中文摘要：

针对生产过程中由于设备劣化引起产品缺陷率增大以及顾客需求波动问题,构建了综合考虑设备劣化和需求随机的最优生产周期模型。利用伽马过程对上游生产单元的劣化过程进行建模,并假设当其劣化量达到中间某一水平时,生产活动从＂受控＂转变为＂失控＂状态;以此为基础,在假设下游需求随机的条件下,以最小化单位产品的总成本为优化目标建立了数学模型;借助数值实例演示了本模型的有效性,并对相关参数作了敏感性分析。分析结果表明：本文所提模型对于描述设备劣化程度对产品质量的影响,降低企业运行成本（库存、返工、维护等）有一定的指导意义。

英文摘要：

During production,machine deterioration and stochastic demand can cause an increased probability of producing defective items and a shortage of WIPs,respectively. Hence,an optimal production period model considering machine deterioration upstream and stochastic demand downstream was formulated. First,a gamma process was introduced to model the degradation of the upstream machine; after the degradation state exceeded a predetermined threshold,the production state transformed from ＂in-control＂to ＂out-of-control. ＂Based on the abovementioned descriptions,a mathematical model with an objective function for minimizing the total expected cost per unit was derived,assuming the downstream demand rate was stochastic. Finally,a numerical example was provided to illustrate the application of the proposed model,and sensitivity analysis of the model with respect to some key parameters was performed. Results show that the proposed model has certain instructive significance in quality control and for cost reduction of imperfect production systems.