In this paper some important properties of the generalized Pólya process are derived and their applications are discussed. The generalized Pólya process is defined based on the stochastic intensity. By interpreting the defined stochastic intensity of the generalized Pólya process, the restarting property of the process is discussed. Based on the restarting property of the process, the joint distribution of the number of events is derived and the conditional joint distribution of the arrival times is also obtained. In addition, some properties of the compound process defined for the generalized Pólya process are derived. Furthermore, a new type of repair is defined based on the process and its application to the area of reliability is discussed. Several examples illustrating the applications of the obtained properties to various areas are suggested.

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SUMMARYRedundancy or standby is a technique that has been widely applied to improving system reliability and availability in system design. In this paper, a general method for modelling standby system is proposed and system performance measures are derived. It is shown that the proposed general standby system includes the cases of cold, hot and warm standby systems with units of exponential distribution, which were studied in the literature, as special cases. An optimal allocation problem for a standby system is also discussed.

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