Confidence Limits for Systems Consisting of Units with Exponential Distribution of Time to Failure

2007 ◽  
pp. 282-327
Keyword(s):  
Exponential Distribution ◽  
Time To Failure ◽  
Confidence Limits

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.

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.

scholarly journals A Note on the Time to Failure of a Two-Unit Parallel Redundant System with Deterioration on a Lattice

2020 ◽  
Vol 6 (1) ◽  
pp. 3-14
Author(s):  
Tadashi Dohi ◽  
Junjun Zheng ◽  
Hiroyuki Okamura
Keyword(s):  
Laplace Transform ◽  
Closed Form ◽  
Exponential Distribution ◽  
System Failure ◽  
Time To Failure ◽  
Redundant System ◽  
Bivariate Exponential Distribution ◽  
Multi Stage ◽  
Bivariate Exponential ◽  
The Laplace Transform

In this paper, we consider a two-unit parallel redundant system with deterioration on a lattice, where each unit has multi-stage deterioration levels, say, n levels. The transition from one deterioration level to the subsequent level occurs following the well-known Marshall-Olkin bivariate exponential distribution. We derive the closed form of the Laplace transform of the time to system failure in the two-unit parallel redundant system with deterioration on n×n lattice without repair and simultaneous failure, as well as the simple system on 3×3 lattice.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document