The stress-strength model and its generalizations : theory and applications

By Samuel Kotz, Y. Lumelskii, Marianna Pensky. 2003

374 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f64122e9afcc6bb642b33431c7a9421c65a4e2da

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In Mechanics of Materials

Citations in the corpus

Estimation of P(Y < X) for the Three-Parameter Generalized Exponential Distribution (2008, methodology): “A book length treatment of the different methods can be found in Kotz et al. (2003).”
Estimation of P[Y<X]P[Y<X] for generalized Pareto distribution (2010, background): “The theoretical and practical results on the theory and applications of the stress–strength relationships in industrial and economic systems during the last decades are collected and digested in Kotz et al. (2003).”
CONFIDENCE LIMITS FOR STRESS STRENGTH RELIABILITY INVOLVING WEIBULL MODELS (2010, background): “…PðX24X1Þ ¼ c1 b1 Z 1 0 e ðx1=b2Þ c2 x1 b1 c1 1 e ðx1=b1Þ c1 dx1: ð2Þ The integral in (2) can be evaluated analytically as an infinite series expression (see Kotz et al., 2003, p. 53) involving gamma functions, but we found the above integral was easier to evaluate numerically (see Section 4)…”
On the existence of a normal approximation to the distribution of the ratio of two independent normal random variables (2013, methodology): “A very useful graphical way of comparing any pair of distributions F and G is provided by the Relative Operating Characteristic (ROC) curve, which as presented in Kotz et al. (2003) consists of the points [G (z) , F (z)] for z ∈ R.”
On estimating the reliability in a multicomponent stress-strength model based on Chen distribution (2020, background): “We refer to Kotz, Lumelskii, and Pensky (2003) for different applications of such estimation problems.”
On estimation of R=P(Y<X) for exponential distribution under progressive type-II censoring (2012, background): “[2] provided an excellent review of the development of this model till that time.”
Generalized exponential distribution: Existing results and some recent developments (2007, methodology): “For an excellent account of all these methods the readers are referred to the recent monograph of Kotz, Lumelskii and Pensky [18].”
On the one parameter unit-Lindley distribution and its associated regression model for proportion data (2018, neutral): “ Suppose that X and Y are two independent unit-Lindley random variables with parameters 1 and 2 , respectively, having p.d.f's fX ( ) and fY ( ). Then the stress-strength reliability measure, (Kotz et al., 2003) is given by: R = P (Y < X ) = Z 1 0 fX (x j 1 ) F Y (x j 2 ) dx = 2 2 (1 2 2 +2”
A copula-based approach to account for dependence in stress-strength models (2013, background): “A comprehensive account of this topic is given by Kotz et al. (2003).”
Inference on Reliability in Two-parameter Exponential Stress–strength Model (2007, background): “If µ1 = µ2, then the form for R, as shown in (2), is quite complex, and only large sample approach is available (see Kotz et al. 2003, Section 4.2.3).”
The exponentiated discrete Weibull Distribution (2015, neutral): “A complete review is available in Kotz et al. (2003).”