Design of Rectifying Screening Inspections under a Bivariate Normal Distribution

이변량 정규분포 하에서 선별형 스크리닝 검사의 설계

  • Hong, Sung-Hoon (Department of Industrial & Information Systems Engineering, Chonbuk National University) ;
  • Choi, Ik-Jun (Department of Industrial & Information Systems Engineering, Chonbuk National University) ;
  • Lee, Yoon-Dong (Applied Statistics, Konkuk University) ;
  • Lee, Min-Koo (Department of Information and Statistics, Chungnam National University) ;
  • Kwon, Hyuck-Moo (Department of Systems and Management Engineering, Pukyong National University)
  • 홍성훈 (전북대학교 산업정보시스템공학과) ;
  • 최익준 (전북대학교 산업정보시스템공학과) ;
  • 이윤동 (건국대학교 응용통계학과) ;
  • 이민구 (충남대학교 정보통계학과) ;
  • 권혁무 (부경대학교 시스템경영공학과)
  • Published : 2007.12.31

Abstract

Owing to the rapid growth in automated manufacturing systems, screening inspection becomes an attractive practice for removing nonconforming items, and it has been suggested that inspection will essentially become an inherent part of modem manufacturing processes. In this paper, we propose rectifying screening inspections which allow quality practitioners to use performance and surrogate variables interchangeably in real-time applications. Two screening inspections are considered; a statistically-based screening inspection to reduce the current proportion of nonconforming items to a specified AOQ(average outgoing quality) after screening, and an economically-based screening inspection where the tolerance limit is determined so that the expected total cost is minimized. It is assumed that the performance variable and the surrogate variable are jointly normally distributed. For two screening inspections, methods of finding the optimal solutions are presented and numerical examples are also given.

Keywords

References

  1. Bai, D.S. and Kwon, H.M. (1995), 'Economic Design of a Two-Stage Screening Procedure with a Prescribed Outgoing Quality', Metrika, Vol. 42(1), pp, 1-18 https://doi.org/10.1007/BF01894285
  2. Bai, D.S., Kwon, H.M, and Lee, M.K.(1995), 'An Economic Two-Stage Screening Procedure with a Prescribed Outgoing Quality in Logistic and Normal Models', Naval Research Logistics, Vol. 42, pp. 1081-1097 https://doi.org/10.1002/1520-6750(199510)42:7<1081::AID-NAV3220420707>3.0.CO;2-X
  3. Bisgaard, S., Hunter, W.G., and Pallesen, L. (1984), 'Economic Selection of Quality of Manufactured Product', Technometrics, Vol. 26, pp. 9-18 https://doi.org/10.2307/1268411
  4. Boys, R.J. and Dunsmore, I.R.(1987), 'Diagonostic and Sampling Models in Screening', Biometrika, Vol. 74, pp. 356-374
  5. Cho, B.R. and Govindaluri, M.S. (2002), 'Optimal Screening Limits in Multi-Stage Assemblies' International Journal of Production Research, Vol: 40, pp. 1993-2009 https://doi.org/10.1080/0020754210122266
  6. Cho, B.R., Kim Y.J., Kimbler, D.L., and Phillips, M.D. (2000), 'An Integrated Joint Optimization Procedure for Robust and Tolerance Design', International Journal of Production Research, Vol. 38, pp, 2309-2325 https://doi.org/10.1080/00207540050028115
  7. Drezner, Z. and Wesolowsky, G.O.(1995), 'Multivariate Screening Procedures for Quality Cost Minimization, IIE Transactions, Vol. 27, pp. 300-304 https://doi.org/10.1080/07408179508936744
  8. Duffuaa, S.O. and Al-Najjar, H,J.(1995), 'An Optimal Complete Inspection Plan for Critical Multicharacteristic Components', Journal of Operational Research Society. Vol. 46, pp, 930-942 https://doi.org/10.2307/3009905
  9. Govindaluri, M.S., Shin, S., and Cho, B.R (2004), 'Tolerance optimization Using the Lambert W Function: An Empirical Approach', International Journal of Production Research, Vol. 42, pp, 3235-3251 https://doi.org/10.1080/00207540410001696311
  10. Hong, S.H., (2006), 'Design of Rectifying Screening Procedures Using a Surrogate Variable', Journal of the Korean Institute of Industrial Engineers, Vol. 32, pp, 51-60
  11. Hong, S.H. and Cho, B.R. (2007), 'Joint Optimization of Process Target Mean and Tolerance Limits with Measurement Errors under Multi-Decision Alternatives', European Journal of Operational Research, Vol. 183, pp, 327-335 https://doi.org/10.1016/j.ejor.2006.09.063
  12. Hong, S.H. and Elsayed, E.A.(1998), 'Economic Complete Inspections with Multi-Decision Alternatives', International Journal of Production Research, Vol. 36, pp. 3367-3378 https://doi.org/10.1080/002075498192102
  13. Hong, S.H., Kim, S.B., Kwon, H.M., and Lee, M.K. (1998), 'Economic Design of Screening Procedures When the Rejected Items Are Reprocessed', European Journal of Operational Research Vol. 108, pp. 65-73 https://doi.org/10.1016/S0377-2217(97)00204-X
  14. Hong, S.H., Kwon, H.M., Lee, M.K., and Cho, B.R. (2006), 'Joint Optimization in Process Target and Tolerance Limit for L-Type Quality Characteristic, International Journal of Production Research, Vol. 44, pp. 3051-3060 https://doi.org/10.1080/00207540500478736
  15. Hong, S.H., Lee, M.K., Kwon, H.M, and Kim, S.B. (2001), 'A Continuous Screening Procedure Using the Performance and Surrogate Variables', International Journal of Production Research Vol. 39, pp, 2333-2340 https://doi.org/10.1080/00207540110040439
  16. Kim, C.T., Tang, K., and Peters, M. (1994), 'Design of a Two-Stage Procedure for Three-Class Screening', European Journal of Operational Research Vol. 79(3), pp, 431-442 https://doi.org/10.1016/0377-2217(94)90057-4
  17. Kwon, H.M, Hong, S.H., Lee, M.K., and Kim, S.B. (2001), 'A Process Monitoring Procedure Based on a Surrogate Variable for Dichotomous Performance Variable', IIE Transactions, Vol. 33, pp. 1129-1133
  18. Lee, J. and Kwon, W.J.(1999), 'Economic Design of a Two-Stage Control Chart based on Both Performance and Surrogate Variables', Naval Research Logistics, Vol 46, pp. 958-977 https://doi.org/10.1002/(SICI)1520-6750(199912)46:8<958::AID-NAV6>3.0.CO;2-I
  19. Lee, M.K. and Elsayed, E.A. (2002), 'Process Mean and Screening Limits for Filling Processes under Two-Stage Screening Procedure', European Journal of Operational Research Vol. 138(2), pp. 118-126 https://doi.org/10.1016/S0377-2217(01)00128-X
  20. Lee, M.K., Hong, S.H., and Elsayed, E.A. (2001), 'The Optimum Target Value under Single and Two-Stage Screenings', Journal of Quality Technology Vol. 33(4), pp, 506-514 https://doi.org/10.1080/00224065.2001.11980108
  21. Lee, M.K., Kwon, H.M., Hong, S.H., and Kim, Y.J. (2007), 'Determination of the Optimum Target Value for a Production Process with Multiple Products', International Journal of Production Economics, Vol. 107, pp. 173-178 https://doi.org/10.1016/j.ijpe.2006.08.007
  22. Lee, M.K., Kwon, H.M., Hong, S.H., and Ha, J.W.,(2006), 'Economic Selection of Sub-process Mean Values for a Mixture Production Process', International Journal of Production Research, Vol. 44, pp.4367-4376 https://doi.org/10.1080/00207540600597112
  23. Li, L. and Owen, D.B. (1979), 'Two-Sided Screening Procedures in the Bivariate Case', Technometrics Vol. 21, pp. 79-85 https://doi.org/10.2307/1268583
  24. Owen, D.B., McIntire, D,. and Seymour, E. (1975), 'Tables Using One or Two Screening Variables to Increase Acceptable Product Under One-Sided Specifications', Journal of Quality Technology Vol. 7pp. 127-138 https://doi.org/10.1080/00224065.1975.11980683
  25. Moskowitz, H., Plante, R., and Duffy, J.(2001), 'Multivariate Tolerance Design Using Quality Loss', IIE Transactions Vol. 33, pp, 437-448
  26. Plante, R. (2002), 'Multivariate Tolerance Design for a Quadratic Design Parameter Model,' IIE Transactions Vol. 34, pp. 565-571
  27. Tang, K (1987), 'Economic Design of a One-Sided Screening Procedure Using a Correlated Variable', Technometrics Vol. 29, pp. 477-485 https://doi.org/10.2307/1269460
  28. Tang, K. (1988a), 'Economic Design of Product Specifications for a Complete Inspection Plan', International Journal of Production Research, Vol. 26, pp, 203-217 https://doi.org/10.1080/00207548808947854
  29. Tang, K (1988b), 'Design of a Two-Stage Screening Procedure Using Correlated Variables: A Loss Function Approach', Naval Research Logistics Vol. 35, pp. 513-533 https://doi.org/10.1002/1520-6750(198810)35:5<513::AID-NAV3220350514>3.0.CO;2-7
  30. Turkman, K.F. and Turkman, M.A.A.(1989), 'Optimal Screening Methods', Journal of the Royal Statistical Society Series B, Vol. 51, pp. 287-295
  31. Wong, A., Meeker, J.B., and Selwyn, M.R. (1985), 'Screening on Correlated Variables: A Bayesian Approach', Technometrics Vol. 27, pp, 423-431 https://doi.org/10.2307/1270209