A Bivariate Pareto Distribution for Modeling Load Sharing Dependence : Relability Modeling

Usually in statistical modeling, one comes up with a model taking into consideration the physical aspects of the situation. In the present study we considered load sharing dependence in a two component parallel system. Though load sharing dependence is popular in reliability studies this dependence is common in socio-economic situations also. Freund (1961) has designed a bivariate exponential model for the life testing of a two component parallel system which incorporates the above said load-sharing dependence. If the operating environment affects both the components differently, then assuming a gamma distribution to model the environment, the above system reduces to assuming two independent Pareto II distributions instead of exponential distribution. Taking into consideration these assumptions we develop a new model which incorporates the load sharing dependence. This model finds application in the areas of survival analysis, reliability analysis and economics.