Various strategies can be applied to improve reliability at certain costs, including equipment redundancy, product storage, and maintenance, which gives rise to the problem of optimally allocating the reliability improvement costs among various strategies and balancing them against the potential loss due to unavailabilities. Motivated by the reliability concerns of air separation units, we use Markov Decision Process to model the stochastic dynamic decision making process of condition-based maintenance assuming bathtub shaped failure rate curves of single units, which is then embedded into a non-convex MINLP (DMP) that considers the trade-off among all the decisions. An initial attempt to directly solve the MINLP (DMP) for a mid-sized problem with several global solvers reveals severe computational difficulties. In response, we propose a custom two-phase algorithm that greatly reduces the required computation effort. The algorithm also shows consistent performance over randomly generated problems around the original example of 4 processing stages and problems of larger sizes.

可以采用各种策略以一定的成本来提高可靠性，包括设备冗余，产品存储和维护，这引起了在各种策略之间最佳地分配可靠性改善成本并使其与因不可用而导致的潜在损失进行平衡的问题。出于对空气分离装置可靠性问题的考虑，我们使用马尔可夫决策过程对基于状态的维护的随机动态决策过程进行建模，假设单个单元的浴缸形故障率曲线，然后将其嵌入到非凸型MINLP（DMP）中）考虑所有决策之间的权衡。最初的尝试直接解决具有多个全局求解器的中型问题的MINLP（DMP），这显示出严重的计算困难。作为回应，我们提出了一种自定义的两阶段算法，可大大减少所需的计算工作量。该算法还显示了围绕4个处理阶段的原始示例以及较大尺寸问题在随机生成的问题上的一致性能。