Hudaverdi, Burcu; Susam, Selim Orhun; Chesneau, Christophe

In this paper, we construct conditional reliability in the context of stress-strength models, taking into account the relationship between applied stress and strength. The Bernstein copula approximation is used to calculate the conditional reliability values. Real data from a rocket motor experiment are considered to evaluate the conditional reliability strength of a motor case and the required stress endurance for the motor.

AtıfScopus4·WoS5·OpenAlex5

İncele

Susam, Selim Orhun; Chesneau, Christophe

In this article, a new semiparametric family of bivariate copulas is proposed and studied. The copulas of this family innovate in their construction; they are based on an original univariate generating function involving the opposite diagonal section of intermediary copulas. Several of their crucial properties are examined. In the practical part, we use them to estimate the reliability parameter in a stress-strength-dependent setting, including an estimation approach based on the Bernstein copula. Finally, their applicability and good performance are confirmed using a data set related to the logarithmic concentrations of two chemical elements in water samples.

AtıfScopus1·WoS1·OpenAlex1

İncele

Chesneau, Christophe; Susam, Selim Orhun

Copulas are essential probability tools for characterizing the joint distribution of random variables. In this article, we contribute to the topic by studying special bivariate copulas. They have the property of being defined with piecewise components and are designed for the analysis of data that have dependence structures with distinct substructures in square zones. The theoretical properties of the copulas are studied, with emphasis on their mathematical validity and some dependence measures. In particular, it is shown that the Kendall tau coefficient has a simple expression that is governed by several parameters, demonstrating the flexibility of the approach. In addition, a real data example is provided to demonstrate the applicability of the copulas. Fair comparisons with other standard copulas motivate their use in other practical scenarios.

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