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395037

Statistical Analysis of Inverse Weibull based on Step-Stress Partially Accelerated Life Tests with Unified Hybrid Censoring Data

Article

Last updated: 29 Dec 2024

Subjects

-

Tags

Mathematical Statistics

Abstract

Accelerated life testing (ALT) is a primary method for rapidly evaluating product reliability. This paper focuses on statistical inference for the invertedWeibull distribution under a step-stress partially ALT (SSPALT) model with a unified hybrid censoring scheme. This censoring scheme enhances the efficiency of statistical analysis and reduces overall test time. The inverted Weibull distribution is widely used in reliability engineering to model various failure mechanisms, including infant mortality, wear-out periods, and general life testing scenarios. For the purpose of estimating the model parameters and acceleration factor, the maximum likelihood approach is applied along with the maximum product of the spacing procedure to generate point and interval estimates. The squared error loss function is used to calculate the Bayes point estimates based on the assumption of independent gamma priors. Since Bayesian estimators cannot be derived analytically, we employ the Markov chain Monte Carlo technique. This method allows us to construct credible intervals for the involved parameters of interest and the Bayesian estimates themselves. Asymptotic confidence intervals and confidence intervals using bootstrap-p and bootstrap-t methods are constructed. Moreover the performances of the various estimators of the SSPALT are compared through the simulation study. Based on the numerical results, the Bayes estimates are better than the corresponding other estimates with respect to smallest precision measures. The lengths of creditable interval for Bayesian estimates less than the approximate and Bootstrap confidence intervals for different sample sizes, observed failures, and censoring schemes, in most cases. Additionally, given different sample sizes, reported failures, and censoring techniques, the percentile Bootstrap confidence intervals give more accurate outcomes than Bootstrap-t in most cases. A real data set is used to illustrate the results derived.

DOI

10.21608/cjmss.2024.319502.1072

Keywords

Step-Stress partially accelerated life tests, Unified hybrid censoring, Inverse Weibull distribution, maximum product of spacing estimation, Bayesian estimation

Authors

First Name

Amal

Last Name

Hassan

MiddleName

Soliman

Affiliation

Department of Mathematical Statistics Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt

Email

amal52_soliman@cu.edu.eg

City

Giza

Orcid

0000-0003-4442-8458

First Name

Abd ELwahab

Last Name

Hagag

MiddleName

-

Affiliation

Department of Mathematical Statistics, Faculty of Commerce, AL-AZHAR University, Cairo, Egypt

Email

wahabstat@yahoo.com

City

-

Orcid

-

First Name

Nader

Last Name

Metwally

MiddleName

-

Affiliation

Department of Mathematical Statistics, Faculty of Commerce, AL-AZHAR University, Cairo, Egypt

Email

mu.nader.sh2010@gmail.com

City

-

Orcid

-

First Name

Omar

Last Name

Sery

MiddleName

Hussein

Affiliation

Department of Mathematical Statistics, Faculty of Commerce, AL-AZHAR University, Cairo, Egypt

Email

omarsery81@yahoo.com

City

-

Orcid

-

Volume

4

Article Issue

1

Related Issue

50936

Issue Date

2025-04-01

Receive Date

2024-09-09

Publish Date

2025-04-01

Page Start

162

Page End

185

Print ISSN

2974-3435

Online ISSN

2974-3443

Link

https://cjmss.journals.ekb.eg/article_395037.html

Detail API

https://cjmss.journals.ekb.eg/service?article_code=395037

Order

395,037

Type

Original Article

Type Code

2,545

Publication Type

Journal

Publication Title

Computational Journal of Mathematical and Statistical Sciences

Publication Link

https://cjmss.journals.ekb.eg/

MainTitle

Statistical Analysis of Inverse Weibull based on Step-Stress Partially Accelerated Life Tests with Unified Hybrid Censoring Data

Details

Type

Article

Created At

29 Dec 2024