Reliability Equivalence Factors in Exponentiated Exponential Distribution

The reliability equivalence factors of parallel system with n independent and identical components will be discussed. The failure rates of the system components are functions of time and follow the exponentiated exponential distribution. We shall introduce two different methods to improve the system designs. The first is the reduction method and the second is called redundancy method which is composed of hot and cold duplication methods. In reduction method, it is assumed that the failure rates of some of the system components are reduced by a factor ρ, 0 < ρ< 1. In the hot duplication method, it is assumed that some of the system components are duplicated in parallel while some of the system components are duplicated in parallel by a perfect switch in the cold duplication method. Therefore, one can make equivalence between the reduction method and the duplication method based on some reliability measures. In other words, the design of the system that is improved according to the reduction method should be equivalent to the design of the system according to one of the redundancy method. The comparison of the designs produce the so-called reliability equivalence factors. The survival function and rth moment time to failures will be used as performance measures of the system reliability to compare different system designs.