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Reliability function is defined under suitable assumptions for dynamic stress-strength scenarios where strength degrades and stress accumulates over time. Methods for numerical evaluation of reliability are suggested under deterministic strength degradation and cumulative damage due to shocks arriving according to a point process, in particular a Poisson process, using simulation method and inversion theorem. These methods are specifically useful in the scenarios where damage distributions do not possess closure property under convolution.The method is also extended for non-identical, dependent damage distributions as well as for random strength degradation. Results from inversion method is compared with known approximate methods and also verified by simulation. As it turns out, the simulation method seems to have an edge in terms of computational burden and has much wider domain of applicability.

Two-stage regression methods are typically used for handling endogeneity in the simultaneous equations models in economics and other social sciences. However, the problem is challenging in the presence of incomplete response and/or incomplete endogenous covariate(s). We propose a Bayesian approach for the joint modelling of incomplete longitudinal continuous response and an incomplete count endogenous covariate, where the incompleteness is caused by the censorship through a selection mechanism. We define latent continuous variables which are left-censored at zero and develop a Gibbs sampling algorithm for the simultaneous estimation of the model parameters. We consider partially varying coefficients regression models containing covariates with fixed and time-varying effects on the response. Our work is motivated by a sample dataset from the Health and Retirement Study (HRS) for modelling the out-of-pocket medical cost, where the number of hospital admissions is considered as an endogenous covariate. Our analysis addresses some of the previously unanswered questions on the physical and financial health of the older population based on HRS data. Simulation studies are performed for assessing the usefulness of the proposed method compared to its competitors.

Summary Population size estimation based on a capture–recapture experiment under a triple‐record system is an interesting problem in various fields including epidemiology and population studies. In many real life scenarios, there is inherent dependence between capture and recapture attempts. We propose a novel model that successfully incorporates the possible dependence and the associated parameters have nice interpretations. We provide estimation methodology for the population size and the associated model parameters based on the maximum likelihood method. The model proposed is applied to analyse real data sets from public health and census coverage evaluation studies. The performance of the estimate proposed is evaluated through extensive simulation study and the results are compared with existing competitors. The results exhibit superiority of the model over the existing competitors both in real data analysis and in a simulation study.

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