TABLE OF CONTENTS In the previous chapter, we studied the probability of the top event considering that the parameters of distribution concerning the basic events were fixed.
In reality, this is not always the case. There are very good reasons for saying that this approach is not always satisfactory. In fact, the data on the reliability of components are generally obtained through tests or even through field data. In both statistical analysis is carried out in order to determine the parameters of distributions, wherein we consider these parameters that constitute themselves as random variables. Hence, for every parameter, we define a distribution, or the first moments, or just a simple factor of error, etc.
Concerning a component, whose lifetime follows a distribution depending on a parameter, we obtain, within the framework of a standard statistical study, an estimator (preferably an estimator with good properties!), whose distribution enables us to obtain confidence intervals of the parameter at desired levels of confidence, and then the confidence intervals for the probability of this component's failure. Obviously an analysis with the same aim as that of the preceding analysis can be carried out within a Bayesian analysis framework.
Within the framework of the reliability of the systems, and in particular, in matters concerning the FTs, the previous analysis dealing with the components of the system is considered a data, and we seek to start from there to obtain an interval of confidence for the probability of the top event.
The fact of considering...
