隨著科技技術的進步，產品推陳出新的速度越來越快，而使得產品生命週期縮短，造成市場上會同時存在舊與新世代產品，並且一段時間後，舊世代產品可能會下市，市場上只會剩下新世代產品，促使消費者考慮各種因素決定何時換成新世代產品，而將舊世代產品換成新世代產品的動作則稱為「汰換」。在之前的文獻中，只討論了將舊世代產品汰換為新世代產品，但並未討論舊與新世代產品間，會有系統相容上需要更換的成本，也就是汰換成本。在本論文中會假設汰換過程中，需要付出汰換成本，汰換成本會隨著時間有所變化，並且還要付出新世代產品的購買成本，購買成本也會隨著時間有所變化，使得消費者在考慮汰換為新世代產品的過程中更加複雜。一般來說，產品會隨著使用時間的增加，會有不可避免的退化而導致失效，本論文假設產品在失效後會以小修處理，使產品回復到失效前的狀態。本論文以尋求最佳汰換時間為目標，建構汰換為新世代產品的期望總成本模型，並分為兩種情況，分別為不計汰換成與考量汰換成本兩種情況，並以最低期望總成本為目標，尋求最佳汰換時間，最後以數值分析探討各個成本參數對最佳汰換時間的影響。

With the progress of technology, new generation product is released faster and faster, leading to product lifecycle becomes shorter. Hence, old and new generation products may be simultaneous on the market. Furthermore, old generation products may phase out when new generation products are released for a period of time, and there will not be any old generation product on the market. In this case, consumers may be forced to consider various factors to replace old generation product by the new generation product, which is called “switch-over”. When the old generation product is switched-over to the new generation product, the switch-over cost and the purchasing cost of the new generation product are required, and the both of two costs may be time-varied. In practice, any product deteriorates with age and the number of failures will increase. When the product fails, minimal repair will be carried out to restore back operating condition. In this paper, the expected total cost model is established for switching-over to a new generation product to find the optimal switch-over time. Two cases are considered which are with and without switch-over cost as the old product is switched over to the new generation. For both cases, the optimal switch-over times are derived such that the expected total cost is minimized. Finally, the impact of each cost parameter on the optimal switch-over time is investigated through numerical examples.

[1]張嘉文，「汰換為新世代產品之最佳時間」，國立台灣科技大學工業管理系碩士論文 2019。
[2]Barlow, R. E. and L. C. Hunter, “Optimum preventive maintenance policies,” Operations Research, 8(1), 90-100 (1960).
[3]T. Nakagawa and M. Kowada, “Analysis of a system with minimal repair and its application to replacement policy,” European Journal of Operational Research, 12(2), 176-182 (1983).
[4]Sheu, S. H., Chang, C. C., Chen, Y. L., and Zhang, Z. G., “A periodic replacement model based on cumulative repair-cost limit for a system subjected to shocks,” IEEE Transactions on Reliability, 59(2), 374-382 (2010).
[5]Nakagawa, T., “Modified periodic replacement with minimal repair at failure,” IEEE Transactions on Reliability, 30(2), 165-168 (1981).
[6]Boland, P. J., and Proschan, F, “Periodic replacement with increasing minimal repair costs at failure,” Operations Research, 30(6), 1183-1189 (1982).
[7]Nguyen, D. G., and Murthy, D. N. P., “Optimal replace-repair strategy for servicing products sold with warranty,” European Journal of Operational Research, 39(2), 206-212 (1989).
[8]Chen, M., and Feldman, R. M., “Optimal replacement policies with minimal repair and age-dependent costs,” European Journal of Operational Research, 98(1), 75-84 (1997).
[9]Yun, W. Y., & Choi, C. H., “Optimum replacement intervals with random time horizon,” Journal of Quality in Maintenance Engineering, 6(4), 269-274 (2000).
[10]Jiang, X., Makis, V., and Jardine, A. K., “Optimal repair/replacement policy for a general repair model,” Advances in Applied Probability, 33(1), 206-222 (2001).
[11]Lai, M. T., “A periodical replacement model based on cumulative repair‐cost limit,” Applied Stochastic Models in Business and Industry, 23(6), 455-464 (2007).
[12]Wang, G. J., and Zhang, Y. L., “An optimal replacement policy for a two-component series system assuming geometric process repair,” Computers & Mathematics with Applications, 54(2), 192-202 (2007).
[13]Chang, C. C., Sheu, S. H., and Chen, Y. L., “Optimal number of minimal repairs before replacement based on a cumulative repair-cost limit policy,” Computers & Industrial Engineering, 59(4), 603-610 (2010).
[14]Lim, J. H., Qu, J., and Zuo, M. J., “Age replacement policy based on imperfect repair with random probability,” Reliability Engineering & System Safety, 149, 24-33 (2016).
[15]Park, M., and Pham, H., “Cost models for age replacement policies and block replacement policies under warranty,” Applied Mathematical Modelling, 40, 5689-5702 (2016).
[16]Kusaka, Y., and Suzuki, H., “Equipment replacement behavior under innovative technological advances,” Journal of the Operations Research Society of Japan, 33(1), 76-99 (1990).
[17]Bylka, S., Sethi, S., and Sorger, G., “Minimal forecast horizons in equipment replacement models with multiple technologies and general switching costs,” Naval Research Logistics, 39(4), 487-507 (1992).
[18]Chand, S., McClurg, T., and Ward, J., “A single‐machine replacement model with learning,” Naval Research Logistics, 40(2), 175-192 (1993).
[19]Bethuyne, G., “Optimal replacement under variable intensity of utilization and technological progress,” The Engineering Economist, 43(2), 85-105 (1998).
[20]Rogers, J. L., and Hartman, J. C., “Equipment replacement under continuous and discontinuous technological change,” IMA Journal of Management Mathematics, 16(1), 23-36 (2005).
[21]Yatsenko, Y., and Hritonenko, N., “Discrete–continuous analysis of optimal equipment replacement,” International Transactions in Operational Research, 17(5), 577-593 (2010).