By Min Xie, Kim-Leng Poh, Yuan-Shun Dai

ISBN-10: 030648496X

ISBN-13: 9780306484964

ISBN-10: 0306486369

ISBN-13: 9780306486364

Computing platforms are of growing to be significance as a result of their broad use in lots of parts together with these in safety-critical platforms. This publication describes the elemental versions and methods to the reliability research of such structures. an in depth overview is equipped and versions are labeled into differing types. a few Markov versions are prolonged to the research of a few particular computing structures akin to mixed software program and undefined, imperfect debugging tactics, failure correlation, multi-state platforms, heterogeneous subsystems, and so forth. one of many goals of the presentation is that in accordance with the sound research and straightforwardness of the techniques, using Markov versions could be larger carried out within the computing approach reliability.

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**Additional info for Computing System Reliability: Models and Analysis**

**Example text**

Suppose that a computing system has three states after each run. The states are perfect, degraded, and failed states denoted by state 1, 2 and 3. The state of the current run will just affect the state of the next run. The matrix of one step transition probability is This is a discrete time, discrete state Markov chain (DTMC) that is depicted by the transition graph in Fig. 7. According to the Chapman-Kolmogorov equation, the two-step transition matrix can be obtained as 24 Basic Reliability Concepts Thereafter, if the system initially stays at a perfect state, then the probability that the system still stays at that state after 2 runs should be The four-step transition matrix is The probability that the system does not stay at the failed state after 4 runs is Continuous-time Markov chain Similar to the case of DTMC, the discrete-state and continuous-time Markov process is usually called the continuous time Markov chain.

These four Markov models are described in more details in the following sections. Discrete-Time Markov chain The discrete-state process is referred to as chain, so the discrete-state and discrete-time Markov process is usually called discrete time Markov chain (DTMC). 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.

First, the state diagram is drawn as a DTMC with transition probability matrix P. Then, the process in continuous time is set up by making the time spent in a transition from state i to state j have Cdf Chapman-Kolmogorov equations The second step converts the Markov state diagram developed in the preceding step into a set of equations. g. Trivedi (1982). Computing System Reliability 35 Solving the equations Solving the state equations is sometimes complicated. An analytical solution of the state equations is feasible only for simple problems.

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