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All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Towards automatic Markov reliability modeling of computer architectures

The analysis and evaluation of reliability measures using time-varying Markov models is required for Processor-Memory-Switch (PMS) structures that have competing processes such as standby redundancy and repair, or renewal processes such as transient or intermittent faults. The task of generating these models is tedious and prone to human error due to the large number of states and transitions involved in any reasonable system. Therefore model formulation is a major analysis bottleneck, and model verification is a major validation problem. The general unfamiliarity of computer architects with Markov modeling techniques further increases the necessity of automating the model formulation. This paper presents an overview of the Automated Reliability Modeling (ARM) program, under development at NASA Langley Research Center. ARM will accept as input a description of the PMS interconnection graph, the behavior of the PMS components, the fault-tolerant strategies, and the operational requirements. The output of ARM will be the reliability of availability Markov model formulated for direct use by evaluation programs. The advantages of such an approach are (a) utility to a large class of users, not necessarily expert in reliability analysis, and (b) a lower probability of human error in the computation.

Liceaga, C. A.↗
NASA NTRS1990

State reduction for semi-Markov reliability models

Semi-Markov processes have proved to be an effective and convenient tool to construct models of systems that achieve reliability by redundancy and reconfiguration. These models are able to depict complex system architectures and to capture the dynamics of fault arrival and system recovery. A disadvantage of this approach is that the models can be extremely large, which poses both a model construction and a computational problem. Techniques are needed to reduce the model size. Because these systems are used in critical applications where failure can be expensive, there must be an analytically derived bound for the error produced by the model reduction technique. Automatic model generation programs have been written to help the reliability analyst produce models of complex systems. Because of the importance of these programs, the model reduction technique needs to be precise and easily implemented. This paper presents a model reduction technique called trimming that can be applied to a popular class of systems. An error bound for the trimming procedure is derived that uses readily available system parameters. The trimming procedure is precisely described and appears easy to implement in a model generation program.

Reduced order systems↗
NASA NTRS1996

Probabilistic Independence Networks for Hidden Markov Probability Models

In this paper we explore hidden Markov models(HMMs) and related structures within the general framework of probabilistic independence networks (PINs). The paper contains a self-contained review of the basic principles of PINs. It is shown that the well-known forward-backward (F-B) and Viterbi algorithms for HMMs are special cases of more general enference algorithms for arbitrary PINs.

random variables pattern recognition signal proces↗
NASA NTRS1987

Automated model generation for reliability analysis programs

Semi-Markov models (a generalization of Markov models) can be used to calculate the reliability of virtually any fault-tolerant system. However, the process of delineating all of the states and transitions in the model of a complex system can be devastatingly tedious and error-prone. The ASSIST program allows the user to describe the semi-Markov model in a high-level language. Instead of specifying the individual states of the model, the user specifies the rules governing the behavior of the system, and these are used by ASSIST to automatically generate the model. A small number of statements in the abstract language can be used to describe a very large, complex model. Because no assumptions are made about the system being modeled, the ASSIST program can be used to generate models describing the behavior of any type of system. The ASSIST program and its input language are described and illustrated by examples.

Johnson, Sally C.↗
NASA NTRS1989

Markov reliability models for digital flight control systems

The reliability of digital flight control systems can often be accurately predicted using Markov chain models. The cost of numerical solution depends on a model's size and stiffness. Acyclic Markov models, a useful special case, are particularly amenable to efficient numerical solution. Even in the general case, instantaneous coverage approximation allows the reduction of some cyclic models to more readily solvable acyclic models. After considering the solution of single-phase models, the discussion is extended to phased-mission models. Phased-mission reliability models are classified based on the state restoration behavior that occurs between mission phases. As an economical approach for the solution of such models, the mean failure rate solution method is introduced. A numerical example is used to show the influence of fault-model parameters and interphase behavior on system unreliability.

Mcgough, John↗
NASA NTRS1991

Model reduction by trimming for a class of semi-Markov reliability models and the corresponding error bound

Semi-Markov processes have proved to be an effective and convenient tool to construct models of systems that achieve reliability by redundancy and reconfiguration. These models are able to depict complex system architectures and to capture the dynamics of fault arrival and system recovery. A disadvantage of this approach is that the models can be extremely large, which poses both a model and a computational problem. Techniques are needed to reduce the model size. Because these systems are used in critical applications where failure can be expensive, there must be an analytically derived bound for the error produced by the model reduction technique. A model reduction technique called trimming is presented that can be applied to a popular class of systems. Automatic model generation programs were written to help the reliability analyst produce models of complex systems. This method, trimming, is easy to implement and the error bound easy to compute. Hence, the method lends itself to inclusion in an automatic model generator.

White, Allan L.↗
NASA NTRS1995

Reduction Of Sizes Of Semi-Markov Reliability Models

Trimming technique reduces computational effort by order of magnitude while introducing negligible error. Error bound depends on only three parameters from semi-Markov model: maximum sum of rates for failure transitions leaving any state, maximum average holding time for recovery-mode state, and operating time for system. Error bound computed before any model generated, enabling modeler to decide immediately whether or not model can be trimmed. Trimming procedure specified by precise and easy description, making it easy to include trimming procedure in program generating mathematical models for use in assessing reliability. Typical application of technique in design of digital control systems required to be extremely reliable. In addition to aerospace applications, fault-tolerant design has growing importance in wide range of industrial applications.

White, Allan L.↗
NASA NTRS1990

Closed-form solution of decomposable stochastic models

Markov and semi-Markov processes are increasingly being used in the modeling of complex reconfigurable systems (fault tolerant computers). The estimation of the reliability (or some measure of performance) of the system reduces to solving the process for its state probabilities. Such a model may exhibit numerous states and complicated transition distributions, contributing to an expensive and numerically delicate solution procedure. Thus, when a system exhibits a decomposition property, either structurally (autonomous subsystems), or behaviorally (component failure versus reconfiguration), it is desirable to exploit this decomposition in the reliability calculation. In interesting cases there can be failure states which arise from non-failure states of the subsystems. Equations are presented which allow the computation of failure probabilities of the total (combined) model without requiring a complete solution of the combined model. This material is presented within the context of closed-form functional representation of probabilities as utilized in the Symbolic Hierarchical Automated Reliability and Performance Evaluator (SHARPE) tool. The techniques adopted enable one to compute such probability functions for a much wider class of systems at a reduced computational cost. Several examples show how the method is used, especially in enhancing the versatility of the SHARPE tool.

Sjogren, Jon A.↗
NASA NTRS1989

Projection methods for the numerical solution of Markov chain models

Projection methods for computing stationary probability distributions for Markov chain models are presented. A general projection method is a method which seeks an approximation from a subspace of small dimension to the original problem. Thus, the original matrix problem of size N is approximated by one of dimension m, typically much smaller than N. A particularly successful class of methods based on this principle is that of Krylov subspace methods which utilize subspaces of the form span(v,av,...,A(exp m-1)v). These methods are effective in solving linear systems and eigenvalue problems (Lanczos, Arnoldi,...) as well as nonlinear equations. They can be combined with more traditional iterative methods such as successive overrelaxation, symmetric successive overrelaxation, or with incomplete factorization methods to enhance convergence.

Saad, Youcef↗
NASA NTRS1984

Upper and lower bounds for semi-Markov reliability models of reconfigurable systems

This paper determines the information required about system recovery to compute the reliability of a class of reconfigurable systems. Upper and lower bounds are derived for these systems. The class consists of those systems that satisfy five assumptions: the components fail independently at a low constant rate, fault occurrence and system reconfiguration are independent processes, the reliability model is semi-Markov, the recovery functions which describe system configuration have small means and variances, and the system is well designed. The bounds are easy to compute, and examples are included.

White, A. L.↗
NASA NTRS1983

Reliability with imperfect diagnostics

A reliability estimation method for systems that continually accumulate faults because of imperfect diagnostics is developed and an application for redundant digital avionics is presented. The present method assumes that if a fault does not appear in a short period of time, it will remain hidden until a majority of components are faulty and the system fails. A certain proportion of a component's faults are detected in a short period of time, and a description of their detection is included in the reliability model. A Markov model of failure during flight for a nonreconfigurable five-plex is presented for a sequence of one-hour flights followed by maintenance.

White, A. L.↗
NASA NTRS1990

The cost of unreliability in the avionics suite of a launch vehicle

The main objective of the Advanced Launch System (ALS) program is to realize a substantial reduction in recurring launch costs over present launch systems. A methodology is presented for assessing the impact of the reliability of the avionics suite on the recurring launch cost of the ALS. The methodology is illustrated by focusing on two architectures. The first is a distillation of a typical architecture for this type of application. The second is a simplified implementation of the Advanced Information Processing System (AIPS) technology developed at the Charles Stark Draper Laboratory, Inc. Both architectures utilize redundancy of hardware to tolerate faults. the key contributors to the cost of unreliability are identified and modeled utilizing Markov modeling techniques for each of the two architectures. The results are presented along with the more traditional costs for these avionics suites.

Rosch, Gene↗