A remark on of limit reliability function of large series–parallel systems with assisting components

Abstract

In the reliability investigation of large scale systems the problem of the complexity of their reliability functions arises. This problem may be approximately solved by assuming that the number of the system components tends to infinity and finding the limit reliability function of the system. The results for series, parallel, series–parallel and parallel–series systems are given in R.E. Barlow, F. Proschan, Statistical Theory of Reliability and Life Testing, Probability Models, Holt Rinehart and Winston, New York, 1975; K. Kołowrocki, On a Class of Limit Reliability Functions for Series–Parallel and Parallel–Series Systems, Monograph, Gdynia Maritime Academy Press, 1993; K. Kołowrocki, Reliability Engineering and System Safety 39 (1993) 11–23. In the paper as a partial extension of these results, theorems which determinate necessary and sufficient conditions for a reliability function to be an asymptotic reliability function of the series–parallel system with assisting components are given. The problem is solved for the system which the number of its series components is of order of the number of its parallel components. Moreover, some examples are presented.