By Ojeda J.L., Cristobal J.A.

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22 Basic Reliability Concepts A general discrete-time chain is a sequence of discrete random variables in which is dependent on all previous outcomes The analysis of this type of chain can easily become unmanageable, especially for long-term evaluation. Fortunately, in many practical situations, the influence of the earlier outcomes on its future one tends to diminish rapidly with time. For mathematical tractabiiity, we can assume that on i previous outcomes, where deriving is dependent only is a fixed and finite number.

10. Consider that a state diagram can be expressed as a sequence of transitions, as shown in Fig. 10. 4. Nonhomogeneous Poisson Process (NHPP) Models A counting process, N(t), is obtained by counting the number of certain events occurring in the time interval [0, t). The simplest model is the Poisson process model which assumes that time between failures are exponentially distributed and has independent increment, and it has a constant failure occurrence rate over time. Such a model is also a Markov model that has been discussed before.

4 can alternatively be represented by the reliability block diagrams if we view each link as a block, depicted by Fig. 1. The choice of reliability block diagram or network diagram depends on the convenience of their usage and description for certain specific problems. Usually, the reliability block diagram is mainly used in a modular system that consists of many independent modules and each module can be easily represented by a reliability block. The network diagram is often used in networked system where processing nodes are connected and communicated through links, such as the distributed computing system, local/wide area networks and the wireless communication channels, etc.

### A bootstrap approach to model checking for linear models under length-biased data by Ojeda J.L., Cristobal J.A.

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