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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 NTRS2016

[MaRS Project]

The Space Exploration Division of the Safety and Mission Assurances Directorate is responsible for reducing the risk to Human Space Flight Programs by providing system safety, reliability, and risk analysis. The Risk & Reliability Analysis branch plays a part in this by utilizing Probabilistic Risk Assessment (PRA) and Reliability and Maintainability (R&M) tools to identify possible types of failure and effective solutions. A continuous effort of this branch is MaRS, or Mass and Reliability System, a tool that was the focus of this internship. Future long duration space missions will have to find a balance between the mass and reliability of their spare parts. They will be unable take spares of everything and will have to determine what is most likely to require maintenance and spares. Currently there is no database that combines mass and reliability data of low level space-grade components. MaRS aims to be the first database to do this. The data in MaRS will be based on the hardware flown on the International Space Stations (ISS). The components on the ISS have a long history and are well documented, making them the perfect source. Currently, MaRS is a functioning excel workbook database; the backend is complete and only requires optimization. MaRS has been populated with all the assemblies and their components that are used on the ISS; the failures of these components are updated regularly. This project was a continuation on the efforts of previous intern groups. Once complete, R&M engineers working on future space flight missions will be able to quickly access failure and mass data on assemblies and components, allowing them to make important decisions and tradeoffs.

Aruljothi, Arunvenkatesh↗

NASA NTRS1973

A reliability and comparative analysis of two standby system configurations.

Equations are derived which enable one to calculate the system reliability for parallel or triple modular redundant systems with standby spares. Software error detection is introduced into the TMR/Spares system configuration in order to utilize fully all of the units. An indication of the sensitivity of the system reliability to an increase in the number of spares, partitioning, switching, variations in the powered and unpowered failures rates, and time is presented. A comparison of the parallel and the TMR/Spares system configurations, under similar conditions, is given.

Taylor, D. S.↗

NASA NTRS2017

A Framework for Reliability and Safety Analysis of Complex Space Missions

Long duration and complex mission scenarios are characteristics of NASA's human exploration of Mars, and will provide unprecedented challenges. Systems reliability and safety will become increasingly demanding and management of uncertainty will be increasingly important. NASA's current pioneering strategy recognizes and relies upon assurance of crew and asset safety. In this regard, flexibility to develop and innovate in the emergence of new design environments and methodologies, encompassing modeling of complex systems, is essential to meet the challenges.

Safety Analysis↗

NASA NTRS1992

Ceramic component reliability with the restructured NASA/CARES computer program

The Ceramics Analysis and Reliability Evaluation of Structures (CARES) integrated design program on statistical fast fracture reliability and monolithic ceramic components is enhanced to include the use of a neutral data base, two-dimensional modeling, and variable problem size. The data base allows for the efficient transfer of element stresses, temperatures, and volumes/areas from the finite element output to the reliability analysis program. Elements are divided to insure a direct correspondence between the subelements and the Gaussian integration points. Two-dimensional modeling is accomplished by assessing the volume flaw reliability with shell elements. To demonstrate the improvements in the algorithm, example problems are selected from a round-robin conducted by WELFEP (WEakest Link failure probability prediction by Finite Element Postprocessors).

Powers, Lynn M.↗

NASA NTRS1992

Ceramic component reliability with the restructured NASA/CARES computer program

Powers, Lynn M.↗

NASA NTRSDate not supplied

Accounting for Point Estimate Uncertainty in Space Systems Reliability and Risk Analysis

Understanding and accounting for uncertainty in risk analysis is a critical step in the management and communication of risk in engineered systems. The component and system-level analysis to determine the probability of a negative outcome and its consequence is often quantified by a point estimate. Many Program and Enterprise decisions involving technical concerns and issues rely on reliability engineering activities to produce quantified risk analysis to inform the decision making process. At NASA, it is common to use a Probabilistic Risk Analysis (PRA) to inform the overall risk to Loss of Mission or Loss of Crew that involves integration across all spacecraft subsystem fault trees to produce an overall probability of mission failure. The point estimate is an estimate of this overall probability and is an immediate result of a fault tree model. It is the result of a model where the probability of each event is taken to be equal to its mean. The value provides an approximation of the overall mean without running any uncertainty calculations (e.g., no sampling). Using only the point estimate can lead to a false sense of precision and the point estimate may not match the resulting mean when uncertainty is taken into consideration. This paper will explore five conditions that can cause the PRA model mean to diverge from the point estimate and will provide engineers and managers insight into the importance of understanding uncertainty in the elements of PRA models.

Paul J Collier↗

NASA NTRS1991

Software reliability experiments data analysis and investigation

The objectives are to investigate the fundamental reasons which cause independently developed software programs to fail dependently, and to examine fault tolerant software structures which maximize reliability gain in the presence of such dependent failure behavior. The authors used 20 redundant programs from a software reliability experiment to analyze the software errors causing coincident failures, to compare the reliability of N-version and recovery block structures composed of these programs, and to examine the impact of diversity on software reliability using subpopulations of these programs. The results indicate that both conceptually related and unrelated errors can cause coincident failures and that recovery block structures offer more reliability gain than N-version structures if acceptance checks that fail independently from the software components are available. The authors present a theory of general program checkers that have potential application for acceptance tests.

Walker, J. Leslie↗

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 NTRS1976

Reliability and coverage analysis of non-repairable fault-tolerant memory systems

A method was developed for the construction of probabilistic state-space models for nonrepairable systems. Models were developed for several systems which achieved reliability improvement by means of error-coding, modularized sparing, massive replication and other fault-tolerant techniques. From the models developed, sets of reliability and coverage equations for the systems were developed. Comparative analyses of the systems were performed using these equation sets. In addition, the effects of varying subunit reliabilities on system reliability and coverage were described. The results of these analyses indicated that a significant gain in system reliability may be achieved by use of combinations of modularized sparing, error coding, and software error control. For sufficiently reliable system subunits, this gain may far exceed the reliability gain achieved by use of massive replication techniques, yet result in a considerable saving in system cost.

Cox, G. W.↗

NASA NTRS1994

Using Finite-Element Analysis In Estimating Reliability

Method of estimating design survivability of structural component incorporates finite-element and probabilistic properties of materials. Involves evaluation of design parameters through direct comparisons of survivability of component expressed in terms of percentages of like components that survive at various lifetimes. Probabilistic properties of materials, given in terms of Weibull parameters, coupled with stress field computed by finite-element analysis to determine fatigue life based on initiation of cracks. Method applied to rotating disk containing bolt holes, representative of disks used in aerospace propulsion turbines. Also used in early stages of design process to optimize life-based designs, reducing testing of full-sized components needed to validate designs.

Zaretsky, Erwin V.↗

NASA NTRS1973

System statistical reliability model and analysis

A digital computer code was developed to simulate the time-dependent behavior of the 5-kwe reactor thermoelectric system. The code was used to determine lifetime sensitivity coefficients for a number of system design parameters, such as thermoelectric module efficiency and degradation rate, radiator absorptivity and emissivity, fuel element barrier defect constant, beginning-of-life reactivity, etc. A probability distribution (mean and standard deviation) was estimated for each of these design parameters. Then, error analysis was used to obtain a probability distribution for the system lifetime (mean = 7.7 years, standard deviation = 1.1 years). From this, the probability that the system will achieve the design goal of 5 years lifetime is 0.993. This value represents an estimate of the degradation reliability of the system.

Lekach, V. S.↗

NASA NTRS2005

Key Reliability Drivers of Liquid Propulsion Engines and A Reliability Model for Sensitivity Analysis

This paper is to address the in-flight reliability of a liquid propulsion engine system for a launch vehicle. We first establish a comprehensive list of system and sub-system reliability drivers for any liquid propulsion engine system. We then build a reliability model to parametrically analyze the impact of some reliability parameters. We present sensitivity analysis results for a selected subset of the key reliability drivers using the model. Reliability drivers identified include: number of engines for the liquid propulsion stage, single engine total reliability, engine operation duration, engine thrust size, reusability, engine de-rating or up-rating, engine-out design (including engine-out switching reliability, catastrophic fraction, preventable failure fraction, unnecessary shutdown fraction), propellant specific hazards, engine start and cutoff transient hazards, engine combustion cycles, vehicle and engine interface and interaction hazards, engine health management system, engine modification, engine ground start hold down with launch commit criteria, engine altitude start (1 in. start), Multiple altitude restart (less than 1 restart), component, subsystem and system design, manufacturing/ground operation support/pre and post flight check outs and inspection, extensiveness of the development program. We present some sensitivity analysis results for the following subset of the drivers: number of engines for the propulsion stage, single engine total reliability, engine operation duration, engine de-rating or up-rating requirements, engine-out design, catastrophic fraction, preventable failure fraction, unnecessary shutdown fraction, and engine health management system implementation (basic redlines and more advanced health management systems).

Huang, Zhao-Feng↗

NASA NTRS1989

Probabilistic structural analysis methods for improving Space Shuttle engine reliability

Probabilistic structural analysis methods are particularly useful in the design and analysis of critical structural components and systems that operate in very severe and uncertain environments. These methods have recently found application in space propulsion systems to improve the structural reliability of Space Shuttle Main Engine (SSME) components. A computer program, NESSUS, based on a deterministic finite-element program and a method of probabilistic analysis (fast probability integration) provides probabilistic structural analysis for selected SSME components. While computationally efficient, it considers both correlated and nonnormal random variables as well as an implicit functional relationship between independent and dependent variables. The program is used to determine the response of a nickel-based superalloy SSME turbopump blade. Results include blade tip displacement statistics due to the variability in blade thickness, modulus of elasticity, Poisson's ratio or density. Modulus of elasticity significantly contributed to blade tip variability while Poisson's ratio did not. Thus, a rational method for choosing parameters to be modeled as random is provided.

Boyce, L.↗

NASA NTRS2007

Reliability and Creep/Fatigue Analysis of a CMC Component

High temperature ceramic matrix composites (CMC) are being explored as viable candidate materials for hot section gas turbine components. These advanced composites can potentially lead to reduced weight and enable higher operating temperatures requiring less cooling; thus leading to increased engine efficiencies. There is a need for convenient design tools that can accommodate various loading conditions and material data with their associated uncertainties to estimate the minimum predicted life as well as the failure probabilities of a structural component. This paper presents a review of the life prediction and probabilistic analyses performed for a CMC turbine stator vane. A computer code, NASALife, is used to predict the life of a 2-D woven silicon carbide fiber reinforced silicon carbide matrix (SiC/SiC) turbine stator vane due to a mission cycle which induces low cycle fatigue and creep. The output from this program includes damage from creep loading, damage due to cyclic loading and the combined damage due to the given loading cycle. Results indicate that the trends predicted by NASALife are as expected for the loading conditions used for this study. In addition, a combination of woven composite micromechanics, finite element structural analysis and Fast Probability Integration (FPI) techniques has been used to evaluate the maximum stress and its probabilistic distribution in a CMC turbine stator vane. Input variables causing scatter are identified and ranked based upon their sensitivity magnitude. Results indicate that reducing the scatter in proportional limit strength of the vane material has the greatest effect in improving the overall reliability of the CMC vane.

Murthy, Pappu L. N.↗

NASA NTRS1971

On reliability modeling and analysis of ultrareliable fault-tolerant digital systems.

The processes of protective redundancy, namely, standby replacement (SR) redundancy and hybrid redundancy (a combination of SR and multiple-line voting redundancy), find application in the architecture of fault-tolerant digital computers and enable them to be ultrareliable and self-repairing. The claims to ultrareliability lead to the challenge of quantitatively evaluating and assigning a value to the probability of survival as a function of the mission durations intended. This note presents various mathematical models, and derives and displays quantitative evaluations of system reliability as a function of various mission parameters of interest to the system designer.

Mathur, F. P.↗

NASA NTRS1987

Reliability and throughput analysis of a concatenated coding scheme

The performance of a concatenated coding scheme for error control in ARQ systems is analyzed for both random-noise and burst-noise channels. In particular, the probability of undetected error and the system throughput are calculated. In this scheme, the inner code is used for both error correction and error detection, and the outer code is used for error detection only. Interleaving/deinterleaving is assumed within the outer code. A retransmission is requested if either the inner code or the outer code detects the presence of errors. Various coding examples are considered. The results show that concatenated coding can provide extremely high system reliability (i.e., low probability of undetected error) and high system throughput.

Deng, Robert H.↗

NASA NTRS1982

A history and analysis of hydrogen maser reliability

Hydrogen masers an integral part of the Deep Space Network, provide extremely accurate navigation about the outer planets, as well as precise location of tracking stations. Reliability of equipment over extended periods of time was considered. The Deep Space Network has a number of hydrogen masers deployed and in the test cycle, which enabled an analysis of reliability of several generations and breeds of construction. A history and analysis of hydrogen maser reliability over a three-year period was compiled several types of masers.

Curtright, J. B.↗