S Chaube - Department of Mathematics, Statistics and Computer, G. B. Pant University of Agriculture and Technolog
Mangey Ram - Department of Mathematics, Graphic Era University, Dehradun-۲۴۸۰۰۲
S. B. Singh - Mathematics, G. B. Pant University of Ag. & Tech.

In this paper authors have considered a system having three units A, B۱ and B۲. A is controlled by a controller and B۱ and B۲ are independent. Two repairmen are involved in repair of the system. One of the repairmen (the first) is the foreman (boss) and the other an assistant (apprentice). Whenever any unit fails, repair is undertaken by boss. If the boss is busy in repairing and at the same time other unit fails then the repair is undertaken by apprentice. The mathematical model obtained has been analyzed with the application of Copula. The Laplace transforms of the transition state probabilities being in various complex systems have been obtained. Using Abel’s lemma steady state behavior of the system has also been examined. MTTF and important characteristic of reliability measures have also been evaluated.

Reliability, Availability, Systems modeling and analysis, MTTF