Bayesian inference on reliability in a multicomponent stress-strength bathtub-shaped model based on record values

Abstract

In the literature, there are a well-developed estimation techniques for the reliability assessment in multicomponent stress-strength models when the information about all the experimental units are available. However, in real applications, only observations that exceed (or fall below) the current value may be recorded. In this paper, assuming that the components of the system follow bathtub-shaped distribution, we investigate Bayesian estimation of the reliability of a multicomponent stress-strength system when the available data are reported in terms of record values. Considering squared error, linex and entropy loss functions, various Bayes estimates of the reliability are derived. Because there are not closed forms for the Bayes estimates, we will use Lindley’s method to calculate the approximate Bayes estimates. Further, for comparison purposes, the maximum likelihood estimate of the reliability parameter is obtained. Finally, simulation studies are conducted in order to evaluate the performances of the proposed procedures and analysis of real data sets is provided.

Multicomponent stress-strength reliability based on a right long-tailed distribution

“…Such a structure for data is observed in many studies. For more details, one can refer to [3,23,[37][38][39][40]. On the other hand, there are other studies that the basic data structure for random stress and strength samples in the above model is considered as a matrix.…”

“…Thereafter, many authors have shown considerable interest in the MSS model. Some recent efforts regard to the issue, can be found in [3,4,14,[21][22][23][24][25][26][27][31][32][33]37] for the Topp-Leone, exponentiated Pareto distribution, Kumaraswamy, unit-Gompertz, unit generalized Rayleigh, Geometric, Chen, proportional reversed hazard rate family, bivariate Kumaraswamy, Weibull, the general class of inverted Exponentiated models, inverted exponentiated Rayleigh, Burr XII, and bathtub-shaped distributions, respectively.…”

Reliability Estimation in Multicomponent Stress-Strength Based on Inverse Weibull Distribution

“…Multicomponent stress-strength (MCSS) models have great applications range from communication and industrial systems to logistic and military systems. For examples, an aircraft generally contains more than one engine (k) and assume that for takeoff at least s (1 ≤ s ≤ k) engines are needed, see Hanagal [3], Turkkan and Pham-Gia [4], Serkan [5,6], Serkan and Funda [7], Shawky and Al-Gashgari [8], Pak et al [9,10], and Rao et al [11]. SS models have been discussed in the literature many a times.…”

Estimation of multicomponent stress-strength reliability following Weibull distribution based on upper record values

“…A considerable amount of the literature on the estimation of reliability in the multicomponent system for some lifetime distributions has been studied by several authors; see for examples; Rao [19], Rao et al [20], Rao [21], Kizilaslan and Nadar [22]. Recently, Pak et al [23] investigated Bayesian estimation of the reliability of an MSS system for the bathtub-shaped distribution when the available data are reported in terms of record values. Jamal et al [24] considered maximum likelihood and Bayesian estimation methods for MSS reliability for Pareto distribution based on the upper record values.…”