**1. Introduction**

Both the reliability function and the survival function have the same property, which is the measurement of the life span of a particular system or organism. In systems and equipment, it is called the reliability function, but for the organism, it is called the survival function.

Sometimes, especially in the analysis of survival functions, the failure events are few, so we need to include prior information, which can be used by the Bayes method. When merging the prior information with the observations to obtain the posterior distribution according to the Bayes rule, a problem may appear to us, which is the problem of prior data conflict with views, in regular Bayes method, this problem is not checked and is not addressed and thus unreal estimators are obtained, In this thesis, we will use an approach to address this problem, which is the prior data conflict problem, and thus this method is called the Robust Bayes Procedure.

What is meant by the prior data conflict is when the information of the prior distribution is combined with the distribution of observations, which may cause us this problem, meaning that the data under study are less homogeneous when the information of the prior distribution is combined with it, and thus we obtain unreal estimations without realizing.

In analyzing the problem, the researcher relied on two models of failure, the first model is the Weibull distribution with two parameters to match the continuous data, the second model is the Binomial distribution to match the discrete data to identify the behavior of the capabilities in these two types of data and the appropriateness of the robust methods to deal with the existence of the problem prior data conflict.
