RELIABILITY ESTIMATION FOR TRUNCATED DISTRIBUTIONS

Abstract

In most studies of systems.. eliability, the failure distributions

of these systems are considered such that.the lifetimes of these systems take values from zero to infinity. In many applications, we may note that these lifetimes have limits which are neither zero nor infinity. So, it would be more realistic in these applications if these lifetimes assumed not to be less or greater than a given age.. It is necessary to state the difference between the truncated distributions, the translated distributions and the censored distributions. In truncated distributions, the random variable is assumed to take values in a specified interval such that any value is measured from the origin. For example, consider

a system with lifetime ranging from A to B. This means that the minimum lifetime of the system is A (measured from the begining of time which is taken as zero)and the maximum lifetime is B (measured from the beg.inning of time which is taken as zero). In translated distributions, the random variable takes values in a specified interval also, but these values are not measured from the origin. They are measured from the point f trans- lation. Thus when taking deviations of the random values from the trans lated point we shall have them as if it were measured from the origin. In other words, it turns to be a random variable with non translated distribution. The question of censored distributions arises when we are able to know the individual values of observations below (or above)a given value only. Suppose for example, that the distribution of lifetimes of an electric lamp is normal.