Redundancy Allocation Optimization for Multistate Systems With Failure Interactions Using Semi-Markov Process

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
Jing Wang ◽  
Mian Li
Keyword(s):  
Markov Process ◽  
System Analysis ◽  
Research Work ◽  
Process Models ◽  
Redundancy Allocation ◽  
Allocation Problems ◽  
Multistate Systems ◽  
Semi Markov Process ◽  
Failure Interaction ◽  
Main Subsystem

Failure interactions and multiple states are two common phenomena in engineering systems. However, most of the redundancy allocation problems assume binary states and ignore failure interactions, which will cause inaccurate and misleading results. Although some research work focuses on the multistate systems, failure interactions have been ignored. This paper, for the first time, solves the redundancy allocation problems considering the systems having both multiple states and failure interactions. The system studied in this paper is a kind of multistate system containing a main subsystem and an auxiliary subsystem with the failure interaction existing from the auxiliary subsystem to the main subsystem. Semi-Markov process is proposed as the model for the system analysis, and a reliability measure, availability, is obtained based on the proposed semi-Markov process models. The system availability is used as the constraint in the redundancy allocation problem. A case study from a navy application is presented to demonstrate the applicability of the proposed method.

Redundancy Allocation for Reliability Design of Engineering Systems With Failure Interactions

2014 ◽  
Author(s):  
Jing Wang ◽  
Mian Li
Keyword(s):  
Analytical Model ◽  
Interaction Model ◽  
Optimization Methods ◽  
Failure Rates ◽  
Engineering Systems ◽  
Analytic Hierarchy ◽  
Redundancy Allocation ◽  
Reliability Design ◽  
Allocation Problems ◽  
Failure Interaction

In reliability design, allocating redundancy through various optimization methods is one of the important ways to improve the system reliability. Generally, in these redundancy allocation problems, it is assumed that failures of components are independent. However, under this assumption failure rates can be underestimated since failure interactions can significantly affect the performance of systems. This paper first proposed an analytical model describing the failure rates with failure interactions. Then a Modified Analytic Hierarchy Process (MAHP) is proposed to solve the redundancy allocation problems for systems with failure interactions. This method decomposes the system into several blocks and deals with those down-sized blocks before diving deep into the most appropriate component for redundancy allocation. Being simple and flexible, MAHP provides an intuitive way to design a complex system and complex explicit objective functions for the entire system is not required in the proposed approach. More importantly, with the help of the proposed analytical failure interaction model, MAHP can capture the effect of failure interactions. Results from case studies clearly demonstrate the applicability of the analytical model for failure interactions and MAHP for reliability design.

Redundancy Allocation for Multistate Systems With Component Dependencies and Load Sharing

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Jing Wang ◽  
Mian Li
Keyword(s):  
Markov Process ◽  
Process Model ◽  
Load Sharing ◽  
Two Component System ◽  
System Availability ◽  
Redundancy Allocation ◽  
Markov Process Model ◽  
Dependent Failures ◽  
Binary State ◽  
Semi Markov Process

Binary-state and component independent assumptions will lead to doubtful and misleading redundancy allocation schemes which may not satisfy the reliability requirements for real engineering applications. Most published works proposed methods to remove the first assumption by studying the degradation cases where multiple states of a component are from the best state to the degradation states then to the completely failed state. Fewer works focused on removing the second assumption and they only discussed dependent failures which are only a special case of component dependency. This work uses the Semi-Markov process to describe a two-component system for redundancy allocation. In this work, multiple states of a component are represented by multiple output levels, which are beyond the scope of degradation, and the component dependency is not limited to failure dependency only. The load sharing is also taken care of in the proposed work. The optimal redundancy allocation scheme is obtained by solving the corresponding redundancy allocation optimization problem with the reliability measure, the system availability, obtained through the Semi-Markov process model being constraint. Two case studies are presented, demonstrating the applicability of the propose method.

Redundancy Allocation for Reliability Design of Engineering Systems With Failure Interactions

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Jing Wang ◽  
Mian Li
Keyword(s):  
Analytical Model ◽  
System Reliability ◽  
Optimal Allocation ◽  
Interaction Model ◽  
Failure Rates ◽  
Engineering Systems ◽  
Redundancy Allocation ◽  
Reliability Design ◽  
Allocation Problems ◽  
Failure Interaction

Optimal allocation of redundancies is one of the most important ways of improving system reliability. Generally, in these redundancy allocation problems, it is assumed that failures of components are independent. However, under this assumption failure rates can be underestimated since failure interactions can significantly affect the performance of systems. In this paper, we first propose an analytical model to describe the failure rates with failure interactions, followed by a modified analytical hierarchy process (MAHP) which is proposed to solve redundancy allocation problems with failure interactions. MAHP decomposes the system into several blocks and deals with those downsized blocks before diving deep into the most appropriate component for redundancy allocation. Being simple and flexible, MAHP provides an intuitive way to design a complex system and the explicit function of the entire system reliability is not required in the proposed approach. More importantly, with the help of the proposed analytical failure interaction model, MAHP can capture the effect of failure interactions. Results from case studies clearly demonstrate the applicability of the analytical model for failure interactions and MAHP for reliability design.

Partially observable semi-Markov reward processes

1993 ◽  
Vol 30 (3) ◽  
pp. 548-560 ◽  
Author(s):  
Yasushi Masuda
Keyword(s):  
Markov Process ◽  
Counting Process ◽  
Probabilistic Interpretation ◽  
Real Domain ◽  
Semi Markov Process ◽  
Reward Process ◽  
Markov Reward ◽  
Partially Observable ◽  
Joint Behavior

The main objective of this paper is to investigate the conditional behavior of the multivariate reward process given the number of certain signals where the underlying system is described by a semi-Markov process and the signal is defined by a counting process. To this end, we study the joint behavior of the multivariate reward process and the multivariate counting process in detail. We derive transform results as well as the corresponding real domain expressions, thus providing clear probabilistic interpretation.

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