Stress-strength reliability estimation for the inverted exponentiated Rayleigh distribution under unified progressive hybrid censoring with application

Sadia Anwar; Showkat Ahmad Lone; Aysha Khan; Salmeh Almutlak; Sadia Anwar; Showkat Ahmad Lone; Aysha Khan; Salmeh Almutlak

doi:10.3934/era.2023204

Electronic Research Archive

2023, Volume 31, Issue 7: 4011-4033. doi: 10.3934/era.2023204

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Stress-strength reliability estimation for the inverted exponentiated Rayleigh distribution under unified progressive hybrid censoring with application

1.
Department of Mathematics, College of Arts and Sciences, Wadi Ad Dawasir (11991), Prince Sattam Bin Abdul Aziz University, Al-Kharj, Kingdom of Saudi Arabia
2.
Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Kingdom of Saudi Arabia

Received: 01 April 2023 Revised: 01 April 2023 Accepted: 06 April 2023 Published: 22 May 2023

In this paper, we studied the estimation of a stress-strength reliability model ($R = P(X>Y)$) based on inverted exponentiated Rayleigh distribution under the unified progressive hybrid censoring scheme (unified PHCS). The maximum likelihood estimates of the unknown parameters were obtained using the stochastic expectation-maximization algorithm (stochastic EMA). The asymptotic confidence intervals were also created. Under squared error and Linex and generalized entropy loss functions, the Gibbs sampler together with Metropolis-Hastings algorithm was provided to compute the Bayes estimates and the credible intervals. Extensive simulations were performed to see the effectiveness of the proposed estimation methods. Also, parallel to the development of reliability studies, it is necessary to study its application in different sciences such as engineering. Therefore, droplet splashing data under two nozzle pressures were proposed to exemplify the theoretical outcomes.
- inverted exponentiated Rayleigh,
- Metropolis-Hastings algorithm,
- unified PHCS,
- stress-strength reliability,
- stochastic expectation-maximization
Citation: Sadia Anwar, Showkat Ahmad Lone, Aysha Khan, Salmeh Almutlak. Stress-strength reliability estimation for the inverted exponentiated Rayleigh distribution under unified progressive hybrid censoring with application[J]. Electronic Research Archive, 2023, 31(7): 4011-4033. doi: 10.3934/era.2023204

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Abstract

In this paper, we studied the estimation of a stress-strength reliability model ($R = P(X>Y)$) based on inverted exponentiated Rayleigh distribution under the unified progressive hybrid censoring scheme (unified PHCS). The maximum likelihood estimates of the unknown parameters were obtained using the stochastic expectation-maximization algorithm (stochastic EMA). The asymptotic confidence intervals were also created. Under squared error and Linex and generalized entropy loss functions, the Gibbs sampler together with Metropolis-Hastings algorithm was provided to compute the Bayes estimates and the credible intervals. Extensive simulations were performed to see the effectiveness of the proposed estimation methods. Also, parallel to the development of reliability studies, it is necessary to study its application in different sciences such as engineering. Therefore, droplet splashing data under two nozzle pressures were proposed to exemplify the theoretical outcomes.

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