1991) Optimal inspection schedule in the imperfect production system under general shift distribution. Journal of the Chinese Institute of Industrial Engineers, 8(2), 73–81.

    Google Scholar 

  • Lindsay, G.F. and Bishop, A.B. (1964) Allocation of screening inspection effort - a dynamic programming approach. Management Science, 10, 342–352.

    Google Scholar 

  • Makis, V. (1998) Optimal lot sizing and inspection policy for an EMQ model with imperfect inspection. Naval Research Logistics, 45, 165–186.

    Google Scholar 

  • Menipaz, E. (1978) A taxonomy of economically based quality control procedures. International Journal of Production Research, 16(2), 153–167.

    Google Scholar 

  • Peters, M.H. and Williams, W.W. (1984) Location of quality inspection stations: an experimental assessment of five normative rules.Decision Sciences, 15, 389–408.

    Google Scholar 

  • Pruzan, P.M. and Jackson, J.T.R. (1967) A dynamic programming application in production line inspection. Technometrics, 9, 73–81.

    Google Scholar 

  • Rabinowitz, G. and Emmons, H. (1997) Optimal and heuristic inspection schedules for multistage production systems. IIETransactions, 29(12), 1063–1071.

    Google Scholar 

  • Rabinowitz, G. and Yahalom, O. (2001) Imperfect inspection of a multi-attribute deteriorating production system - a continuous time model. Quality and Reliability Engineering International 17, 1–12.

    Google Scholar 

  • Rahim, M.A. (1994) Joint determination of production quality, inspection schedule and control chart design. IIETransactions, 26(6), 2–11.

    Google Scholar 

  • Rahim, M.A. and Banerjee, P.K. (1993) A generalized model for the economic design of _xx control chart for production systems with increasing failure rate and early replacement. Naval Research Logistics, 40, 787–809.

    Google Scholar 

  • Raz, T. (1986) A survey of models for allocating of inspection effort in multistage production systems. Journal of Quality Technology, 18(4), 239–247.

    Google Scholar 

  • Raz, T. and Kaspi, M. (1991) Location and sequencing of imperfect inspection operations in serial multi-stage production systems.International Journal of Production Research, 29(8), 1645–1659.

    Google Scholar 

  • Rosenblatt, M.J. and Lee, H.L. (1986a) A comparative study of continuous and periodic inspection policies in deteriorating production systems. IIETransact ions, 18, 2–9.

    Google Scholar 

  • Rosenblatt, M.J. and Lee, H.L. (1986b) Economic production cycles with imperfect production process. IIETransactions, 18, 48–55.

    Google Scholar 

  • Ruey, Y.Y. (1997) Optimal inspection and replacement policies for multi-state deteriorating systems. European Journal of Operational Research, 96(2), 248–259.

    Google Scholar 

  • Seog, J.C., Park, Y.H. and Park, E.H. (1996) Quality costs in multistage manufacturing systems. Computers and Industrial Engineering, 31(1-2), 115–118.

    Google Scholar 

  • Trippi, R.R. (1975) The warehouse location formulation as a special type of inspection problem. Management Science, 986–988.

  • Tseng, S.T. (1996) Optimal preventive maintenance policy for deteriorating production systems. IIETransactions, 28, 687–694.

    Google Scholar 

  • Wein, A.S. (1992) Random yield rework and scrap in a multi-stage batch manufacturing environment. Operations Research, 40, 551–563.

    Google Scholar 

  • White, L.S. (1966) The analysis of a single class of multistage inspection plans. Management Science, 21, 685–693.

    Google Scholar 

  • White, L.S. (1969) Shortest route models for the allocation of inspection efforts on a production line. Management Science, 15, 249–259.

    Google Scholar 

  • Woo, W.K. and Metcalfe, T.E. (1972) Optimal allocation of inspection effort in multistage manufacturing processes. Western Electric Engineer, 16, 8–16.

    Google Scholar 

  • Yum, B.J. and McDowell, E.D. (1981) The optimal allocation of inspection effort in a class of nonserial production systems. IIE Transactions, 13, 285–293.

    Google Scholar 

  • Yum, B.J. and McDowell, E.D. (1987) Optimal inspection policies in a serial production system Including scrap rework and repair: an MILP approach. International Journal of Production Research, 25(10), 1451–1464

    Google Scholar 

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Emmons, H., Rabinowitz, G. Inspection allocation for multistage deteriorating production systems. IIE Transactions 34, 1031–1041 (2002). https://doi.org/10.1023/A:1019658111999

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