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Article
Publication date: 6 February 2019

Sanku Dey and Fernando Antonio Moala

The purpose of this paper is to deal with the Bayesian and non-Bayesian estimation methods of multicomponent stress-strength reliability by assuming the Chen distribution.

Abstract

Purpose

The purpose of this paper is to deal with the Bayesian and non-Bayesian estimation methods of multicomponent stress-strength reliability by assuming the Chen distribution.

Design/methodology/approach

The reliability of a multicomponent stress-strength system is obtained by the maximum likelihood (MLE) and Bayesian methods and the results are compared by using MCMC technique for both small and large samples.

Findings

The simulation study shows that Bayes estimates based on γ prior with absence of prior information performs little better than the MLE with regard to both biases and mean squared errors. The Bayes credible intervals for reliability are also shorter length with competitive coverage percentages than the condence intervals. Further, the coverage probability is quite close to the nominal value in all sets of parameters when both sample sizes n and m increases.

Originality/value

The lifetime distributions used in reliability analysis as exponential, γ, lognormal and Weibull only exhibit monotonically increasing, decreasing or constant hazard rates. However, in many applications in reliability and survival analysis, the most realistic hazard rate is bathtub-shaped found in the Chen distribution. Therefore, the authors have studied the multicomponent stress-strength reliability under the Chen distribution by comparing the MLE and Bayes estimators.

Details

International Journal of Quality & Reliability Management, vol. 36 no. 2
Type: Research Article
ISSN: 0265-671X

Keywords

Article
Publication date: 6 March 2017

Srinivasa Rao Gadde

The purpose of this paper is to consider the estimation of multicomponent stress-strength reliability. The system is regarded as alive only if at least s out of k (s<k) strengths…

Abstract

Purpose

The purpose of this paper is to consider the estimation of multicomponent stress-strength reliability. The system is regarded as alive only if at least s out of k (s<k) strengths exceed the stress. The reliability of such a system is obtained when strength, stress variates are from Erlang-truncated exponential (ETE) distribution with different shape parameters. The reliability is estimated using the maximum likelihood (ML) method of estimation when samples are drawn from strength and stress distributions. The reliability estimators are compared asymptotically. The small sample comparison of the reliability estimates is made through Monte Carlo simulation. Using real data sets the authors illustrate the procedure.

Design/methodology/approach

The authors have developed multicomponent stress-strength reliability based on ETE distribution. To estimate reliability, the parameters are estimated by using ML method.

Findings

The simulation results indicate that the average bias and average mean square error decreases as sample size increases for both methods of estimation in reliability. The length of the confidence interval also decreases as the sample size increases and simulated actual coverage probability is close to the nominal value in all sets of parameters considered here. Using real data, the authors illustrate the estimation process.

Originality/value

This research work has conducted independently and the results of the author’s research work are very useful for fresh researchers.

Details

International Journal of Quality & Reliability Management, vol. 34 no. 3
Type: Research Article
ISSN: 0265-671X

Keywords

Article
Publication date: 3 January 2020

Mayank Kumar Jha, Sanku Dey and Yogesh Mani Tripathi

The purpose of this paper is to estimate the multicomponent reliability by assuming the unit-Gompertz (UG) distribution. Both stress and strength are assumed to have an UG…

Abstract

Purpose

The purpose of this paper is to estimate the multicomponent reliability by assuming the unit-Gompertz (UG) distribution. Both stress and strength are assumed to have an UG distribution with common scale parameter.

Design/methodology/approach

The reliability of a multicomponent stress–strength system is obtained by the maximum likelihood (MLE) and Bayesian method of estimation. Bayes estimates of system reliability are obtained by using Lindley’s approximation and Metropolis–Hastings (M–H) algorithm methods when all the parameters are unknown. The highest posterior density credible interval is obtained by using M–H algorithm method. Besides, uniformly minimum variance unbiased estimator and exact Bayes estimates of system reliability have been obtained when the common scale parameter is known and the results are compared for both small and large samples.

Findings

Based on the simulation results, the authors observe that Bayes method provides better estimation results as compared to MLE. Proposed asymptotic and HPD intervals show satisfactory coverage probabilities. However, average length of HPD intervals tends to remain shorter than the corresponding asymptotic interval. Overall the authors have observed that better estimates of the reliability may be achieved when the common scale parameter is known.

Originality/value

Most of the lifetime distributions used in reliability analysis, such as exponential, Lindley, gamma, lognormal, Weibull and Chen, only exhibit constant, monotonically increasing, decreasing and bathtub-shaped hazard rates. However, in many applications in reliability and survival analysis, the most realistic hazard rates are upside-down bathtub and bathtub-shaped, which are found in the unit-Gompertz distribution. Furthermore, when reliability is measured as percentage or ratio, it is important to have models defined on the unit interval in order to have plausible results. Therefore, the authors have studied the multicomponent stress–strength reliability under the unit-Gompertz distribution by comparing the MLEs, Bayes estimators and UMVUEs.

Details

International Journal of Quality & Reliability Management, vol. 37 no. 3
Type: Research Article
ISSN: 0265-671X

Keywords

Article
Publication date: 5 March 2021

Mayank Kumar Jha, Yogesh Mani Tripathi and Sanku Dey

The purpose of this article is to derive inference for multicomponent reliability where stress-strength variables follow unit generalized Rayleigh (GR) distributions with common…

Abstract

Purpose

The purpose of this article is to derive inference for multicomponent reliability where stress-strength variables follow unit generalized Rayleigh (GR) distributions with common scale parameter.

Design/methodology/approach

The authors derive inference for the unknown parametric function using classical and Bayesian approaches. In sequel, (weighted) least square (LS) and maximum product of spacing methods are used to estimate the reliability. Bootstrapping is also considered for this purpose. Bayesian inference is derived under gamma prior distributions. In consequence credible intervals are constructed. For the known common scale, unbiased estimator is obtained and is compared with the corresponding exact Bayes estimate.

Findings

Different point and interval estimators of the reliability are examined using Monte Carlo simulations for different sample sizes. In summary, the authors observe that Bayes estimators obtained using gamma prior distributions perform well compared to the other studied estimators. The average length (AL) of highest posterior density (HPD) interval remains shorter than other proposed intervals. Further coverage probabilities of all the intervals are reasonably satisfactory. A data analysis is also presented in support of studied estimation methods. It is noted that proposed methods work good for the considered estimation problem.

Originality/value

In the literature various probability distributions which are often analyzed in life test studies are mostly unbounded in nature, that is, their support of positive probabilities lie in infinite interval. This class of distributions includes generalized exponential, Burr family, gamma, lognormal and Weibull models, among others. In many situations the authors need to analyze data which lie in bounded interval like average height of individual, survival time from a disease, income per-capita etc. Thus use of probability models with support on finite intervals becomes inevitable. The authors have investigated stress-strength reliability based on unit GR distribution. Useful comments are obtained based on the numerical study.

Details

International Journal of Quality & Reliability Management, vol. 38 no. 10
Type: Research Article
ISSN: 0265-671X

Keywords

Article
Publication date: 29 September 2022

Rani Kumari, Chandrakant Lodhi, Yogesh Mani Tripathi and Rajesh Kumar Sinha

Inferences for multicomponent reliability is derived for a family of inverted exponentiated densities having common scale and different shape parameters.

Abstract

Purpose

Inferences for multicomponent reliability is derived for a family of inverted exponentiated densities having common scale and different shape parameters.

Design/methodology/approach

Different estimates for multicomponent reliability is derived from frequentist viewpoint. Two bootstrap confidence intervals of this parametric function are also constructed.

Findings

Form a Monte-Carlo simulation study, the authors find that estimates obtained from maximum product spacing and Right-tail Anderson–Darling procedures provide better point and interval estimates of the reliability. Also the maximum likelihood estimate competes good with these estimates.

Originality/value

In literature several distributions are introduced and studied in lifetime analysis. Among others, exponentiated distributions have found wide applications in such studies. In this regard the authors obtain various frequentist estimates for the multicomponent reliability by considering inverted exponentiated distributions.

Details

International Journal of Quality & Reliability Management, vol. 40 no. 4
Type: Research Article
ISSN: 0265-671X

Keywords

Article
Publication date: 12 February 2020

Oussama Adjoul, Khaled Benfriha and Améziane Aoussat

This paper proposes a new simultaneous optimization model of the industrial systems design and maintenance. This model aims to help the designer in searching for technical…

Abstract

Purpose

This paper proposes a new simultaneous optimization model of the industrial systems design and maintenance. This model aims to help the designer in searching for technical solutions and the product architecture by integrating the maintenance issues from the design stage. The goal is to reduce the life-cycle cost (LCC) of the studied system.

Design/methodology/approach

Literature indicates that the different approaches used in the design for maintenance (DFM) methods are limited to the simultaneous characterization of the reliability and the maintainability of a multicomponent system as well as the modeling of the dynamic maintenance. This article proposes to go further in the optimization of the product, by simultaneously characterizing the design, in terms of reliability and maintainability, as well as the dynamic planning of the maintenance operations. This combinatorial characterization is performed by a two-level hybrid algorithm based on the genetic algorithms.

Findings

The proposed tool offers, depending on the life-cycle expectation, the desired availability, the desired business model (sales or rental), simulations in terms of the LCCs, and so an optimal product architecture.

Research limitations/implications

In this article, the term “design” is limited to reliability properties, possible redundancies, component accessibility (maintainability), and levels of monitoring information.

Originality/value

This work is distinguished by the use of a hybrid optimization algorithm (two-level computation) using genetic algorithms. The first level is to identify an optimal design configuration that takes into account the LCC criterion. The second level consists in proposing a dynamic and optimal maintenance plan based on the maintenance-free operating period (MFOP) concept that takes into account certain criteria, such as replacement costs or the reliability of the system.

Article
Publication date: 29 July 2014

Kanchan Jain, Isha Dewan and Monika Rani

Joint reliability importance (JRI) of components is the effect of a change of their reliability on the system reliability. The authors consider two coherent multi-component…

Abstract

Purpose

Joint reliability importance (JRI) of components is the effect of a change of their reliability on the system reliability. The authors consider two coherent multi-component systems – a series-in-parallel (series subsystems arranged in parallel) and a parallel-in-series (parallel subsystems arranged in series) system. It is assumed that all the components in the subsystems are independent but not identically distributed. The subsystems do not have any component in common. The paper aims to discuss these issues.

Design/methodology/approach

For both the systems, the expressions for the JRI of two or more components are derived. The results are extended to include subsystems where some of the components are replicated.

Findings

The findings are illustrated by considering bridge structure as a series-in-parallel system wherein some of the components are repeated in different subsystems. Numerical results have also been provided for a series-in-parallel system with unreplicated components. JRI for various combinations of components for both the illustrations are given through tables or figures.

Originality/value

Chang and Jan (2006) and Gao et al. (2007) found the JRI of two components of series-in-parallel system when the components are identical and independently distributed. The authors derive the JRI of m=2 components for series-in-parallel and parallel-in-series systems when components are independent but need not be identically distributed. Expressions are obtained for the above-mentioned systems with replicated and unreplicated components in different subsystems. These results will be useful in analyzing the joint effect of reliability of several components on the system reliability. This will be of value to design engineers for designing systems that function more effectively and for a longer duration.

Details

International Journal of Quality & Reliability Management, vol. 31 no. 7
Type: Research Article
ISSN: 0265-671X

Keywords

Article
Publication date: 8 July 2022

Da Teng, Yun-Wen Feng, Jun-Yu Chen and Cheng Lu

The purpose of this paper is to briefly summarize and review the theories and methods of complex structures’ dynamic reliability. Complex structures are usually assembled from…

Abstract

Purpose

The purpose of this paper is to briefly summarize and review the theories and methods of complex structures’ dynamic reliability. Complex structures are usually assembled from multiple components and subjected to time-varying loads of aerodynamic, structural, thermal and other physical fields; its reliability analysis is of great significance to ensure the safe operation of large-scale equipment such as aviation and machinery.

Design/methodology/approach

In this paper for the single-objective dynamic reliability analysis of complex structures, the calculation can be categorized into Monte Carlo (MC), outcrossing rate, envelope functions and extreme value methods. The series-parallel and expansion methods, multi-extremum surrogate models and decomposed-coordinated surrogate models are summarized for the multiobjective dynamic reliability analysis of complex structures.

Findings

The numerical complex compound function and turbine blisk are used as examples to illustrate the performance of single-objective and multiobjective dynamic reliability analysis methods. Then the future development direction of dynamic reliability analysis of complex structures is prospected.

Originality/value

The paper provides a useful reference for further theoretical research and engineering application.

Details

International Journal of Structural Integrity, vol. 13 no. 5
Type: Research Article
ISSN: 1757-9864

Keywords

Article
Publication date: 1 June 2015

Jorge Alberto Achcar and Fernando Antonio Moala

The purpose of this paper is to provide a new method to estimate the reliability of series system by using copula functions. This problem is of great interest in industrial and…

Abstract

Purpose

The purpose of this paper is to provide a new method to estimate the reliability of series system by using copula functions. This problem is of great interest in industrial and engineering applications.

Design/methodology/approach

The authors introduce copula functions and consider a Bayesian analysis for the proposed models with application to the simulated data.

Findings

The use of copula functions for modeling the bivariate distribution could be a good alternative to estimate the reliability of a two components series system. From the results of this study, the authors observe that they get accurate Bayesian inferences for the reliability function considering large samples sizes. The Bayesian parametric models proposed also allow the assessment of system reliability for multicomponent systems simultaneously.

Originality/value

Usually, the studies of systems reliability engineering assume independence among the component lifetimes. In the approach the authors consider a dependence structure. Using standard classical inference methods based on asymptotical normality of the maximum likelihood estimators for the parameters the authors could have great computational difficulties and possibly, not accurate inference results, which there is not found in the approach.

Details

International Journal of Quality & Reliability Management, vol. 32 no. 6
Type: Research Article
ISSN: 0265-671X

Keywords

Article
Publication date: 1 May 1990

Usha Sharma and K.B. Misra

A large number of research articles have appeared in the literature during the last two decades on the subject of system reliability optimisation, each with a view to providing…

Abstract

A large number of research articles have appeared in the literature during the last two decades on the subject of system reliability optimisation, each with a view to providing simple, exact and efficient techniques. Here, an efficient, fast and exact technique is proposed for solving integer‐programming problems that normally arise in optimal reliability design problems. The algorithm presented is superior to any of the earlier methods available so far, being based on functional evaluations and a limited systematic search close to the boundary of resources. Thus it can quickly solve even very large system problems. It can also be effectively used with other operations research problems involving integer‐programming formulations.

Details

International Journal of Quality & Reliability Management, vol. 7 no. 5
Type: Research Article
ISSN: 0265-671X

Keywords

1 – 10 of 282