In this paper, we investigate reliability and availability of repairable systems with two types of failure. The first one is to one unit and the second one is to M units in parallel structure. Let failure rate and repair rate of [type1, type2] components are assumed to be exponentially distributed. The expressions of availability and reliability characteristics such as the system reliability and the mean time to failure are derived for two systems. We used several cases to analyze graphically the effect of various system parameters on the reliability system and availability system.

Present study investigates the fuzzy reliability of some systems using intuitionistic fuzzy Weibull lifetime distribution, in which the lifetime parameters are assumed to be fuzzy parameter due to uncertainty and inaccuracy of data. Expressions for fuzzy reliability, fuzzy mean time to failure, fuzzy hazard function and their ${\alpha}$-cut have been discussed when systems follow intuitionistic fuzzy Weibull lifetime distribution. A numerical example is also taken to illustrate the methodology to calculate the fuzzy reliability characteristics of systems.

Based on increasing concave ordering a new class of life distribution is introduced. The new class of life distribution is named used better than aged in increasing concave ordering and is denoted by UBAC(2). The implication of our proposed class of life distribution with other classes is given. The properties of UBAC(2) under convolution, discrete mixture and formation of a coherent system are studied. Finally a characterization of the proposed class of life distributions by Laplace transform is discussed.

This investigation deals with reliability and sensitivity analysis of a repairable embedded system with standby wherein repairman takes multiple vacations. The hardware system consists of 'M' operating and 'S' standby components. The repairman can leave for multiple vacations of random length during its idle time. Whenever any operating unit fails, it is immediately replaced by a standby unit if available. Moreover, governing equations of an embedded system are constructed using appropriate birth-death rates. The vacation and repair time of repairman are exponentially distributed. The matrix method is used to find the steady-state probabilities of the number of failed components in the embedded system as well as other performance measures. Reliability indexes are presented. Further, numerical experiments are carried out for various system characteristics to examine the effects of different parameter. Using a special class of neuro-fuzzy systems i.e. Adaptive Network-based Fuzzy Interference Systems (ANFIS), we also approximate various performance measures. Finally, the conclusions and future research directions are provided.