In this paper, we introduce SYSTEMS consisting of several production units, each of which include several subunits working in PARALLEL. Meanwhile, each subunit is working independently. The input and output of each production unit are the sums of the inputs and outputs of its subunits, respectively. We consider each of these subunits as an independent decision making unit (DMU) and create the production possibility set (PPS) produced by these DMUs, in which the frontier points are considered as efficient DMUs. Then we introduce models for obtaining the efficiency of the production subunits. Using super-efficiency models, we categorize all efficient subunits into different efficiency classes. Then we follow by presenting the sensitivity analysis and stability problem for efficient subunits, including extreme efficient and non-extreme efficient subunits, assuming simultaneous perturbations in all inputs and outputs of subunits such that the efficiency of the subunit under evaluation declines while the efficiencies of other subunits improve.

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.

In this paper the real time operation of an automatic teller machine (ATM) is analyzed using a Timed Petri Net (TPN) model. In the modeling, the probability of arrivals, the speed and attentiveness of customers (clients) are taken to account. Different parameters are based on the statistical data. The model is simulated for 24 hours. The diagrams of number of succeeded customers, failed references to ATM, idle times of ATM and wait times of customers are the outputs of TPN model.