Inference on Stress-Strength Reliability for Log-Normal Distribution based on Lower Record Values

Inference on Stress-Strength Reliability for Log-Normal Distribution based on Lower Record Values

NkemnoleE. Bridget Samiyu M. Abiodun 

Department of Mathematics, University of Lagos, Lagos, Nigeria.

Corresponding Author Email:,
July 2019
15 November 2017
31 December 2017
| Citation



Research has suggested that there are components or devices which survive due to their strength. Although, these devices survive under a certain level of stress but when a higher level of stress is applied on them, they failed because they can’t sustain it. The likelihood that these components are functional during a certain level of stress under a stated condition and a specified operational environment is regarded as its reliability, which in reliability engineering studies can be used to control, evaluate and estimate the capability and lifetime of a device. This study aims to further contribute to the estimation of the stress-strength reliability parameter, where and are independent lognormal distributions based only on the first-observed lower record values. The Maximum Likelihood Estimator (MLE) of R and its asymptotic distribution are obtained as well as the confidence interval. Different parametric bootstrap confidence intervals are also proposed. Simulation and real data set representing Block-Moulding Machine experiment data (of Tola Block industry, Lagos, Nigeria) are fitted using the lognormal distribution and used to estimate the stress-strength parameters and reliability. Empirical analysis shows that the proposed model helps to establish a proficient structure for stress-strength reliability models.


Lognormal Distribution, Reliability, Interval Estimation, Lower record values, Stress-Strength Reliability

1. Introduction
2. Related Literature
3. Methodology
4. Empirical Results and Discussion
5. Conclusion

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