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All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Modeling Reliability Growth

Reliability growth has been modelled as an exponential decline in the cumulative failure rate that continues indefinitely as long as testing continues. Contrary to this, most reliability growth data show a brief high initial failure rate due to infant mortality followed by a long period of constant low failure rate. A two part failure rate model with an initial exponential decline followed by a constant failure rate usually fits the data and provides a more realistic description of reliability growth. The reliability growth process consists of testing, experiencing failures, finding the failure causes, and redesigning the system to remove them. The cost of reliability growth increases with the number of inherent failure modes and the time needed for them to occur and be removed. The failure modes with the lower failure rates will tend to occur later, as their Mean Time Before Failure (MTBF) is the inverse of the failure rate. Reliability growth testing has diminishing returns, since it takes longer to find and remove the less probable failures.This paper first discusses the reliability bathtub curve and then explains that reliability growth is produced by testing, identifying failure causes, and designing to remove them. A simple model of reliability growth is introduced, with a brief group of early failures followed by a constant failure rate. The cumulative failure rate n(t)/t can decline as rapidly as1/t or t-1butdeclines more slowly if additiona lfailures occur. The 56-failure Crow data seti s used to demonstrate the two-phase model of reliability growth followed by a constant failure rate. 13 additional data sets are modeled, with 9 of the 14 data sets showing reliability growth approximately as n(t)/t =1/t or t-1and substantial final failure rates. The model fits most of the data sets, but 4of the 14 show no reliability growth. The reliability growth period typically includes six failures and extends one-quarter or half the total test time. As reliability growth testing continues, the cumulative failure rate should be tracked to estimate the reliability growth exponent and the final failure rate.

reliability growth modeling↗
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 NTRS1989

Recalibrating software reliability models

In spite of much research effort, there is no universally applicable software reliability growth model which can be trusted to give accurate predictions of reliability in all circumstances. Further, it is not even possible to decide a priori which of the many models is most suitable in a particular context. In an attempt to resolve this problem, techniques were developed whereby, for each program, the accuracy of various models can be analyzed. A user is thus enabled to select that model which is giving the most accurate reliability predictions for the particular program under examination. One of these ways of analyzing predictive accuracy, called the u-plot, in fact allows a user to estimate the relationship between the predicted reliability and the true reliability. It is shown how this can be used to improve reliability predictions in a completely general way by a process of recalibration. Simulation results show that the technique gives improved reliability predictions in a large proportion of cases. However, a user does not need to trust the efficacy of recalibration, since the new reliability estimates produced by the technique are truly predictive and so their accuracy in a particular application can be judged using the earlier methods. The generality of this approach would therefore suggest that it be applied as a matter of course whenever a software reliability model is used.

Brocklehurst, Sarah↗
NASA NTRS1990

Recalibrating software reliability models

In spite of much research effort, there is no universally applicable software reliability growth model which can be trusted to give accurate predictions of reliability in all circumstances. Further, it is not even possible to decide a priori which of the many models is most suitable in a particular context. In an attempt to resolve this problem, techniques were developed whereby, for each program, the accuracy of various models can be analyzed. A user is thus enabled to select that model which is giving the most accurate reliability predicitons for the particular program under examination. One of these ways of analyzing predictive accuracy, called the u-plot, in fact allows a user to estimate the relationship between the predicted reliability and the true reliability. It is shown how this can be used to improve reliability predictions in a completely general way by a process of recalibration. Simulation results show that the technique gives improved reliability predictions in a large proportion of cases. However, a user does not need to trust the efficacy of recalibration, since the new reliability estimates prodcued by the technique are truly predictive and so their accuracy in a particular application can be judged using the earlier methods. The generality of this approach would therefore suggest that it be applied as a matter of course whenever a software reliability model is used.

Brocklehurst, Sarah↗
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 NTRS1985

Synthetic bounds for semi-Markov reliability models

Upper and lower bounds are derived for the probability of failure for a class of highly reliable process control computers. The bounds are synthetic in the sense that the descriptions of component failure and system recovery are assumed to be obtained from different sources. The reliability model is constructed under the assumption that the processes are independent.

White, A. L.↗
NASA NTRS1990

Noninteractive macroscopic reliability model for whisker-reinforced ceramic composites

Considerable research is underway in the field of material science focusing on incorporating silicon carbide whiskers into silicon nitride and alumina matrices. These composites show the requisite thermal stability and thermal shock resistance necessary for use as components in advanced gas turbines and heat exchangers. This paper presents a macroscopic noninteractive reliability model for whisker-reinforced ceramic composites. The theory is multiaxial and is applicable to composites that can be characterized as transversely isotropic. Enough processing data exists to suggest this idealization encompasses a significantly large class of fabricated components. A qualitative assessment of the model is made by presenting reliability surfaces in several different stress spaces and for different values of model parameters.

Duffy, Stephen F.↗
NASA NTRS1986

Provably conservative approximations to complex reliability models

Complex models can be the bases for derivation of provably conservative and optimistic reliability models that incorporate a reduced state space and fewer transitions; they accordingly possess solutions that are more cost-effective than those of the original complex models. Design space can thereby be extensively explored without incurring the expense of multiple complex model solutions. A conservative-optimistic pair of derived models produces a band that includes the solution to the complex model. Sensitivity analysis can be performed on this pair of models to determine those parameters of the original model that are most sensitive to change and therefore require further expense in obtaining tighter specifications.

Smotherman, M.↗
NASA NTRS1993

Digraph reliability model processing advances and applications

This paper describes a new algorithm, called SourceDoubls, which efficiently solves for singletons and doubletons of a digraph reliability model. Compared with previous methods, the SourceDoubls algorithm provides up to a two order of magnitude reduction in the amount of time required to solve large digraph models. This significant increase in model solution speed allows complex digraphs containing thousands of nodes to be used as knowledge bases for real time automated monitoring and diagnosis applications. Currently, an application to provide monitoring and diagnosis of the Space Station Freedom Data Management System is under development at NASA/Ames Research Center and NASA/Johnson Space Center. This paper contains an overview of this system and provides details of how it will use digraph models processed by the SourceDoubls algorithm to accomplish its task.

Iverson, D. L.↗
NASA NTRS1990

Extension of a noninteractive reliability model for ceramic matrix composites

Developments in the processing of high temperature ceramic composites demand innovative and progressive design protocols that adequately predict the thermal and mechanical behavior of these materials. The focus here is the extension of a reliability model for orthotropic ceramic composites. The approach chosen to describe failures leads to a noninteractive formulation of reliability that is phenomenological. This particular criterion, which was constructed using tensorial invariant theory, allows six potential failure modes to emerge.

Duffy, Stephen F.↗
NASA NTRS1989

Time dependent reliability model incorporating continuum damage mechanics for high-temperature ceramics

Presently there are many opportunities for the application of ceramic materials at elevated temperatures. In the near future ceramic materials are expected to supplant high temperature metal alloys in a number of applications. It thus becomes essential to develop a capability to predict the time-dependent response of these materials. The creep rupture phenomenon is discussed, and a time-dependent reliability model is outlined that integrates continuum damage mechanics principles and Weibull analysis. Several features of the model are presented in a qualitative fashion, including predictions of both reliability and hazard rate. In addition, a comparison of the continuum and the microstructural kinetic equations highlights a strong resemblance in the two approaches.

Duffy, Stephen F.↗
NASA NTRS1986

Software reliability modeling and analysis

A discrete and, as approximation to it, a continuous model for the software reliability growth process are examined. The discrete model is based on independent multinomial trials and concerns itself with the joint distribution of the first occurrence time of its underlying events (bugs). The continuous model is based on the order statistics of N independent nonidentically distributed exponential random variables. It is shown that the spacings between bugs are not necessarily independent or exponentially (geometrically) distributed. However, there is a statistical rationale for viewing them so conditionally. Some identifiability problems are pointed out and resolved. In particular, it appears that the number of bugs in a program is not identifiable. Estimated upper bounds and confidence bounds for the residual program eror content are given based on the spacings of the first k bugs removed.

Scholz, F.-W.↗
NASA NTRS1992

Advanced techniques in reliability model representation and solution

The current tendency of flight control system designs is towards increased integration of applications and increased distribution of computational elements. The reliability analysis of such systems is difficult because subsystem interactions are increasingly interdependent. Researchers at NASA Langley Research Center have been working for several years to extend the capability of Markov modeling techniques to address these problems. This effort has been focused in the areas of increased model abstraction and increased computational capability. The reliability model generator (RMG) is a software tool that uses as input a graphical object-oriented block diagram of the system. RMG uses a failure-effects algorithm to produce the reliability model from the graphical description. The ASSURE software tool is a parallel processing program that uses the semi-Markov unreliability range evaluator (SURE) solution technique and the abstract semi-Markov specification interface to the SURE tool (ASSIST) modeling language. A failure modes-effects simulation is used by ASSURE. These tools were used to analyze a significant portion of a complex flight control system. The successful combination of the power of graphical representation, automated model generation, and parallel computation leads to the conclusion that distributed fault-tolerant system architectures can now be analyzed.

Palumbo, Daniel L.↗
NASA NTRS1998

Reliability Modeling of Brittle Anisotropic Materials

A significant effort is being made to develop testing and design methodologies that will account for the lack of ductility and the strength anisotropy exhibited by brittle single crystals such as NiAl. The present approach is to modify existing test methods and brittle design methodologies, such as those applied to ceramics and glasses, and to experimentally verify the results. This paper focuses on the basic materials properties and strength behavior of a NiAl single crystal alloy and the development of a reliability model for the design of components subjected to multiaxial stresses.

Conceivably↗