scholarly journals Optimum Times for Step-Stress Cumulative Exposure Model Using Log-Logistic Distribution with Known Scale Parameter

2016 ◽  
Vol 38 (1) ◽  
Author(s):  
Abedel-Qader Al-Masri ◽  
Mohammed Al-Haj Ebrahem
Keyword(s):  
Scale Parameter ◽  
Asymptotic Variance ◽  
Life Time ◽  
Cumulative Exposure ◽  
Exposure Model ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Cumulative Exposure Model ◽  
Simple Step ◽  
Design Stress

In this paper we assume that the life time of a test unit follows a log-logistic distribution with known scale parameter. Tables of optimum times of changing stress level for simple step-stress plans under a cumulative exposure model are obtained by minimizing the asymptotic variance of the maximum likelihood estimator of the model parameters at the design stress with respect to the change time.

Simple step-stress model for an extension of the exponential distribution with type-I censoring

2015 ◽  
Vol 32 (8) ◽  
pp. 906-920 ◽  
Author(s):  
Firoozeh Haghighi
Keyword(s):  
Exponential Distribution ◽  
Maximum Likelihood Estimates ◽  
Cumulative Exposure ◽  
Exposure Model ◽  
Type I ◽  
Stress Model ◽  
Content Type ◽  
Type I Censoring ◽  
Cumulative Exposure Model ◽  
Simple Step

Purpose – The purpose of this paper is to design a simple step-stress model under type-I censoring when the failure time has an extension of the exponential distribution. Design/methodology/approach – The scale parameter of the distribution is assumed to be a log-linear function of the stress and a cumulative exposure model is hold. The maximum likelihood estimates of the parameters, as well as the corresponding Fisher information matrix are derived. Two real examples are given to show the application of an extension of the exponential distribution in reliability studies and a numerical example is presented to illustrate the method discussed here. Findings – A simple step-stress test under cumulative exposure model and type-I censoring for an extension of the exponential distribution is presented. Originality/value – The work is original.

ESTIMATIONS FOR A SIMPLE STEP-STRESS MODEL WITH PROGRESSIVELY TYPE-II CENSORED DATA

2005 ◽  
Vol 12 (05) ◽  
pp. 385-395
Author(s):  
SHUO-JYE WU ◽  
HSIU-MEI LEE ◽  
DAR-HSIN CHEN
Keyword(s):  
Failure Time ◽  
Cumulative Exposure ◽  
Exposure Model ◽  
Model Parameters ◽  
Stress Model ◽  
Type Ii ◽  
Failure Time Distribution ◽  
Type Ii Censored Data ◽  
Simple Step ◽  
Log Linear

With today's high technology, some life tests result in no or very few failures by the end of test. In such cases, an approach is to do life test at higher-than-usual stress conditions in order to obtain failures quickly. This study discusses the point and interval estimations of parameters on the simple step-stress model in accelerated life testing with progressive type II censoring. An exponential failure time distribution with mean life that is a log-linear function of stress and a cumulative exposure model are considered. We derive the maximum likelihood estimators of the model parameters. Confidence intervals for the model parameters are established by using pivotal quantity and can be applied to any sample size. A numerical example is investigated to illustrate the proposed methods.

scholarly journals Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1786 ◽  
Author(s):  
A. M. Abd El-Raheem ◽  
M. H. Abu-Moussa ◽  
Marwa M. Mohie El-Din ◽  
E. H. Hafez
Keyword(s):  
Simulation Study ◽  
Stress Test ◽  
Real Data ◽  
Accelerated Life Test ◽  
Maximum Likelihood Estimates ◽  
Cumulative Exposure ◽  
Exposure Model ◽  
Model Parameters ◽  
Data Set ◽  
Accelerated Life

In this article, a progressive-stress accelerated life test (ALT) that is based on progressive type-II censoring is studied. The cumulative exposure model is used when the lifetime of test units follows Pareto-IV distribution. Different estimates as the maximum likelihood estimates (MLEs) and Bayes estimates (BEs) for the model parameters are discussed. Bayesian estimates are derived while using the Tierney and Kadane (TK) approximation method and the importance sampling method. The asymptotic and bootstrap confidence intervals (CIs) of the parameters are constructed. A real data set is analyzed in order to clarify the methods proposed through this paper. Two types of the progressive-stress tests, the simple ramp-stress test and multiple ramp-stress test, are compared through the simulation study. Finally, some interesting conclusions are drawn.

Practical lifetime estimation strategy based on partially step-stress-accelerated degradation tests

2017 ◽  
Vol 231 (5) ◽  
pp. 605-614 ◽  
Author(s):  
Yong Soo Kim ◽  
Si-Il Sung
Keyword(s):  
Asymptotic Variance ◽  
Reliability Estimation ◽  
Cumulative Exposure ◽  
Exposure Model ◽  
Test Plan ◽  
Test Scenario ◽  
Lifetime Estimation ◽  
Estimation Strategy ◽  
Accelerated Degradation ◽  
Development Scenarios

The number of samples available for testing of a newly developed item is quite small, and only limited reliability information is available in many real cases. Therefore, a multi-purpose test plan is essential for reliability estimation. To reflect real product development scenarios, this study presents a practical lifetime estimation strategy based on a partially step-stress-accelerated degradation test (PSSADT) with three stress levels. The PSSADT plan assumes that the degradation path follows a Wiener process and that the cumulative exposure model holds. The proposed test plan determines the stress level in the final loaded step that minimizes the asymptotic variance of the maximum likelihood estimator of the qth quantile of the lifetime distribution under the use condition. Finally, the test scenario, which includes the necessary validity check of the acceleration model, is illustrated with an example.

On optimal operational sequence of components in a warm standby system

2018 ◽  
Vol 55 (4) ◽  
pp. 1014-1024 ◽  
Author(s):  
Maxim Finkelstein ◽  
Nil Kamal Hazra ◽  
Ji Hwan Cha
Keyword(s):  
Open Problem ◽  
Cumulative Exposure ◽  
Exposure Model ◽  
Virtual Age ◽  
Cumulative Exposure Model ◽  
Standby System ◽  
Stochastic Precedence ◽  
Warm Standby

Abstract We consider an open problem of obtaining the optimal operational sequence for the 1-out-of-n system with warm standby. Using the virtual age concept and the cumulative exposure model, we show that the components should be activated in accordance with the increasing sequence of their lifetimes. Lifetimes of the components and the system are compared with respect to the stochastic precedence order and its generalization. Only specific cases of this optimal problem were considered in the literature previously.

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