Failure Rate, Vitality, and Residual Lifetime Measures: Characterizations Based on Stress-strength Bivariate Model with Application to an Automated Life Test Data

Mohamed S. Eliwa; Abhishek Tyagi; Morad Alizadeh; Mahmoud El-Morshedy

doi:10.19139/soic-2310-5070-1321

Failure Rate, Vitality, and Residual Lifetime Measures: Characterizations Based on Stress-strength Bivariate Model with Application to an Automated Life Test Data

Mohamed S. Eliwa, Abhishek Tyagi, Morad Alizadeh, Mahmoud El-Morshedy

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this article, we introduce some reliability concepts for the bivariate Pareto Type II distribution including joint hazard rate function, CDF for parallel and series systems, joint mean residual lifetime, and joint vitality function. The maximum likelihood and Bayesian estimation methods are utilized to estimate the model parameters. Simulation is carried out to assess the performance of the maximum likelihood and Bayesian estimators, and it is found that the two approaches work quite well in estimation process. Finally, a real lifetime data is analyzed to show the flexibility and the importance of the introduced bivariate mode.

Original language	English
Pages (from-to)	256-266
Number of pages	11
Journal	Statistics, Optimization and Information Computing
Volume	12
Issue number	1
DOIs	https://doi.org/10.19139/soic-2310-5070-1321
State	Published - Jan 2024

Keywords

Bayes theorem
Bivariate distributions
Failure analysis
Maximum likelihood method
Simulation
Statistics and numerical data

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10.19139/soic-2310-5070-1321

Cite this

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title = "Failure Rate, Vitality, and Residual Lifetime Measures: Characterizations Based on Stress-strength Bivariate Model with Application to an Automated Life Test Data",

abstract = "In this article, we introduce some reliability concepts for the bivariate Pareto Type II distribution including joint hazard rate function, CDF for parallel and series systems, joint mean residual lifetime, and joint vitality function. The maximum likelihood and Bayesian estimation methods are utilized to estimate the model parameters. Simulation is carried out to assess the performance of the maximum likelihood and Bayesian estimators, and it is found that the two approaches work quite well in estimation process. Finally, a real lifetime data is analyzed to show the flexibility and the importance of the introduced bivariate mode.",

keywords = "Bayes theorem, Bivariate distributions, Failure analysis, Maximum likelihood method, Simulation, Statistics and numerical data",

author = "Eliwa, \{Mohamed S.\} and Abhishek Tyagi and Morad Alizadeh and Mahmoud El-Morshedy",

note = "Publisher Copyright: {\textcopyright} 2024 International Academic Press",

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doi = "10.19139/soic-2310-5070-1321",

language = "English",

volume = "12",

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Failure Rate, Vitality, and Residual Lifetime Measures: Characterizations Based on Stress-strength Bivariate Model with Application to an Automated Life Test Data. / Eliwa, Mohamed S.; Tyagi, Abhishek; Alizadeh, Morad et al.
In: Statistics, Optimization and Information Computing, Vol. 12, No. 1, 01.2024, p. 256-266.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - Failure Rate, Vitality, and Residual Lifetime Measures

T2 - Characterizations Based on Stress-strength Bivariate Model with Application to an Automated Life Test Data

AU - Eliwa, Mohamed S.

AU - Tyagi, Abhishek

AU - Alizadeh, Morad

AU - El-Morshedy, Mahmoud

PY - 2024/1

Y1 - 2024/1

N2 - In this article, we introduce some reliability concepts for the bivariate Pareto Type II distribution including joint hazard rate function, CDF for parallel and series systems, joint mean residual lifetime, and joint vitality function. The maximum likelihood and Bayesian estimation methods are utilized to estimate the model parameters. Simulation is carried out to assess the performance of the maximum likelihood and Bayesian estimators, and it is found that the two approaches work quite well in estimation process. Finally, a real lifetime data is analyzed to show the flexibility and the importance of the introduced bivariate mode.

AB - In this article, we introduce some reliability concepts for the bivariate Pareto Type II distribution including joint hazard rate function, CDF for parallel and series systems, joint mean residual lifetime, and joint vitality function. The maximum likelihood and Bayesian estimation methods are utilized to estimate the model parameters. Simulation is carried out to assess the performance of the maximum likelihood and Bayesian estimators, and it is found that the two approaches work quite well in estimation process. Finally, a real lifetime data is analyzed to show the flexibility and the importance of the introduced bivariate mode.

KW - Bayes theorem

KW - Bivariate distributions

KW - Failure analysis

KW - Maximum likelihood method

KW - Simulation

KW - Statistics and numerical data

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M3 - Article

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SN - 2311-004X

VL - 12

SP - 256

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JO - Statistics, Optimization and Information Computing

JF - Statistics, Optimization and Information Computing

IS - 1

ER -

Failure Rate, Vitality, and Residual Lifetime Measures: Characterizations Based on Stress-strength Bivariate Model with Application to an Automated Life Test Data

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Keywords

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