Statistical Inference for a Lognormal Step-Stress Model With Type-I Censoring

Author

Lin, Chien-Tai ; Chou, Cheng-Chieh

Author_Institution

Dept. of Math., Tamkang Univ., Taipei, Taiwan

Volume

61

Issue

2

fYear

2012

fDate

6/1/2012 12:00:00 AM

Firstpage

361

Lastpage

377

Abstract

We consider a k -step step-stress model under Type-I censoring. We obtain the maximum likelihood estimates (MLE) of the parameters assuming a cumulative exposure model with lifetimes being lognormal distributed. A two-stage algorithm integrating a modified simulated annealing algorithm with a Newton-Raphson method is proposed to compute the MLE of the parameters. We also derive the confidence intervals for the parameters using asymptotic distributions, a likelihood ratio test, and parametric bootstrap resampling methods. The performance of the point and interval estimation of the parameters are evaluated through a Monte Carlo simulation study.

Keywords

Monte Carlo methods; Newton-Raphson method; life testing; log normal distribution; maximum likelihood estimation; simulated annealing; Monte Carlo simulation; Newton-Raphson method; asymptotic distribution; cumulative exposure model; interval estimation; k-step step-stress model; lognormal step-stress model; maximum likelihood estimates; parametric bootstrap resampling method; simulated annealing; statistical inference; type-I censoring; Algorithm design and analysis; Convergence; Data models; Mathematical model; Maximum likelihood estimation; Simulated annealing; Stress; Accelerated life test; Fisher information matrix; bootstrap; cumulative exposure model; maximum likelihood method; simulated annealing algorithm;

fLanguage

English

Journal_Title

Reliability, IEEE Transactions on

Publisher

ieee

ISSN

0018-9529

Type

jour

DOI

10.1109/TR.2012.2194178

Filename

6191341