Reliability Studies of the Skew-Normal Distribution and Its Application to a Strength-Stress Model

The skew-normal distribution proposed by Azzalini [1] is suitable for the analysis of data exhibiting a unimodal empirical distribution function but having some skewness present, a structure often occurring in data analysis. In this paper we study the skew-normal distribution from a reliability point of view. More specifically, we obtain the failure rate, the mean residual life function (MRLF) and the reliability function of the skew-normal distribution. We also compare it with the normal distribution with respect to certain stochastic orderings and prove that the failure rate of the skew-normal distribution is increasing, a property enjoyed by the normal distribution. Appropriate machinery is developed to obtain the reliability in the strength-stress model where the variables involved follow the skew-normal distribution. Finally, data from Roberts [2] is analyzed to illustrate the results.