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 Parameter Estimation Based on the Frèchet Progressive Type II Censored Data with Binomial Removals

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Mohamed Mubarak
Keyword(s):  
Censored Data ◽  
Time Distribution ◽  
Maximum Likelihood Method ◽  
Failure Time ◽  
Likelihood Method ◽  
Type Ii ◽  
Failure Time Distribution ◽  
Sampling Distributions ◽  
Progressive Type ◽  
Type Ii Censored Data

This paper considers the estimation problem for the Frèchet distribution under progressive Type II censoring with random removals, where the number of units removed at each failure time has a binomial distribution. We use the maximum likelihood method to obtain the estimators of parameters and derive the sampling distributions of the estimators, and we also construct the confidence intervals for the parameters and percentile of the failure time distribution.

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.

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.

scholarly journals Estimation procedures on Type-II censored data from a scaled Muth distribution

2021 ◽  
pp. 148-158
Author(s):  
Hayrinisa Demirci BIÇER
Keyword(s):  
Censored Data ◽  
Mean Squared Error ◽  
Real Life ◽  
Model Parameters ◽  
Type Ii ◽  
Monte Carlo Simulation Study ◽  
Anal Ysis ◽  
Squared Error ◽  
Type Ii Censored Data ◽  
Censoring Scheme

In the present paper, we consider the estimation problem for the scaled Muth distribution under Type-II censoring scheme. In order to estimate the model parameters α and β, the maximum likelihood, the least-squares, and the maximum spacing estimators are derived. To show estimation efficiencies of the estimators obtained with this paper, we present an exten- sive Monte-Carlo simulation study in which the estimators are compared according to bias and mean squared error criteria. Furthermore, we evaluate the applicability of the scaled Muth distribution by taking into account both full and Type-II censored data situations by an anal- ysis conducted on a real-life dataset.

scholarly journals Point and Interval Estimation for a Simple Step-Stress Model with Type-II Censoring

2007 ◽  
Vol 39 (1) ◽  
pp. 35-47 ◽  
Author(s):  
N. Balakrishnan ◽  
Debasis Kundu ◽  
Keung Tony Ng ◽  
Nandini Kannan
Keyword(s):  
Interval Estimation ◽  
Stress Model ◽  
Type Ii ◽  
Type Ii Censoring ◽  
Simple Step
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