Constant Stress Partially Accelerated Life Tests for Extended Generalized log Logistic Distribution Based on Type I Censored Competing Risks Data

Elgabry Gamalat; Rezk Hoda

doi:doi:10.11648/j.sjams.20210901.12

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Constant Stress Partially Accelerated Life Tests for Extended Generalized log Logistic Distribution Based on Type I Censored Competing Risks Data

Elgabry Gamalat, Rezk Hoda

Published in Science Journal of Applied Mathematics and Statistics (Volume 9, Issue 1)

Received: 22 January 2021 Accepted: 7 February 2021 Published: 23 February 2021

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Abstract

As a result of technology improvement getting information about products and materials lifetimes under usual conditions. Therefore accelerated life testing or partially accelerated life testing usually are used to truncate the tests survives. The test items under accelerated life testing run under accelerated conditions and partially life tests run under both accelerated and use conditions. The main idea of accelerated life testing that the acceleration element is not unknown or the mathematical model relating the lifetime of the unit and the stress is known or can be assumed. In some cases, neither acceleration factor nor life-stress relations are not unknown. This paper concerned with studying and discussed the constant–stress partially accelerated life test (CPALT) under type I censored (T.I.C) competing risks data. Failure times resulting from T.I.C competing risks data are assumed to follow the Extended generalized log logistic (EGLL) distribution because this model is completely flexible to study positive data. This distribution is applied in various fields, for example lifetime studies, economics, finance and insurance. The maximum likelihood (ML) method is used to estimate the parameters under TIC competing risks data. The simulation algorithm is performed to assess the theoretical results of the maximum likelihood estimates based on TIC competing risks data.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 9, Issue 1)
DOI	10.11648/j.sjams.20210901.12
Page(s)	15-19
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Constant Stress Partially Accelerated Life Test, Type I Censored Data, Cot Ending Failure Causes, Maximum Likelihood Method

References

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[2]	A. Abdel-Hamid, E K. Al-Hussaini. Inference and Optimal Design Based on Step—Partially Accelerated Life Tests for the Generalized Pareto Distribution under Progressive Type-I Censoring, Communications in Statistics - Simulation and Computation, 44, (2014); 1750-1769.
[3]	AS. Hassan, MS. Assar, AN, Zaky Constant-stress partially accelerated life tests for inverted Weibull distribution with multiple censored data. Int J Adv Stat Probab 3 (1) (2015): 72–82.
[4]	A S. Hassan, S. G. Nassr, S. Pramanik, S. S. Maiti. Estimation in Constant Stress Partially Accelerated Life Tests for Weibull Distribution Based on Censored Competing Risks Data, Annals of Data Science, 7 (7) (2019): 45-62.
[5]	H H. Abu-Zinadah and N. S. Ahmed Competing Risks Model with Partially Step-Stress Accelerate Life Tests in Analyses Lifetime Chen Data under Type-II Censoring Scheme, Open Physics, 7 (1) (2019): 192-199.
[6]	A. A. Ismail. Inference in the generalized exponential distribution under partially accelerated tests with progressive Type-II censoring", Theoretical and Applied Fracture Mechanics, 59 (2012): 49-56.
[7]	A.A. Ismail, A.A. Al-babtain, Planning failure-censored constant-stress partially accelerated life test, Journal of Systems Engineering and Electronics, 26 (3) (2015): 644-650.
[8]	Ali A. Ismail, A. Al Tamimi. Optimum Constant- Stress Partially Accelerated Life Test Plans Using Type-I Censored Data from the Inverse Weibull Distribution, Strength of Materials, 9 (3), (2018): 1-9.
[9]	A. A. Ismail, M. M. Al-Harbi, Statistical Inference of Constant-Stress Partially Accelerated Life Test Model Using Failure-Censored Data from the Linear Failure Rate Distribution, Strength of Materials, 51, (2019): 122-129.
[10]	X. Li, H. Zheng, Estimation and Optimum Constant-Stress Partially Accelerated Life Test Plans for Gompertz Distribution with Type with Type-I Censoring, Communications in Statistics - Theory and Methods (2015): 1-15.
[11]	S. Zarrin, M. Kamal, S. Saxena, Estimation constant stress partially accelerated life tests for Rayleing distribution under Type-I Censoring, Reliability Theory and Applications 4 (27) 2012 41–52.
[12]	Mohamad A. Fawzy. Prediction of Kumaraswamy distribution in constant‐stress model based on type‐I hybrid censored data, Statistical Analysis and Data Mining: The ASA Data Science Journal, 13 (2020): 205-215.
[13]	S. Lima, and G. Corderio, The Extended Log-Logistic Distribution: Properties and Application, Annals of the Brazilian Academy of Sciences, 89 (2017), 3-17.
[14]	DR. Cox The analysis of exponentially distributed with two types of failure. J R Stat Ser B 21 (1959): 411–421.
[15]	MJ. Crowder Classical competing risks model. Chapman & Hall/CRC, (2001) New York.

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APA Style

Elgabry Gamalat, Rezk Hoda. (2021). Constant Stress Partially Accelerated Life Tests for Extended Generalized log Logistic Distribution Based on Type I Censored Competing Risks Data. Science Journal of Applied Mathematics and Statistics, 9(1), 15-19. https://doi.org/10.11648/j.sjams.20210901.12

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ACS Style

Elgabry Gamalat; Rezk Hoda. Constant Stress Partially Accelerated Life Tests for Extended Generalized log Logistic Distribution Based on Type I Censored Competing Risks Data. Sci. J. Appl. Math. Stat. 2021, 9(1), 15-19. doi: 10.11648/j.sjams.20210901.12

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AMA Style

Elgabry Gamalat, Rezk Hoda. Constant Stress Partially Accelerated Life Tests for Extended Generalized log Logistic Distribution Based on Type I Censored Competing Risks Data. Sci J Appl Math Stat. 2021;9(1):15-19. doi: 10.11648/j.sjams.20210901.12

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@article{10.11648/j.sjams.20210901.12,
  author = {Elgabry Gamalat and Rezk Hoda},
  title = {Constant Stress Partially Accelerated Life Tests for Extended Generalized log Logistic Distribution Based on Type I Censored Competing Risks Data},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {9},
  number = {1},
  pages = {15-19},
  doi = {10.11648/j.sjams.20210901.12},
  url = {https://doi.org/10.11648/j.sjams.20210901.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20210901.12},
  abstract = {As a result of technology improvement getting information about products and materials lifetimes under usual conditions. Therefore accelerated life testing or partially accelerated life testing usually are used to truncate the tests survives. The test items under accelerated life testing run under accelerated conditions and partially life tests run under both accelerated and use conditions. The main idea of accelerated life testing that the acceleration element is not unknown or the mathematical model relating the lifetime of the unit and the stress is known or can be assumed. In some cases, neither acceleration factor nor life-stress relations are not unknown. This paper concerned with studying and discussed the constant–stress partially accelerated life test (CPALT) under type I censored (T.I.C) competing risks data. Failure times resulting from T.I.C competing risks data are assumed to follow the Extended generalized log logistic (EGLL) distribution because this model is completely flexible to study positive data. This distribution is applied in various fields, for example lifetime studies, economics, finance and insurance. The maximum likelihood (ML) method is used to estimate the parameters under TIC competing risks data. The simulation algorithm is performed to assess the theoretical results of the maximum likelihood estimates based on TIC competing risks data.},
 year = {2021}
}

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TY  - JOUR
T1  - Constant Stress Partially Accelerated Life Tests for Extended Generalized log Logistic Distribution Based on Type I Censored Competing Risks Data
AU  - Elgabry Gamalat
AU  - Rezk Hoda
Y1  - 2021/02/23
PY  - 2021
N1  - https://doi.org/10.11648/j.sjams.20210901.12
DO  - 10.11648/j.sjams.20210901.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 15
EP  - 19
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20210901.12
AB  - As a result of technology improvement getting information about products and materials lifetimes under usual conditions. Therefore accelerated life testing or partially accelerated life testing usually are used to truncate the tests survives. The test items under accelerated life testing run under accelerated conditions and partially life tests run under both accelerated and use conditions. The main idea of accelerated life testing that the acceleration element is not unknown or the mathematical model relating the lifetime of the unit and the stress is known or can be assumed. In some cases, neither acceleration factor nor life-stress relations are not unknown. This paper concerned with studying and discussed the constant–stress partially accelerated life test (CPALT) under type I censored (T.I.C) competing risks data. Failure times resulting from T.I.C competing risks data are assumed to follow the Extended generalized log logistic (EGLL) distribution because this model is completely flexible to study positive data. This distribution is applied in various fields, for example lifetime studies, economics, finance and insurance. The maximum likelihood (ML) method is used to estimate the parameters under TIC competing risks data. The simulation algorithm is performed to assess the theoretical results of the maximum likelihood estimates based on TIC competing risks data.
VL  - 9
IS  - 1
ER  -

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Author Information

Elgabry Gamalat

Department of Statistics, Faculty of Commerce, AL-Azhar University, Cairo, Egypt
Rezk Hoda

Department of Statistics, Faculty of Commerce, AL-Azhar University, Cairo, Egypt

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Plain Text BibTeX RIS

APA Style

Elgabry Gamalat, Rezk Hoda. (2021). Constant Stress Partially Accelerated Life Tests for Extended Generalized log Logistic Distribution Based on Type I Censored Competing Risks Data. Science Journal of Applied Mathematics and Statistics, 9(1), 15-19. https://doi.org/10.11648/j.sjams.20210901.12

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ACS Style

Elgabry Gamalat; Rezk Hoda. Constant Stress Partially Accelerated Life Tests for Extended Generalized log Logistic Distribution Based on Type I Censored Competing Risks Data. Sci. J. Appl. Math. Stat. 2021, 9(1), 15-19. doi: 10.11648/j.sjams.20210901.12

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AMA Style

Elgabry Gamalat, Rezk Hoda. Constant Stress Partially Accelerated Life Tests for Extended Generalized log Logistic Distribution Based on Type I Censored Competing Risks Data. Sci J Appl Math Stat. 2021;9(1):15-19. doi: 10.11648/j.sjams.20210901.12

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@article{10.11648/j.sjams.20210901.12,
  author = {Elgabry Gamalat and Rezk Hoda},
  title = {Constant Stress Partially Accelerated Life Tests for Extended Generalized log Logistic Distribution Based on Type I Censored Competing Risks Data},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {9},
  number = {1},
  pages = {15-19},
  doi = {10.11648/j.sjams.20210901.12},
  url = {https://doi.org/10.11648/j.sjams.20210901.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20210901.12},
  abstract = {As a result of technology improvement getting information about products and materials lifetimes under usual conditions. Therefore accelerated life testing or partially accelerated life testing usually are used to truncate the tests survives. The test items under accelerated life testing run under accelerated conditions and partially life tests run under both accelerated and use conditions. The main idea of accelerated life testing that the acceleration element is not unknown or the mathematical model relating the lifetime of the unit and the stress is known or can be assumed. In some cases, neither acceleration factor nor life-stress relations are not unknown. This paper concerned with studying and discussed the constant–stress partially accelerated life test (CPALT) under type I censored (T.I.C) competing risks data. Failure times resulting from T.I.C competing risks data are assumed to follow the Extended generalized log logistic (EGLL) distribution because this model is completely flexible to study positive data. This distribution is applied in various fields, for example lifetime studies, economics, finance and insurance. The maximum likelihood (ML) method is used to estimate the parameters under TIC competing risks data. The simulation algorithm is performed to assess the theoretical results of the maximum likelihood estimates based on TIC competing risks data.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Constant Stress Partially Accelerated Life Tests for Extended Generalized log Logistic Distribution Based on Type I Censored Competing Risks Data
AU  - Elgabry Gamalat
AU  - Rezk Hoda
Y1  - 2021/02/23
PY  - 2021
N1  - https://doi.org/10.11648/j.sjams.20210901.12
DO  - 10.11648/j.sjams.20210901.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 15
EP  - 19
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20210901.12
AB  - As a result of technology improvement getting information about products and materials lifetimes under usual conditions. Therefore accelerated life testing or partially accelerated life testing usually are used to truncate the tests survives. The test items under accelerated life testing run under accelerated conditions and partially life tests run under both accelerated and use conditions. The main idea of accelerated life testing that the acceleration element is not unknown or the mathematical model relating the lifetime of the unit and the stress is known or can be assumed. In some cases, neither acceleration factor nor life-stress relations are not unknown. This paper concerned with studying and discussed the constant–stress partially accelerated life test (CPALT) under type I censored (T.I.C) competing risks data. Failure times resulting from T.I.C competing risks data are assumed to follow the Extended generalized log logistic (EGLL) distribution because this model is completely flexible to study positive data. This distribution is applied in various fields, for example lifetime studies, economics, finance and insurance. The maximum likelihood (ML) method is used to estimate the parameters under TIC competing risks data. The simulation algorithm is performed to assess the theoretical results of the maximum likelihood estimates based on TIC competing risks data.
VL  - 9
IS  - 1
ER  -

Copy | Download