Fuzzy set based methods have been proved to be effective in handling many types of uncertainties in different fields, including reliability engineering. This paper presents a new approach on fuzzy reliability, based on the use of beta type distribution as membership function. Considering experts' ideas and by asking operators linguistic variables, a rule base is designed to determine the level of reliability of each component. Hence, we can determine the level of reliability of components with expending low costs. Also in this work a simple approach is presented for reducing the number of rules. The outputs of the presented model are fuzzy sets representing the reliability levels of components. In order to determine the level of reliability as linguistic variables, a new method is presented. Also the validity of the model is investigated by two methods. After determining the level of reliability of each component, the reliability of the composed system can be determined by using t-norm and s-norm functions. The system can be Parallel, Series, Parallel- Series or Series-Parallel. The presented model has been applied in a glass manufacturing company.

One of the most important topics in system reliability and performance measurements is availability analysis. In this paper, the availability of both Series and Parallel Systems is addressed considering repair time threshold. A threshold is considered for the repair time, and if the repair time is less than the threshold, the system can be considered as working, and the repair time can be ignored. On the contrary, if the repair time is longer than the threshold, then the system is considered as not working from the beginning of the system failure until the repair time exceeds the threshold. Both constant and random repair time thresholds are considered. Also, to investigate the instantaneous availability of the Series and Parallel Systems, both identical and non-identical components are incorporated. In addition, user-observed and perceived Systems are incorporated and analyzed. Numerical analysis is conducted, and the results suggest an increase in the instantaneous and steady-state availability, especially in the Series Systems. Based on the results, neglecting repair time threshold can lead to a significant difference in the system's availability, which can have a substantial impact on maintenance plans and company costs.

In this paper, we discuss the usual stochastic, likelihood ratio, dispersive and convex transform order between two Parallel Systems with independent heterogeneous extended generalized exponential components. We also establish the usual stochastic order between Series Systems from two independent heterogeneous extended generalized exponential samples. Finally, we find lower and upper bounds for the Renyi entropy and cumulative residual entropy of Series and Parallel Systems.