A Bayesian Estimation of Reliability Measures of Stepwise Exponential Distribution System

1993 ◽  
Vol 115 (1) ◽  
pp. 61-68
Author(s):  
M. H. Hu
Keyword(s):  
Bayesian Estimation ◽  
Exponential Distribution ◽  
Distribution System ◽  
Failure Process ◽  
Reliability Function ◽  
Distribution Model ◽  
Time To Failure ◽  
Reliability Measures ◽  
Posterior Probability Density ◽  
Mean Time

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 functions of time. Such a system is called a stepwise exponential distribution system. This kind of failure process can take place in various kinds of equipment. This paper deals with the system having components in a series arrangement. Bayesian statistics are used in defining prior and posterior probability density functions of failure and repair rates. These functions provide information for the estimation of several 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. Bayesian estimation of the stepwise exponential distribution model is useful in the planning predictive maintenance of equipment.

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.

scholarly journals Systematic Routine for Setting Confidence Levels for Mean Time to Failure (MTTF)

2014 ◽  
Vol 2 (1) ◽  
pp. 62-69 ◽  
Author(s):  
Jimin Lee ◽  
Robert Yearout ◽  
Donna Parsons
Keyword(s):  
Density Function ◽  
Exponential Distribution ◽  
Failure Rate ◽  
Survival Data ◽  
Reliability Function ◽  
Time To Failure ◽  
Mean Time To Failure ◽  
Arrival Times ◽  
Negative Exponential ◽  
Mean Time

There are circumstances where an item is intentionally tested to destruction.  The purpose of this technique is to determine the failure rate (λ) of a tested item.  For these items, the quality attribute is defined as how long the item will last until failure.  Once the failure rate is determined from the number of survivors and total time of all items tested the mean time to failure (MTTF) which is a typical statistic for survival data analysis issues.  MTTF is calculated by dividing one by failure rate (λ).  From this one obtains the reliability function R(t) = e-λt where t is time.  This allows the cumulative density function F(t) = 1- e-λt  to be determined.  This density function, f(t) = λe-λt is a negative exponential with a standard deviation (σ) = 1/λ.  Thus setting a warranty policy for the tested item is difficult for the practitioner.  An important property of the exponential distribution is that it is memory less.  This means its conditional probability follows P(T > s + t |T > s)=P(T > t) for all s, t ≥0.  The exponential distribution can be used to describe the interval lengths between any two consecutive arrival times in a homogeneous Poisson process.  The purpose of this research paper is to present a simple technique to determine a realistic confidence level. Using the same technique the warranty level for the tested item can be predicted.

Analysis and genetic algorithm optimization of a series system with K-out-of-(n + m): G mixed standby subsystems subject to imperfect switching and elapsed repair time

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Neama Temraz
Keyword(s):  
Genetic Algorithm ◽  
Exponential Distribution ◽  
Failure Process ◽  
Repair Time ◽  
Allocation Problem ◽  
General Distribution ◽  
Time To Failure ◽  
Redundancy Allocation Problem ◽  
Redundancy Allocation ◽  
Content Type

PurposeIn this paper, a new general system consisted of l subsystems connected in series is introduced. Each subsystem connected in K-out-of-(n + m): G mixed standby configuration.Design/methodology/approachThe lifetime of the system's units is assumed to be exponentially distributed and there is elapsed repair time with general distribution. The switch in each subsystem is assumed to be imperfect with the failure process follows an exponential distribution. A genetic algorithm is applied to the system to obtain the optimal solution of the system and solve the redundancy allocation problem.FindingsAnalysis of availability, reliability, mean time to failure and steady-state availability of the system is introduced. The measures of the system are discussed in special two cases when the elapsed repair time follows gamma and exponential distribution. An optimization problem with bi-objective functions is introduced to minimize the cost of the system and maximize the reliability function. A numeric application is introduced to show the implementation and effectiveness of the system and redundancy allocation problem.Originality/valueA new general K-out-of-(n + m): G mixed standby model with elapsed repair time and imperfect switching is introduced.

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.

Real Time Reliability Study of a Model with Increasing Failure Rates

2011 ◽  
Vol 110-116 ◽  
pp. 2774-2779
Author(s):  
Mani Sharifi ◽  
Ehsan Hashemi ◽  
Peyman Farahpour
Keyword(s):  
Failure Rate ◽  
Reliability Function ◽  
Spare Parts ◽  
Time Dependent ◽  
Main Element ◽  
Time To Failure ◽  
Reliability Study ◽  
The Third ◽  
Working Element ◽  
Mean Time

This paper deals with a system with elements with one element is the main element and the other elements are the spare parts of the main element. If one element fails, one of the spare parts starts working immediately. The failure rate of non working elements are zero and the failure rate of working element is time dependent as and the failed elements are not repairable. The system works until all elements failed. In the second part of this paper the differential equations between the state of the system are established and by solving this equation the reliability function of the system () is calculated. In the third part, a numerical example solved to determine the parameters of the system. Nomenclature The notations used in this paper are as follows: : Number of elements, : Failure rate of each element at time, : Probability that the system is in state with spare element at time, : Probability that system works at time, : Mean time to failure of the system,

SOFTWARE RELIABILITY ANALYSIS INCORPORATING SECOND-ORDER ARCHITECTURAL STATISTICS

2005 ◽  
Vol 12 (03) ◽  
pp. 267-290 ◽  
Author(s):  
SWAPNA S. GOKHALE
Keyword(s):  
Sensitivity Analysis ◽  
Reliability Function ◽  
Accurate Estimate ◽  
Second Order ◽  
Time To Failure ◽  
Mean Time To Failure ◽  
Solution Approach ◽  
Composite Approach ◽  
Composite Solution ◽  
Mean Time

Architecture-based techniques for reliability assessment of software applications have received increased attention in the past few years due to the advent of component-based software development paradigm. Most of the prior research efforts in architecture-based analysis use the composite solution approach to solve the architecture-based models in order to estimate application reliability. Though the composite solution approach produces an accurate estimate of application reliability, it suffers from several drawbacks. The most notable drawback of the composite solution approach is that it does not allow an analysis of the sensitivity of the application reliability to the reliabilities of the components comprising the application and the application structure. The hierarchical solution approach on the other hand, has the potential of overcoming the drawbacks of the composite approach. However, in the present form, the hierarchical solution approach produces an estimate of application reliability which is only an approximation of the estimate produced by the composite approach since it does not take into consideration the second-order architectural statistics. Also, although the hierarchical solution approach can be used for sensitivity analysis, mathematical techniques to perform such analysis are lacking. Development of an accurate hierarchical solution approach to estimate application reliability based on its architecture is the focus of this paper. Using the approach described in this paper, an analytical application reliability function which incorporates second-order architectural statistics can be obtained. Sensitivity analysis techniques and expressions to determine the mean time to failure of the application are developed based on this analytical reliability function. We illustrate the reliability prediction, sensitivity analysis, and mean time to failure computation techniques presented in this paper using two case studies.

Reliability and Availability analysis of a cloud computing transition system under multiple failures

2020 ◽  
Vol 37 (6/7) ◽  
pp. 823-835
Author(s):  
Monika Manglik ◽  
Nitesh Rawat ◽  
Mangey Ram
Keyword(s):  
Mathematical Model ◽  
Cloud Computing ◽  
Design Methodology ◽  
Transition System ◽  
Time To Failure ◽  
Reliability Measures ◽  
Variable Technique ◽  
Content Type ◽  
Availability Analysis ◽  
Mean Time

PurposeTo analyze the performance of multistate cloud computing transition system through the various reliability measures is the purpose of this paper.Design/methodology/approachIn this article, a mathematical model for a multistate cloud computing transition system with various types of failures has been analyzed by using the Markov process, supplementary variable technique and Laplace transformation.FindingsVarious reliability measures such that reliability, availability, mean time to failure (MTTF), mean time to repair and cost analysis have also been analyzed. This article presents some geographic illustrations for the practical utility of the model.Originality/valueThe authors developed a mathematical model to analyze the reliability of the cloud computing transition system by considering the possible failures.

scholarly journals Copula based Measures of Repairable Parallel System with Fault Coverage

2020 ◽  
Vol 6 (1) ◽  
pp. 322-344
Author(s):  
Vaishali Tyagi ◽  
Ritu Arora ◽  
Mangey Ram ◽  
Ioannis S. Triantafyllou
Keyword(s):  
Process Time ◽  
Time To Failure ◽  
Supplementary Variable ◽  
Coverage Factor ◽  
Reliability Measures ◽  
Failed State ◽  
Finite State ◽  
Laplace Transformations ◽  
Human Failure ◽  
Mean Time

The main objective of this study is to analyse the reliability behaviour of parallel systems with three types of failure, namely unit failure, human failure and major failure. For this purpose, we apply three different statistical techniques, namely copula, coverage and copula-coverage. More precisely, this study presents a stochastic model for analysing the behaviour of a multi-state system consisting of two non-identical units by incorporating the concept of coverage factor and two types of repair facilities between failed state to a normal state. The system could be characterized as being in a failed state due to unit failures, human failure and major failures, such as catastrophic and environmental failure. All failure rates are constant and it is assumed that these are exponentially distributed whereas, repair rates follow the Gumbel-Hougaard copula distribution. The entire system is modelled as a finite-state Markov process. Time-dependent reliability measures like availability, reliability and mean time to failure (MTTF) are obtained by supplementary variable techniques and Laplace transformations. The present study provides a comparative analysis for reliability measures among the aforementioned techniques, while a discussion referring to which technique makes the system more reliable is also developed. Furthermore, numerical simulations are presented to validate the analytical results.

scholarly journals m-Consecutive-k-out-of-n: F Structures with a Single Change Point

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2203
Author(s):  
Ioannis S. Triantafyllou
Keyword(s):  
Explicit Expression ◽  
Present Article ◽  
Change Point ◽  
Reliability Function ◽  
Time To Failure ◽  
Mean Time To Failure ◽  
Independent Components ◽  
Mean Time ◽  
Shed Light ◽  
General Setup

In the present article, we introduce the m-consecutive-k-out-of-n:F structures with a single change point. The aforementioned system consists of n independent components, of which the first n1 units are identically distributed with common reliability p1, while the remaining ones share a different functioning probability p2. The general setup of the proposed reliability structures is presented in detail, while an explicit expression for determining the number of its path sets of a given size is derived. Additionally, closed formulae for the reliability function and mean time to failure of the aforementioned models are also provided. For illustration purposes, several numerical results and comparisons are presented in order to shed light on the performance of the proposed structure.

Research on Maintenance Strategy of Large-Scale Grab Ship Unloader Based on Reliability

2013 ◽  
Vol 770 ◽  
pp. 289-293
Author(s):  
Guang Jun Liu ◽  
Bang Xin Han ◽  
Guang Yu Tan ◽  
Guang Hui Li ◽  
Yuan Tao Sun
Keyword(s):  
Large Scale ◽  
Distribution Model ◽  
Time To Failure ◽  
Maintenance Strategy ◽  
Failure Data ◽  
Reliability Centered Maintenance ◽  
Maintenance Time ◽  
The Mean ◽  
Scientific Decision ◽  
Mean Time

t is hard to acquire the failure data of ship unloader and the mean time to failure is not independent identically distributed, and there are many defects existed in the maintenance method such as high cost and bad effect. In this work, we propose a method based on Weibull Distribution model to deal with the failure data of a large-scale grab ship unloader, build up the model of MTBF (Mean Time Between Failure) and preventive maintenance time, and show the example with failure data, which provides references to maintenance of the ship unloader. Finally, we present the decision process of the reliability-centered maintenance strategy, maintenance type of the grab ship unloader and the maintenance of the key parts, which provides scientific decision support for the maintenance of the ship unloader equipments.

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