Journal of the Korea Academia-Industrial cooperation Society (한국산학기술학회논문지)

The Korea Academia-Industrial cooperation Society (한국산학기술학회)
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Analysis of an Inspection Process Allowing Consecutive Two-time Testing of Products Using Markov Chains

연속되는 이중 검사를 허용하는 제품품질검사 프로세스에 대한 마르코프 체인을 이용한 분석

  • Ko, Jeong-Han (Department of Industrial Engineering, Ajou University)
  • 고정한 (아주대학교 산업공학과)
  • Received : 2012.05.04
  • Accepted : 2012.06.07
  • Published : 2012.06.30
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Abstract

When a quality inspection process rejects a product unit, consecutive repeated inspections are sometimes conducted for the rejected unit to reduce a false reject possibility. This paper analyzes a special inspection process that allows up to two times of consecutive testing for each product to decrease type I inspection errors. This study uses a Markov chain to model the steps of the inspection process and a product unit's quality states during inspection. Historical inspection results from a company are used as the data for the Markov chain model. Using the Markov chain model and data, this study analyzes the effect of this special inspection rule on the proportion of the final quality levels and scrap rate. The results demonstrate that this inspection process of possible double testing could help reduce unnecessary rejects and consequently decrease material and production costs.

산업현장에서는 품질검사 과정 중의 잘못된 불량판정을 감소시키기 위하여, 각 제품단위에 대하여 불량판정이 나왔을 경우 복수의 검사를 반복하여 수행하는 경우가 있다. 본 논문은 총 두 번까지의 연속된 검사를 허용하는 품질검사 프로세스에 대한 분석을 다루고 있다. 본 논문에서는 제품검사의 단계와 품질판정 상태를 모델링하는 수학적 도구로서 마르코프 체인이 사용되었다. 그리고 산업체의 생산관리 시스템에서 수집된 불량 판정률을 마르코프 체인 모델의 데이터로 사용하였다. 또한 본 논문은 제품의 품질 특성 별 최종 비율과 제품의 폐기율에 대한 이러한 연속적인 이중검사 허용 프로세스의 영향에 대하여 분석을 수행하였다. 분석 결과, 연속이중검사 허용이 정상 제품에 대한 불량판정을 줄이며, 그 결과 재료, 노동 및 기타 비용을 줄이는 데 기여할 수 있다는 것을 확인하였다

Keywords

References

  1. Tomek, L., Mainkar, V., Geist, R. M., & Trivedi, K. S., "Reliability modeling of life-critical, real-time systems", Proceedings of the IEEE, 82(1), pp. 108-121, 1994. https://doi.org/10.1109/5.259430
  2. Sang, H., Wang, G., & Zhou, Z., "Evolutionary multi-objective optimization of inspection frequencies for substation condition-based maintenance", 2011 6th International Forum on Strategic Technology (IFOST), pp. 480-486, 2011.
  3. Zhang, Z., & Love, C., "A simple recursive Markov chain model to determine the optimal replacement policies under general repairs", Computers & Operations Research, 27(4), pp. 321-333, 2000. https://doi.org/10.1016/S0305-0548(99)00053-2
  4. Bukowski, J. V., "Modeling and analyzing the effects of periodic inspection on the performance of safety-critical systems", IEEE Transactions on Reliability, 50(3), pp. 321-329, 2001. https://doi.org/10.1109/24.974130
  5. Klein, M., "Markovian decision models for reject allowance problems", Management Science, 12(5), pp. 349-358, 1966. https://doi.org/10.1287/mnsc.12.5.349
  6. Finkelshtein, A., Herer, Y. T., Raz, T., & Ben-Gal, I., "Economic optimization of off-line inspection in a process subject to failure and recovery", IIE Transactions, 37(11), pp. 995-1009, 2005. https://doi.org/10.1080/07408170500232149
  7. Chen, D., Cao, Y., Trivedi, K. S., & Hong, Y., "Preventive maintenance of multi-state system with phase-type failure time distribution and non-zero inspection time," International Journal of Reliability Quality and Safety Engineering, 10, pp. 323-344, 2003. https://doi.org/10.1142/S0218539303001172
  8. Faddoul, R., Raphael, W., & Chateauneuf, A., "A generalised partially observable Markov decision process updated by decision trees for maintenance optimisation", Structure and Infrastructure Engineering, 7(10), pp. 783-796, 2011. https://doi.org/10.1080/15732470902985827
  9. Wang, C. H., & Sheu, S., "Determining the optimal production-maintenance policy with inspection errors: using a Markov chain", Computers & Operations Research, 30(1), pp. 1-17, 2003. https://doi.org/10.1016/S0305-0548(01)00073-9
  10. Borrero, J., & Akhavan-Tabatabaei, R., "A Markov decision process model for optimal policy making in the maintenance of a single-machine single-product toolset", Proceedings of the 2010 Winter Simulation Conference (WSC), pp. 2594-2605, 2010.
  11. Park, W. & Kim, H., "Performance analysis using Markov chain in WiBro", Journal of the Korea Academia-Industrial Cooperation Society, 11(1), pp. 190-197, 2010. https://doi.org/10.5762/KAIS.2010.11.1.190
  12. Lim, H., "Named entity boundary recognition using hidden Markov model and hierarchical information", Journal of the Korea Academia-Industrial Cooperation Society, 7(2), pp. 182-187, 2006.
  13. Undisclosed company data, "Term project I for IMSE 428", 2008.
  14. Winston, W. L., Introduction to Probability Models: Operations Research, Volume II, Duxbury Press, 4th edition, 2003.