Inferences of the Multicomponent Stress–Strength Reliability for Burr XII Distributions

Yuhlong Lio, Tzong-Ru Tsai, Liang Wang and Ignacio Pascual Cecilio Tejada
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Yuhlong Lio: Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA
Tzong-Ru Tsai: Department of Statistics, Tamkang University, Tamsui District, New Taipei City 25137, Taiwan
Liang Wang: School of Mathematics, Yunnan Normal University, Kunming 650500, China
Ignacio Pascual Cecilio Tejada: Department of Mathematics, Universidad de Almería, 04120 Almería, Spain

Mathematics, 2022, vol. 10, issue 14, 1-28

Abstract: Multicomponent stress–strength reliability (MSR) is explored for the system with Burr XII distributed components under Type-II censoring. When the distributions of strength and stress variables have Burr XII distributions with common or unequal inner shape parameters, the existence and uniqueness of the maximum likelihood estimators are investigated and established. The associated approximate confidence intervals are obtained by using the asymptotic normal distribution theory along with the delta method and parametric bootstrap procedure, respectively. Moreover, alternative generalized pivotal quantities-based point and confidence interval estimators are developed. Additionally, a likelihood ratio test is presented to diagnose the equivalence of both inner shape parameters or not. Conclusively, Monte Carlo simulations and real data analysis are conducted for illustration.

Keywords: multicomponent stress–strength model; Burr XII distribution; maximum likelihood estimation; generalized pivotal estimation; asymptotic theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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