Dependability for Systems with a Partitioned State Space: Markov and Semi-Markov Theory and Computational Implementation

✍ Scribed by Attila Csenki (auth.)

• Publisher: Springer-Verlag New York
• Year: 1994
• Tongue: English
• Leaves: 251
• Series: Lecture Notes in Statistics 90
• Edition: 1
• Category: Library

✦ Synopsis

Probabilistic models of technical systems are studied here whose finite state space is partitioned into two or more subsets. The systems considered are such that each of those subsets of the state space will correspond to a certain performance level of the system. The crudest approach differentiates between 'working' and 'failed' system states only. Another, more sophisticated, approach will differentiate between the various levels of redundancy provided by the system. The dependability characteristics examined here are random variables associated with the state space's partitioned structure; some typical ones are as follows • The sequence of the lengths of the system's working periods; • The sequences of the times spent by the system at the various performance levels; • The cumulative time spent by the system in the set of working states during the first m working periods; • The total cumulative 'up' time of the system until final breakdown; • The number of repair events during a fmite time interval; • The number of repair events until final system breakdown; • Any combination of the above. These dependability characteristics will be discussed within the Markov and semi-Markov frameworks.

✦ Table of Contents

Front Matter....Pages i-ix
Stochastic Processes for Dependability Assessment....Pages 1-13
Sojourn times for Discrete-Parameter Markov Chains....Pages 14-52
The Number of Visits Until Absorption to Subsets of the State Space by a Discrete-Parameter Markov Chain: the Multivariate Case....Pages 53-68
Sojourn Times for Continuous-Parameter Markov Chains....Pages 69-105
The Number of Visits to a Subset of the State Space by a Continuous-Parameter Irreducible Markov Chain During a Finite Time Interval....Pages 106-121
A Compound Measure of Dependability for Continuous-Time Markov Models of Repairable Systems....Pages 122-140
A Compound Measure of Dependability For Continuous- Time Absorbing Markov Systems....Pages 141-150
Sojourn Times for Finite Semi-Markov Processes....Pages 151-166
The Number of Visits to a Subset of the State Space by an Irreducible Semi-Markov Process During a Finite Time Interval: Moment Results....Pages 167-178
The Number of Visits to a Subset of the State Space by an Irreducible Semi-Markov Process during a Finite Time Interval: The Probability Mass Function....Pages 179-204
The Number of Specific Service Levels of a Repairable Semi-Markov System during a Finite Time Interval: Joint Distributions....Pages 205-211
Finite Time-Horizon Sojourn Times for Finite Semi-Markov Processes....Pages 212-230
Back Matter....Pages 235-239

✦ Subjects

Probability Theory and Stochastic Processes