Reliability analysis for a hybrid flow shop with due date consideration

For a hybrid flow-shop (HFS), the number of machines in a stage presents multiple levels because of maintenance, partial failures, unexpected failures, etc. In other words, it is suitable that the capacity of each stage is regarded as a stochastic component. Reliability reveals the performance of an HFS under the stochastic capacity, while certain demand and due date are required. In this paper, the reliability is defined as the probability that an HFS with stochastic capacity can satisfy the makespan for the demand within the due date. We first transform the HFS with stochastic capacity into a multistate hybrid flow-shop network. An efficient algorithm is then proposed to derive an estimated interval for the reliability based on a pair of capacity vectors, which are generated from two estimated demand levels. Two practical cases, including a tile production system and a footwear production system, are presented to demonstrate how the estimated interval is obtained and to investigate efficiency and accuracy of the proposed algorithm. The reliability can be regarded as a quality indicator to understand the capability of the real-world HFS and to guarantee whether the demand can be completed within the desire due date.