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Inferential Survival Analysis for Inverted NH Distribution Under Adaptive Progressive Hybrid Censoring with Application of Transformer Insulation

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Abstract

In this paper, the reliability analysis of the inverted Nadarajah–Haghighi (INH) distribution under an adaptive type-I progressive hybrid censoring scheme (AT-I PHCS) has been investigated. The unknown parameters of the INH distribution based on AT-I PHCS have been estimated using Bayesian and non-Bayesian methods. The asymptotic and two bootstrap confidence intervals are also calculated, as well as maximum likelihood estimates of the unknown parameters. The maximum product spacing estimation method based on AT-I PHCS has been introduced. Bayesian estimates of the unknown parameters are obtained based on symmetric (squared error) loss function. Furthermore, the Markov chain Monte Carlo (MCMC) technique is used to compute the Bayesian estimators and the associated credible intervals. Bootstrap confidence intervals have been discussed for parameters of INH based on AT-I PHCS. A real-life data set is used of progressively censored samples for transformer insulation life testing and compare tests included three levels of constant voltage, which were 35:4, 42:4, and 46:7kv, respectively. Finally, a simulation study is conducted to evaluate the estimators' performance.

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Data availability

The data is included in Sectection V ANALYSIS OF TRANSFORMER TURN.

Code availability

Function “maxlik” of “maxLik” package and “copula” package in the R program has been used.

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Acknowledgements

The authors thank the editor and the reviewer for careful reading of the research article and constructive comments that greatly improved this paper. Also, all those who help in creating or revision this work.

Funding

The authors received no specific funding for this study.

Author information

Authors and Affiliations

  1. Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig, Egypt

    O. E. Abo-Kasem & Wael S. Abu El Azm

  2. Department of Statistics, Faculty of Business Administration, Delta University of Science and Technology, Gamasa, Egypt

    Ehab M. Almetwally

Authors
  1. O. E. Abo-Kasem
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  2. Ehab M. Almetwally
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  3. Wael S. Abu El Azm
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Contributions

INH distribution based on AT-I PHCS have been obtained. Bayesian and non-Bayesian estimation methods have been discussed. The maximum product spacing estimation method based on AT-I PHCS has been introduced. the real-life data set is used of progressively censored samples for transformer insulation life testing and compare tests including three levels of constant voltage.

Corresponding author

Correspondence to Ehab M. Almetwally.

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Conflict of interest

The authors declare that they have no conflicts of interest to report regarding the present study.

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All of the followed procedures were in accordance with the ethical and scientific standards. This article does not contain any studies with human participants performed by the author.

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Appendix 1

Appendix 1

See Tables

Table 10 Average bias, MSE and CI of parameter INH distribution based on AT-I PHCS for case 1, T = 0.2 and different choices of n, m, and scheme
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Table 11 Average bias, MSE and CI of parameter INH distribution based on AT-I PHCS for case 1, T = 1.2 and different choices of n, m, and scheme
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Table 12 Average bias, MSE and CI of parameter INH distribution based on AT-I PHCS for case 2, T = 0.75 and different choices of n, m, and scheme
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Table 13 Average bias, MSE and CI of parameter INH distribution based on AT-I PHCS for case 2, T = 2 and different choices of n, m, and scheme
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Table 14 Average bias, MSE and CI of parameter INH distribution based on AT-I PHCS for case 3, T = 1.2 and different choices of n, m, and scheme
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Table 15 Average, MSE and CI of survival and hazard of INH distribution based on AT-I PHCS for case 1, T = 0.2 and different choices of n, m, and scheme
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Table 16 Average, MSE and CI for survival and hazard of INH distribution based on AT-I PHCS for case 1, T = 1.2 and different choices of n, m, and scheme
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Table 17 Average, MSE and CI for survival and hazard of INH distribution based on AT-I PHCS for case 2, T = 0.75 and different choices of n, m, and scheme
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Table 18 Average, MSE and CI for survival and hazard of INH distribution based on AT-I PHCS for case 2, T = 2 and different choices of n, m, and scheme
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Abo-Kasem, O.E., Almetwally, E.M. & Abu El Azm, W.S. Inferential Survival Analysis for Inverted NH Distribution Under Adaptive Progressive Hybrid Censoring with Application of Transformer Insulation. Ann. Data. Sci. 10, 1237–1284 (2023). https://doi.org/10.1007/s40745-022-00409-5

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