A sequence of independent lifetimes X 1 X 2 X m , X m+1 X n were observed from geometric population with parameter q 1 but later it was found that there was a change in the system at some point of time m and it is reflected in the sequence after X m by change in parameter q 2 . The Bayes estimates of m q 1 q 2 , reliability R 1 t and R 2 t at time t are derived for symmetric and asymmetric loss functions under informative and non informative priors. A simulation study is carried out.

A sequence of independent observations X 1 X 2 X m X m+1 X n was observed on some measurable characteristic X in statistical process control. The shift in process mean is reflected in the sequence after X m . The Bayes estimators of shift point m, and past and future process means, 1 and 2 , are derived using various priors and loss functions. An application in statistical process control is given and a simulation study of the estimators is carried out.

We derive Bayes estimators of reliability and the parameters of a two-parameter geometric distribution under the general entropy loss, minimum expected loss and linex loss, functions for a noninformative as well as beta prior from multiply Type II censored data. We have studied the robustness of the estimators using simulation and we observed that the Bayes estimators of reliability and the parameters of a two-parameter geometric distribution under all the above loss functions appear to be robust with respect to the correct choice of the hyperparameters a(b) and a wrong choice of the prior parameters b(a) of the beta prior.

In this paper, we present a Bayesian approach to inference in reliability studies based on multiply Type-II censored data from a Rayleigh distribution using exponentially weighted minimum expected loss function. In this study, we have obtained Bayes estimator of the parameter, reliability and failure rate of the Rayleigh distribution. Highest posterior density and maximum likelihood estimators are also obtained. A simulated study is carried out to assess the performance of the estimators along with their maximum likelihood estimators under multiply Type-II censoring schemes.

The estimation problem of the parameters of a mixed geometric lifetime model, using Bayesian approach and Type I group censored sample, will be investigated in the case of two subpopulations. The Bayes estimates are derived for squared error, minimum expected, general entropy and linex loss functions under informative and diffuse priors. A practical example given by Nelson (W.B. Nelson, Hazard plotting methods for analysis of the life data with different failure models, J. Qual. Technol. 2 (1970), pp. 126-149) is considered. A simulation study is carried out along with risk.Bayes estimator, geometric model, loss functions, mixture distribution, risk function, simulation, Type I group censoring,