On Reliability Bounds via Conditional Inequalities

1998 ◽  
Vol 35 (01) ◽  
pp. 104-114
Author(s):  
M. Xie ◽  
C. D. Lai
Keyword(s):  
Computational Complexity ◽  
System Reliability ◽  
Minimal Path ◽  
Reliability Bounds ◽  
Minimal Cut ◽  
One Step

In this paper we study an approximation of system reliability using one-step conditioning. It is shown that, without greatly increasing the computational complexity, the conditional method may be used instead of the usual minimal cut and minimal path bounds to obtain more accurate approximations and bounds. We also study the conditions under which the approximations are bounds on the reliability. Some further extensions are also presented.

On Reliability Bounds via Conditional Inequalities

1998 ◽  
Vol 35 (1) ◽  
pp. 104-114 ◽  
Author(s):  
M. Xie ◽  
C. D. Lai
Keyword(s):  
Computational Complexity ◽  
System Reliability ◽  
Minimal Path ◽  
Reliability Bounds ◽  
Minimal Cut ◽  
One Step

In this paper we study an approximation of system reliability using one-step conditioning. It is shown that, without greatly increasing the computational complexity, the conditional method may be used instead of the usual minimal cut and minimal path bounds to obtain more accurate approximations and bounds. We also study the conditions under which the approximations are bounds on the reliability. Some further extensions are also presented.

Narrower System Reliability Bounds With Incomplete Component Information and Stochastic Process Loading

2017 ◽  
Vol 17 (4) ◽  
Author(s):  
Yao Cheng ◽  
Daniel C. Conrad ◽  
Xiaoping Du
Keyword(s):  
System Reliability ◽  
Operating Conditions ◽  
Reliability Estimation ◽  
Design Stage ◽  
Shared Environment ◽  
Limited Information ◽  
Reliability Bounds ◽  
Component Design ◽  
Wide Range ◽  
Stochastic Load

Incomplete component information may lead to wide bounds for system reliability prediction, making decisions difficult in the system design stage. The missing information is often the component dependence, which is a crucial source for the exact system reliability estimation. Component dependence exists due to the shared environment and operating conditions. But it is difficult for system designers to model component dependence because they may have limited information about component design details if outside suppliers designed and manufactured the components. This research intends to produce narrow system reliability bounds with a new way for system designers to consider the component dependence implicitly and automatically without knowing component design details. The proposed method is applicable for a wide range of applications where the time-dependent system stochastic load is shared by components of the system. Simulation is used to obtain the extreme value of the system load for a given period of time, and optimization is employed to estimate the system reliability bounds, which are narrower than those from the traditional method with independent component assumption and completely dependent component assumption. Examples are provided to demonstrate the proposed method.

System Reliability Analysis With Dependent Component Failures During Early Design Stage—A Feasibility Study

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Yao Cheng ◽  
Xiaoping Du
Keyword(s):  
System Reliability ◽  
Reliability Prediction ◽  
Design Stage ◽  
Early Design ◽  
Early Design Stage ◽  
Design Concepts ◽  
Reliability Bounds ◽  
Lack Of Information ◽  
Dependent Component ◽  
Component Failures

It is desirable to predict product reliability accurately in the early design stage, but the lack of information usually leads to the use of independent component failure assumption. This assumption makes the system reliability prediction much easier, but may produce large errors since component failures are usually dependent after the components are put into use within a mechanical system. The bounds of the system reliability can be estimated, but are usually wide. The wide reliability bounds make it difficult to make decisions in evaluating and selecting design concepts, during the early design stage. This work demonstrates the feasibility of considering dependent component failures during the early design stage with a new methodology that makes the system reliability bounds much narrower. The following situation is addressed: the reliability of each component and the distribution of its load are known, but the dependence between component failures is unknown. With a physics-based approach, an optimization model is established so that narrow bounds of the system reliability can be generated. Three examples demonstrate that it is possible to produce narrower system reliability bounds than the traditional reliability bounds, thereby better assisting decision making during the early design stage.

A New GO Methodology Algorithm Based on BDD

2013 ◽  
Vol 791-793 ◽  
pp. 1134-1138
Author(s):  
Jian Fan ◽  
Yi Ren ◽  
Lin Lin Liu
Keyword(s):  
System Reliability ◽  
Binary Decision Diagram ◽  
Analysis Procedure ◽  
Logic Tree ◽  
Minimal Path ◽  
Binary Decision ◽  
Go Model ◽  
Go Methodology ◽  
Minimal Path Sets

To solve the problems on quick achieving reliability and the minimal path sets (MPS) of a system with GO Methodology, a Binary Decision Diagram (BDD) based new GO methodology algorithm is introduced. This technique can avoid the shared signals and combination explosion problems simultaneously. Detailed steps with a case study are presented to explain the analysis procedure of this technique, firstly, establish the GO model and transform it into a directed acyclic diagram (DAG), logic tree and BDD successively; then minimize the BDD according to the Without Rule; at last, this system reliability and MPS can be achieved. The results of the studied case verify the validity and effectiveness of this algorithm.

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