Habib Jafari

In reliability engineering, the δ-shock model is widely used to analyze shock-exposed systems that fail when two consecutive shocks occur within a sufficiently short time interval. In many practical situations, secondary factors influence the mean time between shocks, thereby affecting the system’s mean stopping time. In this paper, we model the mean stopping time as a regression function of such secondary factors and employ an optimal experimental design approach to determine the design points that maximize the information used to estimate the model parameters accurately. We derive the corresponding formulation based on the Bayesian D-optimality criterion and, as an illustrative example, characterize the optimal designs assuming a Poisson arrival process for random shocks. Numerical results demonstrate how the optimal design points vary with the critical threshold δ and the prior distribution of the regression parameters.

In reliability theory, various [ ]-shock models are used to study the shock-exposed systems that are sensitive to the length of intershock times. In this paper, a new generalized [ ]-shock model is introduced and studied, under which a system fails when the intershock time is smaller than a threshold [ ] or larger than another threshold [ ] for the first time, where [ ]. Reliability characteristics of the corresponding lifetimes are investigated under the new model when the intershock times follow an arbitrary distribution. As an illustrative example to demonstrate the practical aspects of the new model in the real world, we discuss the reliability behavior of an adult heart. Furthermore, we present an application of the discrete-time version of the new model in agricultural engineering. Numerical examples illustrate our theoretical findings.

Nonlinear regression models are widely utilized in many scientific disciplines. Precisely estimating an optimal nonlinear regression model is critical, especially when considering potential biases may arise in Bayesian optimal design. The current work introduces Bayesian and nonparametric Bayesian optimal designs based on the length of interconnected intervals for the unit exponential (UE) regression model. In cases where parameter information or historical data are limited, a nonparametric Bayesian method is employed through placing a Dirichlet process (DP) prior on the space of distribution functions. Lastly, the efficiency of various optimal designs is assessed and compared.

Nonlinear regression models are extensively applied across various scientific disciplines. It is vital to accurately fit the optimal nonlinear model while considering the biases of the Bayesian optimal design. We present a Bayesian optimal design by utilising the Dirichlet process as a prior. The Dirichlet process serves as a fundamental tool in the exploration of Nonparametric Bayesian inference, offering multiple representations that are well-suited for application. This research paper introduces a novel one-parameter model, referred to as the ’Unit-Exponential distribution’, specifically designed for the unit interval. Additionally, we employ a stick-breaking representation to approximate the D-optimality criterion considering the Dirichlet process as a functional tool. Through this approach, we aim to identify a Nonparametric Bayesian optimal design.

In actuarial science, it is often of interest to compare stochastically smallest claim amounts from heterogeneous portfolios. In this paper, we obtain the

In this paper, we discuss the stochastic comparison of two classical surplus processes in an one-year insurance period. Under the Marshall-Olkin extended Weibull random aggregate claim amounts, we establish some sufficient conditions for the comparison of aggregate claim amounts in the sense of the usual stochastic order. Applications of our results to the Value-at-Risk and ruin probability are also given. The obtained results show that the heterogeneity of the risks in a given insurance portfolio tends to make the portfolio volatile, which in turn leads to requiring more capital. We also obtain some sufficient conditions for comparing aggregate non-random claim amounts with different occurrence frequency vectors in terms of increasing convex order.