Economic Selection of Optimum Process Mean for a Mixture Production Process

혼합물 생산공정의 최적 공정평균의 경제적 선정

  • Lee, Min-Koo (Department of Information and Statistics, Chungnam National University)
  • 이민구 (충남대학교 정보통계학과)
  • Published : 2005.12.31

Abstract

This paper considers the problem of optimally choosing the sub-process means of a mixture production process where two important ingredients are mixed. The quantity of each ingredient is controlled through each corresponding sub-process. The values of the sub-process mean directly affect the defective rate, production, scrap and reprocessing costs for the mixture production process. After inspecting every incoming item, each conforming item is sold in a regular market for a fixed price and any nonconforming item is scraped. A model is constructed on the basis of the selling price, production, inspection, and scrap and reprocessing costs. The goal is to determine the optimum sub-process mean values based on maximizing expected profit function relating selling price and cost components. A method of finding the optimum sub-process means is presented when the quantities of the two ingredients are assumed to be normally distributed with known variances. A numerical example is given and numerical studies are performed.

Keywords

References

  1. Arcelus, F. J. and Rahim, M. A.(1994), 'Simultaneous Economic Selection of a Variables and an Attribute Target Mean', Journal of Quality Technology, Vol. 26, No. 2, pp. 125-133
  2. Bai, D. S. and Lee, M. K.(1993), 'Optimal Target Values for a Filling Process When Inspection is Based on a Correlated Variable', International Journal of Production Economics, Vol. 32, pp. 327-334 https://doi.org/10.1016/0925-5273(93)90046-N
  3. Boucher, T. O. and Jafari, M. A.(1991), 'The Optimum Target Value for Single Filling Operations with Quality Sampling Plans', Journal of Quality Technology, Vol. 23, No. 1, pp. 44-47
  4. Carlsson, O.(1984), 'Determining the Most Profitable Process Level for a Production Process Under Different Sales Conditions', Journal of Quality Technology, Vol. 16, No. 1, pp. 44-49
  5. Golhar, D. Y.(1987), 'Determination of the Best Mean Contents for a Canning Problem', Journal of Quality Technology, Vol. 19, No.2, pp. 82-84
  6. Golhar, D. Y. and Pollock, S. M.(1988), 'The Determination of the Best Mean and the Upper Limit for a Canning Problem', Journal of Quality Technology, Vol. 20, No. 4, pp. 188-192
  7. Hong, S. H., Kwon, H. M., Lee, M. K. and Kim, S. B.(2001), 'A Continuous Screening Procedure Using the Performance and Surrogate Variables', International Journal of Production Research, Vol. 39, No. 11, pp. 2333-2340 https://doi.org/10.1080/00207540110040439
  8. Hunter, W. G. and Kartha, C. D.(1977), 'Determining the Most Profitable Target Value for a Production Process', Journal of Quality Technology, Vol. 9, No.4, pp. 176-181
  9. Lee, M. K.(2000), 'Determination of Optimum Process Mean and Screening Limit for a Production Process Based on Two Correlated Variables', Journal of the Korean Society for Quality Management, Vol. 28, No. 2, pp. 155-164
  10. 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, pp. 118-126 https://doi.org/10.1016/S0377-2217(01)00128-X
  11. Lee, M. K, Kwon, H. M., Hong, S. H. and Kim, S. B.(2004), 'Economic Selection of Mean Value for a Filling Process under Quadratic Quality Loss', International Journal of Eelisbilitv Quality and safety Engineering, Vol. 11, No. 1, pp. 81-90 https://doi.org/10.1142/S021853930400135X
  12. Lee, M. K, Kwon, H. M., Kim, Y. J., and Bae, J. H.(2005), 'Determination of Optimum Target Values for a Production Process based on Two Surrogate Variables', Lecture Note in Computer Science, Vol. 3483, No.4, pp. 232-240
  13. Phillips, M. D. and Cho B. R.(2000), 'A Nonlinear Model for Determining the Most Economic Process Mean under a Beta Distribution', International Journal of Reliability, Quality and Safety Engineering, Vol. 7, No.1, pp. 61-74 https://doi.org/10.1142/S0218539300000067
  14. Springer, C. H.(1951), 'A Method for Determining the Most Economic Position of a Process Mean', Industrial Quality Control, Vol. 8, pp. 36-39
  15. Teeravaraprug, J., Cho B. R., and Kennedy, W. J.(2002), 'Designing the Most Cost-effective Process Target using Regression Analysis: a case study', Process Control and Quality, Vol. 11, No.1, pp. 467-469