The optimal multi-stress–strength reliability technique for the progressive first failure in the length-bias exponential model using Bayesian and non-Bayesian methods

Abstract

In many real-world situations, systems frequently fail in their demanding operational settings. Researchers pay little attention to the fact that systems typically fail to execute their intended activities when it reaches its extreme operating situations as appropriate. In this paper, we try to develop and study inferential aspect of a system reliability having multiple components based on a progressive first failure censoring scheme assuming unit length-bias exponential distribution. Regarding estimation, asymptotic, boot-p, and boot-t approaches under the interval estimation are adopted, while the maximum likelihood method under the point estimation is considered. The MCMC method is used to get the Bayes estimate of the reliability parameter assuming both the symmetric and asymmetric loss functions. The associated confidence intervals are also reported as appropriate. The effectiveness of the various adopted estimation strategies is evaluated and compared using Monte Carlo simulation studies and examples from real-world applications.

KEYWORDS:

• Multi-level stress–strength reliability
• progressive first failure censoring scheme
• balanced loss functions
• Markov Chain Monte Carlo
• symmetric and asymmetric loss functions
• bootstrap confidence intervals

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project number [PNURSP2024R50], Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.