Reliability Prediction Using Flight Experience - Weibull Adjusted Probability of Survival, WAPS
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Weibull Probability↗
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Weibull crack density coefficient for polydimensional stress states
A structural ceramic analysis and reliability evaluation code has recently been developed encompassing volume and surface flaw induced fracture, modeled by the two-parameter Weibull probability density function. A segment of the software involves computing the Weibull polydimensional stress state crack density coefficient from uniaxial stress experimental fracture data. The relationship of the polydimensional stress coefficient to the uniaxial stress coefficient is derived for a shear-insensitive material with a random surface flaw population.
Gross, Bernard↗
Management of SSME hardware life utilization
Statistical and probabilistic reliability methodologies were developed for the determination of hardware life limits for the Space Shuttle Main Engine (SSME). Both methodologies require that a mathematical reliability model of the engine (system) performance be developed as a function of the reliabilities of the components and parts. The system reliability model should be developed from the Failute Modes and Effects Analysis/Critical Items List. The statistical reliability methodology establishes hardware life limits directly from the failure distributions of the components and parts obtained from statistically-designed testing. The probabilistic reliability methodology establishes hardware life limits from a decision analysis methodology which incorporates the component/part reliabilities obtained from a probabilistic structural analysis, a calibrated maintenance program, inspection techniques, and fabrication procedures. Probilistic structural analysis is recommended as a tool to prioritize upgrading of the components and parts. The Weibull probability distribution is presently being investigated by NASA/MSFC to characterize the failure distribution of the SSME hardware from a limited data base of failures.
Pauschke, J. M.↗
System-Availability And Resource-Allocation Program
ACARA analyzes availability, life-cycle cost, and scheduling of resources. Uses statistical Monte Carlo method to simulate capacity states of system as well as failure and repair of components. Failures of components modeled mathematically by use of combination of exponential and Weibull probability distributions. Schedules replacement of components to optimize performance of system. Made to comply with any constraints on production of components, capacities of resupply vehicles, spares kept on site, crews, and/or equipment. Written in APL2.
Viterna, L. A.↗
Bivariate extreme value distributions
In certain engineering applications, such as those occurring in the analyses of ascent structural loads for the Space Transportation System (STS), some of the load variables have a lower bound of zero. Thus, the need for practical models of bivariate extreme value probability distribution functions with lower limits was identified. We discuss the Gumbel models and present practical forms of bivariate extreme probability distributions of Weibull and Frechet types with two parameters. Bivariate extreme value probability distribution functions can be expressed in terms of the marginal extremel distributions and a 'dependence' function subject to certain analytical conditions. Properties of such bivariate extreme distributions, sums and differences of paired extremals, as well as the corresponding forms of conditional distributions, are discussed. Practical estimation techniques are also given.
Elshamy, M.↗
Incorporating finite element analysis into component life and reliability
A method for calculating a component's design survivability by incorporating finite element analysis and probabilistic material properties was developed. The method evaluates design parameters through direct comparisons of component survivability expressed in terms of Weibull parameters. The analysis was applied to a rotating disk with mounting bolt holes. The highest probability of failure occurred at, or near, the maximum shear stress region of the bolt holes. Distribution of failure as a function of Weibull slope affects the probability of survival. Where Weibull parameters are unknown for a rotating disk, it may be permissible to assume Weibull parameters, as well as the stress-life exponent, in order to determine the disk speed where the probability of survival is highest.
August, Richard↗
Fatigue criterion to system design, life and reliability: A primer
A method for estimating a component's design survivability by incorporating finite element analysis and probabilistic material properties was developed. The method evaluates design parameters through direct comparisons of component survivability expressed in terms of Weibull parameters. The analysis was applied to a rotating disk with mounting bolt holes. The highest probability of failure occurred at, or near, the maximum shear stress region of the bolt holes. Distribution of material failure as a function of Weibull slope affects the probability of survival. Where Weibull parameters are unknown for a rotating disk, it may be permissible to assume Weibull parameters, as well as the stress-life exponent, in order to determine the qualitative effect of disk speed on the probability of survival.
Zaretsky, Erwin V.↗
Wear-Out Sensitivity Analysis Project Abstract
During the course of the Summer 2015 internship session, I worked in the Reliability and Maintainability group of the ISS Safety and Mission Assurance department. My project was a statistical analysis of how sensitive ORU's (Orbital Replacement Units) are to a reliability parameter called the wear-out characteristic. The intended goal of this was to determine a worst case scenario of how many spares would be needed if multiple systems started exhibiting wear-out characteristics simultaneously. The goal was also to determine which parts would be most likely to do so. In order to do this, my duties were to take historical data of operational times and failure times of these ORU's and use them to build predictive models of failure using probability distribution functions, mainly the Weibull distribution. Then, I ran Monte Carlo Simulations to see how an entire population of these components would perform. From here, my final duty was to vary the wear-out characteristic from the intrinsic value, to extremely high wear-out values and determine how much the probability of sufficiency of the population would shift. This was done for around 30 different ORU populations on board the ISS.
Harris, Adam↗
Weibull-Based Design Methodology for Rotating Aircraft Engine Structures
The NASA Energy Efficient Engine (E(sup 3)-Engine) is used as the basis of a Weibull-based life and reliability analysis. Each component's life and thus the engine's life is defined by high-cycle fatigue (HCF) or low-cycle fatigue (LCF). Knowing the cumulative life distribution of each of the components making up the engine as represented by a Weibull slope is a prerequisite to predicting the life and reliability of the entire engine. As the engine Weibull slope increases, the predicted lives decrease. The predicted engine lives L(sub 5) (95 % probability of survival) of approximately 17,000 and 32,000 hr do correlate with current engine maintenance practices without and with refurbishment. respectively. The individual high pressure turbine (HPT) blade lives necessary to obtain a blade system life L(sub 0.1) (99.9 % probability of survival) of 9000 hr for Weibull slopes of 3, 6 and 9, are 47,391 and 20,652 and 15,658 hr, respectively. For a design life of the HPT disks having probable points of failure equal to or greater than 36,000 hr at a probability of survival of 99.9 %, the predicted disk system life L(sub 0.1) can vary from 9,408 to 24,911 hr.
Zaretsky, Erwin↗
Surface flaw reliability analysis of ceramic components with the SCARE finite element postprocessor program
The SCARE (Structural Ceramics Analysis and Reliability Evaluation) computer program on statistical fast fracture reliability analysis with quadratic elements for volume distributed imperfections is enhanced to include the use of linear finite elements and the capability of designing against concurrent surface flaw induced ceramic component failure. The SCARE code is presently coupled as a postprocessor to the MSC/NASTRAN general purpose, finite element analysis program. The improved version now includes the Weibull and Batdorf statistical failure theories for both surface and volume flaw based reliability analysis. The program uses the two-parameter Weibull fracture strength cumulative failure probability distribution model with the principle of independent action for poly-axial stress states, and Batdorf's shear-sensitive as well as shear-insensitive statistical theories. The shear-sensitive surface crack configurations include the Griffith crack and Griffith notch geometries, using the total critical coplanar strain energy release rate criterion to predict mixed-mode fracture. Weibull material parameters based on both surface and volume flaw induced fracture can also be calculated from modulus of rupture bar tests, using the least squares method with known specimen geometry and grouped fracture data. The statistical fast fracture theories for surface flaw induced failure, along with selected input and output formats and options, are summarized. An example problem to demonstrate various features of the program is included.
Gyekenyesi, John P.↗
Surface flaw reliability analysis of ceramic components with the SCARE finite element postprocessor program
The SCARE (Structural Ceramics Analysis and Reliability Evaluation) computer program on statistical fast fracture reliability analysis with quadratic elements for volume distributed imperfections is enhanced to include the use of linear finite elements and the capability of designing against concurrent surface flaw induced ceramic component failure. The SCARE code is presently coupled as a postprocessor to the MSC/NASTRAN general purpose, finite element analysis program. The improved version now includes the Weibull and Batdorf statistical failure theories for both surface and volume flaw based reliability analysis. The program uses the two-parameter Weibull fracture strength cumulative failure probability distribution model with the principle of independent action for poly-axial stress states, and Batdorf's shear-sensitive as well as shear-insensitive statistical theories. The shear-sensitive surface crack configurations include the Griffith crack and Griffith notch geometries, using the total critical coplanar strain energy release rate criterion to predict mixed-mode fracture. Weibull material parameters based on both surface and volume flaw induced fracture can also be calculated from modulus of rupture bar tests, using the least squares method with known specimen geometry and grouped fracture data. The statistical fast fracture theories for surface flaw induced failure, along with selected input and output formats and options, are summarized. An example problem to demonstrate various features of the program is included.
Gyekenyesi, J. P.↗
Explicit 3D continuum fracture modeling with smooth particle hydrodynamics
Impact phenomena shaped our solar system. As usual for most solar system processes, the scales are far different than we can address directly in the laboratory. Impact velocities are often much higher than we can achieve, sizes are often vastly larger, and most impacts take place in an environment where the only gravitational force is the mutual pull of the impactors. The Smooth Particle Hydrodynamics (SPH) technique has been applied in the past to the simulations of giant impacts. In these simulations, the colliding objects were so massive (at least a sizeable fraction of the Earth's mass) that material strength was negligible compared to gravity. This assumption can no longer be made when the bodies are much smaller. To this end, we have developed a 3D SPH code that includes a strength model to which we have added a von Mises yielding relation for stresses beyond the Hugoniot Elastic Limit. At the lower stresses associated with brittle failure, we use a rate-dependent strength based on the nucleation of incipient flaws whose number density is given by a Weibull distribution. Following Grady and Kipp and Melosh et al., we introduce a state variable D ('damage'), 0 less than D less than 1, which expresses the local reduction in strength due to crack growth under tensile loading. Unfortunately for the hydrodynamics, Grady and Kipp's model predicts which fragments are the most probable ones and not the ones that are really formed. This means, for example, that if a given laboratory experiment is modeled, the fragment distribution obtained from the Grady-Kipp theory would be equivalent to a ensemble average over many realizations of the experiment. On the other hand, the hydrodynamics itself is explicit and evolves not an ensemble average but very specific fragments. Hence, there is a clear incompatibility with the deterministic nature of the hydrodynamics equations and the statistical approach of the Grady-Kipp dynamical fracture model. We remedy these shortcomings by making the incipient flaw distribution explicit, i.e., particles carry activation strains which are distributed at random with a probability of occurrence given by the Weibull distribution. If the local principal axis strain exceeds this limit, damage starts to grow. By growing explicit cracks together with statistical cracks (damage) at the sub-particle scale, we ensure that material strength and fragmentation is independent of model resolution. We tested our scheme by simulating laboratory impact experiments on basalt spheres.
Benz, W.↗
SIP qualification and PRA approaches
System in a package (SIP) development is a response to an increasing demand for integration of different functions into one unit to reduce size and cost and improve functionality. Qualification of the newly developed multifunctional electronics are becoming complex at the package level and even more at the second and system levels.
probability risk assessment weibull lognormal ball↗
Effect of Individual Component Life Distribution on Engine Life Prediction
The effect of individual engine component life distributions on engine life prediction was determined. A Weibull-based life and reliability analysis of the NASA Energy Efficient Engine was conducted. The engine s life at a 95 and 99.9 percent probability of survival was determined based upon the engine manufacturer s original life calculations and assumed values of each of the component s cumulative life distributions as represented by a Weibull slope. The lives of the high-pressure turbine (HPT) disks and blades were also evaluated individually and as a system in a similar manner. Knowing the statistical cumulative distribution of each engine component with reasonable engineering certainty is a condition precedent to predicting the life and reliability of an entire engine. The life of a system at a given reliability will be less than the lowest-lived component in the system at the same reliability (probability of survival). Where Weibull slopes of all the engine components are equal, the Weibull slope had a minimal effect on engine L(sub 0.1) life prediction. However, at a probability of survival of 95 percent (L(sub 5) life), life decreased with increasing Weibull slope.
Zaretsky, Erwin V.↗
Computing Reliabilities Of Ceramic Components
CARES/PC computer program performs statistical analysis of data obtained from fracture of simple, uniaxial tensile or flexural specimens of ceramics and estimates Weibull and Batdorf material parameters from these data. CARES/PC is subset of Ceramics Analysis and Reliability Evaluation of Structures (CARES) program (LEW-15168), which calculates fast-fracture reliabilities or failure probabilities of ceramic components by use of Batdorf and Weibull models to describe effects of multiaxial stress states on strengths of materials. CARES/PC written and compiled with the Microsoft FORTRAN v5.0 compiler.
Szatmary, S. A.↗
Probabilistic Study Conducted on Sensor-Based Engine Life Calculation
Turbine engine life management is a very complicated process to ensure the safe operation of an engine subjected to complex usage. The challenge of life management is to find a reasonable compromise between the safe operation and the maximum usage of critical parts to reduce maintenance costs. The commonly used "cycle count" approach does not take the engine operation conditions into account, and it oversimplifies the calculation of the life usage. Because of the shortcomings, many engine components are regularly pulled for maintenance before their usable life is over. And, if an engine has been running regularly under more severe conditions, components might not be taken out of service before they exceed their designed risk of failure. The NASA Glenn Research Center and its industrial and academic partners have been using measurable parameters to improve engine life estimation. This study was based on the Monte Carlo simulation of 5000 typical flights under various operating conditions. First a closed-loop engine model was developed to simulate the engine operation across the mission profile and a thermomechanical fatigue (TMF) damage model was used to calculate the actual damage during takeoff, where the maximum TMF accumulates. Next, a Weibull distribution was used to estimate the implied probability of failure for a given accumulated cycle count. Monte Carlo simulations were then employed to find the profiles of the TMF damage under different operating assumptions including parameter uncertainties. Finally, probabilities of failure for different operating conditions were analyzed to demonstrate the importance of a sensor-based damage calculation in order to better manage the risk of failure and on-wing life.
Guo, Ten-Huei↗
Large-Scale Weibull Analysis of H-451 Nuclear- Grade Graphite Specimen Rupture Data
A Weibull analysis was performed of the strength distribution and size effects for 2000 specimens of H-451 nuclear-grade graphite. The data, generated elsewhere, measured the tensile and four-point-flexure room-temperature rupture strength of specimens excised from a single extruded graphite log. Strength variation was compared with specimen location, size, and orientation relative to the parent body. In our study, data were progressively and extensively pooled into larger data sets to discriminate overall trends from local variations and to investigate the strength distribution. The CARES/Life and WeibPar codes were used to investigate issues regarding the size effect, Weibull parameter consistency, and nonlinear stress-strain response. Overall, the Weibull distribution described the behavior of the pooled data very well. However, the issue regarding the smaller-than-expected size effect remained. This exercise illustrated that a conservative approach using a two-parameter Weibull distribution is best for designing graphite components with low probability of failure for the in-core structures in the proposed Generation IV (Gen IV) high-temperature gas-cooled nuclear reactors. This exercise also demonstrated the continuing need to better understand the mechanisms driving stochastic strength response. Extensive appendixes are provided with this report to show all aspects of the rupture data and analytical results.
Nemeth, Noel N.↗
SCARE: A post-processor program to MSC/NASTRAN for the reliability analysis of structural ceramic components
A computer program was developed for calculating the statistical fast fracture reliability and failure probability of ceramic components. The program includes the two-parameter Weibull material fracture strength distribution model, using the principle of independent action for polyaxial stress states and Batdorf's shear-sensitive as well as shear-insensitive crack theories, all for volume distributed flaws in macroscopically isotropic solids. Both penny-shaped cracks and Griffith cracks are included in the Batdorf shear-sensitive crack response calculations, using Griffith's maximum tensile stress or critical coplanar strain energy release rate criteria to predict mixed mode fracture. Weibull material parameters can also be calculated from modulus of rupture bar tests, using the least squares method with known specimen geometry and fracture data. The reliability prediction analysis uses MSC/NASTRAN stress, temperature and volume output, obtained from the use of three-dimensional, quadratic, isoparametric, or axisymmetric finite elements. The statistical fast fracture theories employed, along with selected input and output formats and options, are summarized. An example problem to demonstrate various features of the program is included.
Gyekenyesi, J. P.↗