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

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 Survival and failure trends of cerebrospinal fluid shunts with distal slit valves: comparative study and literature review

2020 ◽  
Vol 25 (3) ◽  
pp. 209-216
Author(s):  
Jeremy S. Wetzel ◽  
Alex D. Waldman ◽  
Pavlos Texakalidis ◽  
Bryan Buster ◽  
Sheila R. Eshraghi ◽  
...  
Keyword(s):  
Cerebrospinal Fluid ◽  
Failure Rate ◽  
Csf Shunt ◽  
Time To Failure ◽  
Survival Curves ◽  
Mean Time To Failure ◽  
Distal Catheter ◽  
Catheter Obstruction ◽  
Shunt Survival ◽  
Mean Time

OBJECTIVEThe malfunction rates of and trends in various cerebrospinal fluid (CSF) shunt designs have been widely studied, but one area that has received little attention is the comparison of the peritoneal distal slit valve (DSV) shunt to other conventional valve (CV) type shunts. The literature that does exist comes from older case series that provide only indirect comparisons, and the conclusions are mixed. Here, the authors provide a direct comparison of the overall survival and failure trends of DSV shunts to those of other valve type shunts.METHODSThree hundred seventy-two new CSF shunts were placed in pediatric patients at the authors’ institution between January 2011 and December 2015. Only ventriculoperitoneal (VP) shunts were eligible for study inclusion. Ventriculoatrial, lumboperitoneal, cystoperitoneal, subdural-peritoneal, and spinal shunts were all excluded. Rates and patterns of shunt malfunction were compared, and survival curves were generated. Patterns of failure were categorized as proximal failure, distal failure, simultaneous proximal and distal (proximal+distal) failure, removal for infection, externalization for abdominal pseudocyst, and addition of a ventricular catheter for loculated hydrocephalus.RESULTSA total of 232 VP shunts were included in the final analysis, 115 DSV shunts and 117 CV shunts. There was no difference in the overall failure rate or time to failure between the two groups, and the follow-up period was statistically similar between the groups. The DSV group had a failure rate of 54% and a mean time to failure of 17.8 months. The CV group had a failure rate of 50% (p = 0.50) and a mean time to failure of 18.5 months (p = 0.56). The overall shunt survival curves for these two groups were similar; however, the location of failure was significantly different between the two groups. Shunts with DSVs had proportionately more distal failures than the CV group (34% vs 14%, respectively, p = 0.009). DSV shunts were also found to have proximal+distal catheter occlusions more frequently than CV shunts (23% vs 5%, respectively, p = 0.005). CV shunts were found to have significantly more proximal failures than the DSV shunts (53% vs 27%, p = 0.028). However, the only failure type that carried a statistically significant adjusted hazard ratio in a multivariate analysis was proximal+distal catheter obstruction (CV vs DSV shunt: HR 0.21, 95% CI 0.05–0.81).CONCLUSIONSThere appears to be a difference in the location of catheter obstruction leading to the malfunction of shunts with DSVs compared to shunts with CVs; however, overall shunt survival is similar between the two. These failure types are also affected by other factors such etiology of hydrocephalus and endoscope use. The implications of these findings are unclear, and this topic warrants further investigation.

scholarly journals Reliability Assessment of a Cement Industry by Application of Weibull Method

2019 ◽  
pp. 1-11
Author(s):  
Onoriode K. Idiapho ◽  
William E. Odinikuku ◽  
Onomine M. Akusu
Keyword(s):  
Failure Rate ◽  
Manufacturing Industry ◽  
Software Tool ◽  
Cement Industry ◽  
Time To Failure ◽  
Distribution Method ◽  
Mean Time To Failure ◽  
The Mean ◽  
Cement Manufacturing ◽  
Mean Time

The financial cost of downtime can be very significant, especially in manufacturing industries. As a result, no business wants to experience downtime. In this study, the reliability of two identical machines code named GDA and GDB used in a cement manufacturing industry was assessed by analysis of failure times data of components in the machines by applying Weibull distribution method. The estimates of the Weibull parameters, θ and β were obtained using a reliability software tool ‘Windchill Quality Solutions 11.0 Tryout’ and the mean time to failure, failure rate and reliability of the machines was successfully determined. The result obtained showed that, the machines are undergoing rapid wear out as the values of the shape parameter obtained were greater than four. The plots of the failure rate also showed that the machines are in their wear out periods as the failure rate curves were observed to be increasing. The values of the mean time to failure of the two machines were found to be very close. The reliability of the machines was found to be increasing as their values of scale parameter, θ increases with machine GDA having the highest reliability.

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.

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.

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.

scholarly journals Fuzzy-Logic-Based Mean Time to Failure (MTTF) Analysis of Interleaved Dc-Dc Converters Equipped with Redundant-Switch Configuration

2018 ◽  
Vol 9 (1) ◽  
pp. 88 ◽  
Author(s):  
Tohid Rahimi ◽  
Hossein Jahan ◽  
Frede Blaabjerg ◽  
Amir Bahman ◽  
Seyed Hosseini
Keyword(s):  
Fuzzy Logic ◽  
Markov Models ◽  
Reliability Function ◽  
Time To Failure ◽  
Failure Rates ◽  
Mean Time To Failure ◽  
Passive Components ◽  
Multi Phase ◽  
First Time ◽  
Mean Time

Interleaved dc-dc converters in sensitive applications necessitate an enhanced reliability. An interleaved converter equipped with redundant components can fulfill the reliability requirements. Mean Time to Failure (MTTF), as a reliability index, can be used to evaluate the expected life span of the mentioned converters. The Markov model is a helpful tool to calculate the MTTF in such systems. Different scientific reports denote different failure rates with different weight for power elements. Also, in reliability reports, failure rates of active and passive components are uncertain values. In order to approximate the failure rates fuzzy-logic-based Markov models are proposed in this paper. Then it is used to evaluate the MTTF of an interleaved multi-phase dc-dc converter, which is equipped with parallel and standby switch configurations. For the first time, fuzzy curves for MTTFs of the converters and 3D reliability function are derived in this paper. The reliability analyses give an insight to find the appropriate redundant-switch configurations for interleaved dc-dc converters under different conditions. Simulation and experimental results are provided to lend credence to the viability of the studied redundant-switch configurations in interleaved dc-dc boost converter.

The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

2018 ◽  
pp. 439
Author(s):  
Hazim Mansour Gorgees ◽  
Bushra Abdualrasool Ali ◽  
Raghad Ibrahim Kathum
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Reliability Function ◽  
Bayes Estimator ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Technique ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Better Than

     In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

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