scholarly journals Reliability Evaluation of Repairable Parallel-Series Multi-State System Implementing Interval Valued Universal Generating Function

2021 ◽  
Author(s):  
Renu ◽  
Soni Bisht ◽  
S.B. Singh
Keyword(s):  
Generating Function ◽  
Composition Operators ◽  
State System ◽  
Time To Failure ◽  
Transform Method ◽  
Reliability Sensitivity ◽  
In Series ◽  
Mean Time ◽  
Parallel Series ◽  
Universal Generating Function

In this paper, we have studied a repairable parallel-series multi-state system. The proposed system consists of m components in series and n components in parallel in which each component has three possible states. The interval universal generating function (IUGF) is presented, and the corresponding composition operators are defined. The reliability assessment of the considered system is done with the help of the IUGF approach. It is worth mentioning that IUGF got attention from various researchers due to its straightforwardness, less complexity, and universal applications. In the present model, probabilities of different components, reliability, sensitivity, and mean time to failure are evaluated with the help of the Markov process; Laplace-Steiltjes transform method applying IUGF. A numerical example has also been taken to illustrate the proposed technique.

Signature reliability of binary state node in complex bridge networks using universal generating function

2019 ◽  
Vol 36 (2) ◽  
pp. 186-201 ◽  
Author(s):  
Soni Bisht ◽  
S.B. Singh
Keyword(s):  
Generating Function ◽  
Time To Failure ◽  
Content Type ◽  
Reliability Indices ◽  
The Past ◽  
Reliability Characteristics ◽  
Binary State ◽  
Bridge Networks ◽  
Mean Time ◽  
Universal Generating Function

PurposeThe purpose of this paper is to evaluate various reliability measures like reliability, expected lifetime (mean time to failure), signature reliability and compare networks based on the different flows.Design/methodology/approachThe reliability characteristics of complex bridge networks have been evaluated using different algorithms with the help of universal generating function (UGF). Further, the signature reliability of the considered networks has been determined using Owen’s method.FindingsThe present paper proposes an efficient algorithm to compute the reliability indices of complex bridge networks having i.i.d. lifetime components (nodes, edges) with the help of UGF and Owen’s method. This study reveals that a slight change in the complex bridge network affects the reliability significantly. Finally, by the reliability structure function, proposed algorithms are used to find the signature and MTTF. From signature, we have determined the different failure probabilities corresponding to edges of the network.Originality/valueIn this work, we have evaluated reliability characteristics and signature reliability of the complex bridge networks using UGF method and Owen’s method respectively unlike done in the past.

A Bayesian Estimation of Reliability Measures of Stepwise Exponential Distribution System

1991 ◽  
Author(s):  
M. H. Hu
Keyword(s):  
Bayesian Estimation ◽  
Exponential Distribution ◽  
Distribution System ◽  
Failure Process ◽  
Reliability Function ◽  
Distribution Model ◽  
Time To Failure ◽  
Reliability Measures ◽  
In Series ◽  
Mean Time

Abstract This paper presents an analysis method for reliability measures of a system with step changes in failure and repair rates. Both failure and repair time have exponential function of time. Such a system is called a stepwise exponential distribution system. This kind of failure process can take place in various equipments. This paper deals with the system having components in series arrangement. Bayesian statistics is used in defining prior and posterior probability density functions of failure and repair rates. These functions provide information for the estimation of reliability measures: 1) failure and repair rates, 2) mean time to failure, 3) mean time to repair, 4) reliability function and 5) availability. A sample problem is given to illustrate the methodology. The Bayesian estimation of the stepwise exponential distribution model is useful in the planning of equipment predictive maintenance.

AVAILABILITY AND COST ANALYSIS OF A PARALLEL REDUNDANT COMPLEX SYSTEM WITH TWO TYPES OF FAILURE UNDER PREEMPTIVE-RESUME REPAIR DISCIPLINE USING GUMBEL-HOUGAARD FAMILY COPULA IN REPAIR

2008 ◽  
Vol 15 (04) ◽  
pp. 341-365 ◽  
Author(s):  
MANGEY RAM ◽  
S. B. SINGH
Keyword(s):  
Complex System ◽  
Cost Analysis ◽  
Time To Failure ◽  
Preemptive Resume ◽  
Special Cases ◽  
In Series ◽  
State Behaviour ◽  
General Distributions ◽  
Mean Time ◽  
Steady State Behaviour

This paper discusses about the availability of a complex system, which consists of two independent repairable subsystems A and B in (1-out-of-2: F) and (1-out-of-n: F) arrangement respectively. Subsystem A has two identical units arranged in parallel redundancy (1-out-of-2: G), subsystem B has n unit in series (1-out-of-n: F) with two types of failure, viz., partial and catastrophic. Except at two transitions where two types of repair namely exponential and general possible all other transitions have single possibility between any two states. The failure and repair time for both subsystems follow exponential and general distributions respectively. The model is analyzed under "preemptive-resume repair discipline" where A is considered to be in priority while B is non-priority. By employing supplementary variable technique, Laplace transformation and Gumbel-Hougaard family copula various transition state probabilities, availability, Mean Time to Failure (MTTF) and cost analysis (expected profit) are obtained along with steady-state behaviour of the system. Inversions have also been carried out so as to obtain time dependent probabilities, which determine availability of the system at any instant. At last some special cases of the system have been taken.

Sensitivity analysis of a three-unit series system under k-out-of-n redundancy

2017 ◽  
Vol 34 (6) ◽  
pp. 770-784 ◽  
Author(s):  
Nupur Goyal ◽  
Mangey Ram ◽  
Shubham Amoli ◽  
Alok Suyal
Keyword(s):  
Sensitivity Analysis ◽  
Performance Measure ◽  
General Distribution ◽  
Time To Failure ◽  
Reliability Measures ◽  
Mean Time To Failure ◽  
Content Type ◽  
Failure Cost ◽  
In Series ◽  
Mean Time

Purpose The purpose of this paper is to investigate the reliability measures, namely, availability, reliability, mean time to failure and expected profit. The authors also analyse the sensitivity of these reliability measures. Design/methodology/approach Depending upon the real industrial relevance, a generalized system which is easily repairable, extremely reliable and of high quality is expected by the rapid growth of the digital economy. Considering reliability, as one of the performance measure, the authors have designed a complex system which consists of three subsystems, namely, A, B and C in series configuration. The subsystem A consists of n numbers of units which are arranged in parallel configuration, subsystem B consists of two sub-subsystems X and Y align parallel to one another, where X is a type of 1-out-of-n:F. Failure and repair rates are assumed to be follow the general distribution. Findings The system is deeply studied by the usage of the supplementary variable technique, Laplace transformation and Markov’s law. Various conclusive results such as availability and reliability of the system, mean time to failure, cost and sensitivity analysis have been discussed further. Originality/value Through the systematic view of reliability measures of the proposed system, performance of the system can be enhanced under high profit.

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