Estimating the reliability of a series stress-strength system using lognormal kernel

Medjider, Meriem; Lagha, Karima

doi:10.47974/JSMS-1477

Open Access Research Article

Estimating the reliability of a series stress-strength system using lognormal kernel

^*Meriem MedjiderCorresponding authormeriem.medjider@univ-bejaia.dzApplied Mathematics LaboratoryFaculty of Exact SciencesUniversity of BejaiaBejaia, 06000, Algeria0009-0006-6154-1259View full profile → , Karima Laghakarima.lagha@univ-bejaia.dzLaboratory of Modeling and Optimization of SystemsFaculty of Exact SciencesUniversity of BejaiaBejaia, 06000, Algeria0000-0002-0274-9424View full profile →

* Corresponding author · click or hover a name for details

pp. 589–602Vol. 29Issue 6June 2026DOI: 10.47974/JSMS-1477XML

Received:: 05 Nov 2024
Published Online:: 07 Mar 2026
Article type:: Research Article
Language:: EN
Article no.:: JSMS-1477
Pages:: 589–602

Abstract

In this paper, we have estimated the reliability of a system composed of elements connected in series and subject to the same stress, by the nonparametric kernel estimation method using lognormal kernel. This kernel is chosen for its advantageous properties, including an optimal convergence rate for the mean integrated squared error, non-negativity, free from boundary bias, and naturally varying in shape. Asymptotic properties such as bias, variance, and mean squared error have been established for the proposed estimator. Furthermore, we address the selection of the optimal bandwidth parameter an essential aspect of kernel estimation using both the rule of thumb and the unbiased cross validation techniques. Finally, a simulation study is carried out to highlight the performance of the system reliability estimator, based on lognormal kernel and to compare the two bandwidth selection techniques to determine the best one.

Keywords

Stress strength model Reliability Lognormal kernel Bandwidth parameter Nonparametric estimation

Subject Classifications

90B2530C4062G05

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