Estimation of stress–strength reliability from inverse Rayleigh distribution

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

“…• The AB ofR S,k at n = m increases as the value of λ 1 increases for both (S, k) = (1, 3) and (2,4) [see Tables 1-3 (1, 3) 0.9 (10,10) 0.0630 0.0150 0.3400 (10,15) 0.0007 0.0051 0.2300 (15,10) 0.1310 0.0300 0.3830 (15,15) 0.0530 0.0100 0.2740 (15,20) 0.0120 0.0047 0.2100 (20,15) 0.1030 0.0200 0.3050 (20,20) 0.0530 0.0092 0.2410 (2,4) 0.8 (10,10) 0.0680 0.0220 0.4490 (10,15) 0.0130 0.0120 0.3450 (15,10) 0.1670 0.0460 0.4580 (15,15) 0.0750 0.0190 0.3790 (15,20) 0.0170 0.0110 0.3190 (20,15) 0.1300 0.0320 0.3770 (20,20) 0.0680 0.0160 0.3270…”

“…The Bayesian estimate performances of R S,k are measured based on ABs, estimated Risks (ERs) and ALs via R 3.4.3. Three sets of parameter values are considered as (λ 1 , λ 2 , β) = (3, 1.5, 3), (1.5, 1.5, 3), (1.5, 2, 3) and different choices of sample sizes as (n, m) = (10, 10), (10,15), (15,10), (15,15), (15,20), (20,15), (20,20) (a 1 , b 1 ), (a 2 , b 2 ) = (6, 2), (5, 1.5). Also, we take (v = − 2, 2).…”

“…The length of intervals is the main principle of the performance of the ACI. The numerical study is designed through the following steps: and stress random variables (n, m) are chosen to be (10,10), (10,15), (15,10), (15,15), (15,20), (20,15) and (20,20). • The MLEs of λ 1 and λ 2 are obtained from (9), then the MLE of R S,k is obtained by substitutingλ 1 andλ 2 in (10).…”

“…These two data sets were used by Xia et al [29]. The data stand for the strength data measured in MPa, tensile properties of jute fibres were evaluated in accordance with ASTM C 1557-03 at seven different gauge lengths (2,3,5,10,15,20, and 25 mm). Thirty samples were mounted for testing at each of these gauge lengths.…”

“…The reliability in the MSS model based on a simple random sample has been developed in Kuo and Zuo [17] and Pandey and Uddin [18]. 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.…”