Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “reliability growth modeling”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

A Misperception in Reliability Growth Modelling

The Duane reliability growth model is n(t)/t = k t^-alpha (1) The reliability growth rate is alpha, the downward slope of n(t)/t versus t. It usually varies from 0.2 to 0.6. k is a constant. Crow used a 56-failure data set to illustrate reliability growth.1 A graphical Duane model fit to this data gives n(t)/t = 0.640 t^-0.283 (2) A problem in using the Duane-Crow reliability growth model is that it assumes that reliability growth continues and the failure rate decreases throughout the test period. It is more usual that reliability growth stops when the failure rated is low enough. Growth testing is often followed by testing with a low constant failure rate due to rare or uncorrectable failure modes. As more and more low constant rate acceptable failures accumulate after the period of reliability growth, the reliability growth time exponent alpha decreases toward zero. This occurs if constant rate failures are treated as occurring during the reliability growth period. It is more accurate to model a period of initial reliability growth followed by testing without repair to more accurately determine the final constant failure rate. This is done in the abcd model. n(t)/t = a t^-b + c from t = 0 to td (3) = c + d after td, where d = a td^-b (4) The term a t^-b describes the continuous reliability growth that continues out to time td and c is the constant uncorrected failure rate. The parameter d represents an additional constant failure rate due to correctable but uncorrected failure modes. After the reliability growth process is terminated, the failure rate n(t)/t = c + d.

Harry W Jones↗
NASA NTRSDate not supplied

Reliability Growth Modeling and Testing

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 NTRS1991

Reliability growth models for NASA applications

The objective of any reliability growth study is prediction of reliability at some future instant. Another objective is statistical inference, estimation of reliability for reliability demonstration. A cause of concern for the development engineer and management is that reliability demands an excessive number of tests for reliability demonstration. For example, the Space Transportation Main Engine (STME) program requirements call for .99 reliability at 90 pct. confidence for demonstration. This requires running 230 tests with zero failure if a classical binomial model is used. It is therefore also an objective to explore the reliability growth models for reliability demonstration and tracking and their applicability to NASA programs. A reliability growth model is an analytical tool used to monitor the reliability progress during the development program and to establish a test plan to demonstrate an acceptable system reliability.

Taneja, Vidya S.↗
NASA NTRS2024

The abcd Reliability Growth Model

This paper presents a modification of the well-known Duane-Crow reliability growth model. In the abcd reliability growth model, the initial period of exponential decline of the failure rate in the Duane-Crow model may be followed by a period of constant failure rate. Data often show that an exponential decline in failures is followed by a constant failure rate. If a growth model including only the initial period of exponential decline is applied to increasingly longer failure rate data sets, the data will include longer periods of constant failure rate, and the estimated reliability growth rate will decline from an initially high value down toward zero. Using the Duane-Crow model without extending it to include a possible period of constant failure rate may create the mistaken impression that the initial reliability growth continues forever, but at an ever decreasing rate.

Reliability growth↗
NASA NTRS2024

The abcd Reliability Growth Model

This paper presents a modification of the well-known Duane-Crow reliability growth model. In the abcd reliability growth model, the initial period of exponential decline of the failure rate in the Duane-Crow model may be followed by a period of constant failure rate. Data often show that an exponential decline in failures is followed by a constant failure rate. If a growth model including only the initial period of exponential decline is applied to increasingly longer failure rate data sets, the data will include longer periods of constant failure rate, and the estimated reliability growth rate will decline from an initially high value down toward zero. Using the Duane-Crow model without extending it to include a possible period of constant failure rate may create the mistaken impression that the initial reliability growth continues forever, but at an ever decreasing rate.

Reliability growth↗
NASA NTRS1992

An overview of reliability growth models and their potential use for NASA applications

An overview is provided of reliability growth literature over the past 25 years. This includes a thorough literature review of different areas of the application of reliability growth such as design, prediction, tracking/management, and demonstration. Various reliability growth models use different bases on how they characterize growth. Different models are discussed. Also, the use is addressed of reliability growth models to NASA applications. This includes the application of these models to the space shuttle main engine. For potential NASA applications, we classify growth models in two groups, which are characterized.

Taneja, V. S.↗
NASA NTRS1990

Reliability growth modeling analysis of the space shuttle main engines based upon the Weibull process

The Weibull process, identified as the inhomogeneous Poisson process with the Weibull intensity function, is used to model the reliability growth assessment of the space shuttle main engine test and flight failure data. Additional tables of percentage-point probabilities for several different values of the confidence coefficient have been generated for setting (1-alpha)100-percent two sided confidence interval estimates on the mean time between failures. The tabled data pertain to two cases: (1) time-terminated testing, and (2) failure-terminated testing. The critical values of the three test statistics, namely Cramer-von Mises, Kolmogorov-Smirnov, and chi-square, were calculated and tabled for use in the goodness of fit tests for the engine reliability data. Numerical results are presented for five different groupings of the engine data that reflect the actual response to the failures.

Wheeler, J. T.↗
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 NTRS1991

A nonparametric software-reliability growth model

The authors (1985) previously introduced a nonparametric model for software-reliability growth which is based on complete monotonicity of the failure rate. The authors extend the completely monotone software model by developing a method for providing long-range predictions of reliability growth, based on the model. They derive upper and lower bounds on extrapolation of the failure rate and the mean function. These are then used to obtain estimates for the future software failure rate and the mean future number of failures. Preliminary evaluation indicates that the method is competitive with parametric approaches, while being more robust.

Sofer, Ariela↗
NASA NTRS1991

On the use and the performance of software reliability growth models

We address the problem of predicting future failures for a piece of software. The number of failures occurring during a finite future time interval is predicted from the number failures observed during an initial period of usage by using software reliability growth models. Two different methods for using the models are considered: straightforward use of individual models, and dynamic selection among models based on goodness-of-fit and quality-of-prediction criteria. Performance is judged by the relative error of the predicted number of failures over future finite time intervals relative to the number of failures eventually observed during the intervals. Six of the former models and eight of the latter are evaluated, based on their performance on twenty data sets. Many open questions remain regarding the use and the performance of software reliability growth models.

Keiller, Peter A.↗
NASA NTRS1983

A Bayesian modification to the Jelinski-Moranda software reliability growth model

The Jelinski-Moranda (JM) model for software reliability was examined. It is suggested that a major reason for the poor results given by this model is the poor performance of the maximum likelihood method (ML) of parameter estimation. A reparameterization and Bayesian analysis, involving a slight modelling change, are proposed. It is shown that this new Bayesian-Jelinski-Moranda model (BJM) is mathematically quite tractable, and several metrics of interest to practitioners are obtained. The BJM and JM models are compared by using several sets of real software failure data collected and in all cases the BJM model gives superior reliability predictions. A change in the assumption which underlay both models to present the debugging process more accurately is discussed.

Littlewood, B.↗
NASA NTRS1989

Software reliability growth models dominated by randomness

The Jelinski-Moranda and Geometric models for software reliability failed the consistency test which was proposed. These models were challenged to take data which comes from a process which they have correctly modeled and to make predictions about the reliability of that process. It was found that either model, given data precisely from a process it correctly models, will usually fail to make good predictions. These problems are attributed to randomness in the data used as input to the models and a remedy is indicated for this lack of robustness, namely replication of data.

Shen, Wenhui↗
NASA NTRS1988

A nonparametric software reliability growth model

Miller and Sofer have presented a nonparametric method for estimating the failure rate of a software program. The method is based on the complete monotonicity property of the failure rate function, and uses a regression approach to obtain estimates of the current software failure rate. This completely monotone software model is extended. It is shown how it can also provide long-range predictions of future reliability growth. Preliminary testing indicates that the method is competitive with parametric approaches, while being more robust.

Miller, Douglas R.↗
NASA NTRS2014

Reliability Growth in Space Life Support Systems

A hardware system's failure rate often increases over time due to wear and aging, but not always. Some systems instead show reliability growth, a decreasing failure rate with time, due to effective failure analysis and remedial hardware upgrades. Reliability grows when failure causes are removed by improved design. A mathematical reliability growth model allows the reliability growth rate to be computed from the failure data. The space shuttle was extensively maintained, refurbished, and upgraded after each flight and it experienced significant reliability growth during its operational life. In contrast, the International Space Station (ISS) is much more difficult to maintain and upgrade and its failure rate has been constant over time. The ISS Carbon Dioxide Removal Assembly (CDRA) reliability has slightly decreased. Failures on ISS and with the ISS CDRA continue to be a challenge.

life support↗
NASA NTRS1991

Statistical modelling of software reliability

During the six-month period from 1 April 1991 to 30 September 1991 the following research papers in statistical modeling of software reliability appeared: (1) A Nonparametric Software Reliability Growth Model; (2) On the Use and the Performance of Software Reliability Growth Models; (3) Research and Development Issues in Software Reliability Engineering; (4) Special Issues on Software; and (5) Software Reliability and Safety.

Miller, Douglas R.↗
NASA NTRS1982

A Markov chain model for reliability growth and decay

A mathematical model is developed to describe a complex system undergoing a sequence of trials in which there is interaction between the internal states of the system and the outcomes of the trials. For example, the model might describe a system undergoing testing that is redesigned after each failure. The basic assumptions for the model are that the state of the system after a trial depends probabilistically only on the state before the trial and on the outcome of the trial and that the outcome of a trial depends probabilistically only on the state of the system before the trial. It is shown that under these basic assumptions, the successive states form a Markov chain and the successive states and outcomes jointly form a Markov chain. General results are obtained for the transition probabilities, steady-state distributions, etc. A special case studied in detail describes a system that has two possible state ('repaired' and 'unrepaired') undergoing trials that have three possible outcomes ('inherent failure', 'assignable-cause' 'failure' and 'success'). For this model, the reliability function is computed explicitly and an optimal repair policy is obtained.

Siegrist, K.↗