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This paper investigates reliability modeling for systems subject to dependent competing risks considering the impact from a new generalized mixed shock model. Two dependent competing risks are soft failure due to a degradation process, and hard failure due to random shocks. The shock process contains fatal shocks that can cause hard failure instantaneously, and nonfatal shocks that impact the system in three different ways: 1) damaging the unit by immediately increasing the degradation level, 2) speeding up the deterioration by accelerating the degradation rate, and 3) weakening the unit strength by reducing the hard failure threshold. While the first impact from nonfatal shocks comes from each individual shock, the other two impacts are realized when the condition for a new generalized mixed shock model is satisfied. Unlike most existing mixed shock models that consider a combination of two shock patterns, our new generalized mixed shock model includes three classic shock patterns. According to the proposed generalized mixed shock model, the degradation rate and the hard failure threshold can simultaneously shift multiple times, whenever the condition for one of these three shock patterns is satisfied. An example using micro-electro-mechanical systems devices illustrates the effectiveness of the proposed approach with sensitivity analysis.

a b s t r a c tThis paper presents a comprehensive mathematical model for integrated cell formation and inventory lot sizing problem. The proposed model seeks to minimize cell formation costs as well as the costs associated with production, while dynamic conditions, alternative routings, machine capacity limitation, operations sequences, cell size constraints, process deterioration, and machine breakdowns are also taken into account. The total cost consists of machine procurement, cell reconfiguration, preventive and corrective repairs, material handling (intra-cell and inter-cell), machine operation, part subcontracting, finished and unfinished parts inventory cost, and defective parts replacement costs. With respect to the multiple products, multiple process plans for each product and multiple routing alternatives for each process plan which are assumed in the proposed model, the model is combinatorial. Moreover, unreliability conditions are considered, because moving from ''in-control" state to ''out-of-control" state (process deterioration) and machine breakdowns make the model more practical and applicable. To conquer the breakdowns, preventive and corrective actions are adopted. Finally, a Particle Swarm Optimization (PSO)-based meta-heuristic is developed to overcome NP-completeness of the proposed model.

In this study, we introduce reliability models for a device with two dependent failure processes: soft failure due to degradation and hard failure due to random shocks, by considering the declining hard failure threshold according to changes in degradation. Owing to the nature of degradation for complex devices such as microelectromechanical systems, a degraded system is more vulnerable to force and stress during operation. We address two different scenarios of the changing hard failure threshold due to changes in degradation. In Case 1, the initial hard failure threshold value reduces to a lower level as soon as the overall degradation reaches a critical value. In Case 2, the hard failure threshold decreases gradually and the amount of reduction is proportional to the change in degradation. A condition-based maintenance model derived from a failure limit policy is presented to ensure that a device is functioning under a certain level of degradation. Finally, numerical examples are illustrated to explain the developed reliability and maintenance models, along with sensitivity analysis. in Wiley Online Library Recently, reliability analysis of a system with DCFP has been implemented by many researchers. Wang et al. 12 proposed a system reliability model on competitive failure processes of degradation and shocks, when the degradation process is affected by shocks under fuzzy degradation data. Wang and Pham 13 studied a single-unit system subject to the DCFP of degradation and random shocks. They considered two types of shocks in the model: (1) fatal shocks that cause the system to fail immediately and (2) nonfatal shocks that increase the degradation. Ye et al. 14,15 have studied reliability models for systems with dependent soft and hard failures, motivated by applications of ammeters and LEDs, respectively. Peng et al. 16 proposed a reliability model for systems with two dependent/correlated failure processes: soft failure due to degradation that is accumulated by continuous degradation over time and sudden increase due to shocks and hard failure caused by the same shocks. These two failure processes are dependent because arriving random shocks affect both failure processes. To extend the study in Peng et al., 16 Jiang et al. 17 studied the problem when the hard failure threshold is not fixed and can change because of different shock patterns, that is, extreme shock model, m-shock model, and δ-shock model. The hard failure threshold shifts to a lower level when one of the shock patterns occurs. Rafiee et al. 18 extended the model in Peng et al. 16 by introducing new reliability models where the degradation rate can accelerate owing to different shock patterns. As a result of withstanding shocks, the degradation rate is not a constant when the system becomes more prone to fatigue.For a system with two dependent failure processes, this paper investigates a new problem on the decreasing hard failure threshold due to changes in degradation level that creates a direct dependence between hard failure and soft failure....

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