Analysis of stress-strength reliability with m-step strength levels under type I censoring and Gompertz distribution

Neama Salah Youssef Temraz; Neama Salah Youssef Temraz

doi:10.3934/math.20241484

AIMS Mathematics

2024, Volume 9, Issue 11: 30728-30744. doi: 10.3934/math.20241484

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Research article

Analysis of stress-strength reliability with m-step strength levels under type I censoring and Gompertz distribution

Neama Salah Youssef Temraz ^{1,2
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1.
Prince Sattam Bin Abdulaziz University, College of Sciences and Humanities, Saudi Arabia
2.
Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt

Received: 07 September 2024 Revised: 18 October 2024 Accepted: 24 October 2024 Published: 30 October 2024
MSC : 62N05, 62P99

Because of modern technology, product reliability has increased, making it more challenging to evaluate products in real-world settings and raising the cost of gathering sufficient data about a product's lifetime. Instead of using stress to accelerate failures, the most practical way to solve this problem is to use accelerated life tests, in which test units are subjected to varying degrees of stress. This paper deals with the analysis of stress-strength reliability when the strength variable has changed m levels at predetermined times. It is common for the observed failure time data of items to be partially unavailable in numerous reliability and life-testing studies. In statistical analyses where data is censored, lowering the time and expense involved is vital. Maximum likelihood estimation when the stress and strength variables follow the Gompertz distribution was introduced under type I censoring data. The bootstrap confidence intervals were deduced for stress-strength reliability under m levels of strength variable and applying the Gompertz distribution to model time. A simulation study was introduced to find the maximum likelihood estimates, bootstrapping, and credible intervals for stress-strength reliability. Real data was presented to show the application of the model in real life.
Citation: Neama Salah Youssef Temraz. Analysis of stress-strength reliability with m-step strength levels under type I censoring and Gompertz distribution[J]. AIMS Mathematics, 2024, 9(11): 30728-30744. doi: 10.3934/math.20241484

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Abstract

Because of modern technology, product reliability has increased, making it more challenging to evaluate products in real-world settings and raising the cost of gathering sufficient data about a product's lifetime. Instead of using stress to accelerate failures, the most practical way to solve this problem is to use accelerated life tests, in which test units are subjected to varying degrees of stress. This paper deals with the analysis of stress-strength reliability when the strength variable has changed m levels at predetermined times. It is common for the observed failure time data of items to be partially unavailable in numerous reliability and life-testing studies. In statistical analyses where data is censored, lowering the time and expense involved is vital. Maximum likelihood estimation when the stress and strength variables follow the Gompertz distribution was introduced under type I censoring data. The bootstrap confidence intervals were deduced for stress-strength reliability under m levels of strength variable and applying the Gompertz distribution to model time. A simulation study was introduced to find the maximum likelihood estimates, bootstrapping, and credible intervals for stress-strength reliability. Real data was presented to show the application of the model in real life.

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