57] W. Sanders and J. Meyer. Reduced base model construction methods for stochastic activity networks. 58] L. Schmickler. MEDA { mixed Erlang distributions as phase-type representation of empirical functions. Numerical evaluation of performability measures and job completion time in repairable fault-tolerant systems. 37] M. Malhotra. A computationally eecient technique for transient analysis of repairable Markovian systems.tolerant methods for transient analysis of stii Markov chains. 39] M. Malhotra and A. Reibman. Selecting and implementing phase approximations for semi-Markov models. A characterization of the stochastic process underlying a stochastic Petri net. 17] P. Courtois. Computable bounds for conditional steady-state probabilities in large Markov chain and queueing models. 19] A. Cumani. ESP { A package for the evaluation of stochastic Petri nets with phase-type distributed transition times. and identiication of non-exponential distributions by homogeneous Markov processes. 22 6 Conclusion We discussed several types of modeling techniques used in dependability and performability analysis, with a particular emphasis on approaches based on the (entire or partial) generation of the state-space. The common underlying formalisms we consider, continuous-time Markov chains (CTMCs) and Markov reward models (MRMs), are capable of modeling a large class of systems, but they result in large models, diicult to describe and analyze. The description problem is solved by using higher-level formalisms, such as reliability graphs, fault trees, queueing networks, generalized stochastic Petri nets, and stochastic reward nets. With the appropriate software modeling tools, these can then be automatically translated into CTMCs or MRMs. The solution problem, though, remains, since the size of the underlying stochastic process grows combi-natorially. In addition, when modeling activities with very diierent timescales , such as failure and repair of components, and performance-related behavior, such as arrival and departure of jobs, stiiness arises. Advanced numerical techniques, and exact or approximate approaches such as truncation, aggregation, composition , and uid models, can then be eeectively used to obtain numerical solutions. 21 Johnson and Taae 27, 28] have considered matching the rst three moments of mixtures of two Erlang distributions. For more references on this topic, refer to 7]. Generation of the overall CTMC. After the parameters of phase approximations for all the non-exponential distributions have been tted (or estimated), the overall CTMC is generated. This may require the cross-product of phase approximations 39]. A few software packages implementing this approach have been developed. Phase approximations were used in the SURF package 16], although SURF was intended only for a …

The use of redundancy in commercial systems can bring two improvements: 1) more reliable systems less subject to disruption of service due to failures, and 2) a reduction in maintenance and outage costs. This paper is concerned with evaluating the reduction in maintenance and outage cost. We introduce a figure of merit, the cost reduction (CR), to show the cost advantages of redundancy. Using the CR concept, a benefit analysis is carried out for Warm Stand-By (WSB) and Triple Modular Redundancy (TMR). Maintenance and disruption of service are assumed to be the main sources of operating cost and only a policy of corrective maintenance is considered. Results are expressed as a function of the ratio between the outage cost rate and the maintenance cost rate (ro/rm) and the conditions are stated for which 1) WSB and TMR are economically attractive with respect to a non-redundant system, and 2) TMR is economically better than WSB. It is shown that when designing for benefit; 1) maintainability is the main feature when outage costs and maintenance cost have the same order of magnitude. 2) coverage factor is the main feature when disruption of service has a appreciable cost consequence.

Summing up, we can say that the failures can be divided into three classes according to whether they induce single, unidirectional or multiple errors. Each of these three classes can also be divided into two groups : permanent and transient errors. The table of figure 2 gives for each class the main failures encountered.

Modeling of systems featuring hardware and software faults is studied as a means of evaluating the availability and reliability characteristics. The case of a nonredundant computer is studied and it is shown that the unavailability presents an overshoot with respect to its asymptotic value whose height and length are functions of the failure rates associated with the different design errors. Fault-tolerant systems are studied that include protective redundancies both at the hardware level and at the software level; the importance of homogeneous solutions on both levels is shown.

This paper gives a unified approach to modeling digital structures and accounts for i) the hardware failure process and ii) the failure process due to design errors. The instantaneous unavailability, always larger than the value resulting from the hardware performance, shows an appreciable peak with respect to its asymptotic value whose height and length are functions of the failure rates associated with the different design errors. An approximate value for the maximum of this peak is given which, under certain conditions, can be used as a more realistic figure for unavailability than the asymptotic value usually considered.

Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.

Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.