AbstractsMathematics

Our effort in this research work is to develop different cascade reliability models. The evaluation of reliability is considered mainly for cascade systems. For this purpose several distributions are considered namely, exponential, Weibull, gamma, Rayleigh, Lindley, uniform and two-point distribution. First, the attenuation factor K is taken to be a uniform random variable in and#61480; and#61481; 1 , 0 . Then unconditional reliability of the system is given by the expected value of ) (K Rn , where expectation is taken w.r.t. the distribution of K . Then some well known distributions namely, exponential, gamma and Weibull distribution are used to evaluate the reliability of n -cascade system. Again stress-strength is considered as a mixture of either two exponentials or two Rayleighs or two Weibulls, reliability of n cascade system is obtained. More precisely an n -cascade system is also used where components may fail in different ways. For the estimation of cascade system reliability three failure models have been considered. Further, two distributions viz. exponential and Rayleigh are used to find out the expressions of reliability for all the failure models. Again stress-strength distributions are considered as one parameter exponential and the parameters involved are assumed to be random with known prior distribution. Two cases are considered i.e. (i) strength parameter is random but stress parameter is a constant and (ii) stress parameter is random but strength parameter is a constant. In each case, two prior distributions viz. uniform and two-point distributions are considered for the parameter(s) involved. The system reliability of a 2-cascade system is obtained for all the cases. An n -cascade system with ) ( Z Y X P and#61500; and#61500; is considered where Y is the stress on the component subjected to two strengths X and Z . Reliability expressions of an n - cascade system is obtained when stress-strength both are either exponential or Rayleigh or Lindley distribution.%%%References p.96-99, Appendix p.100-121