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The long-life deep-space missions associated with NASA's X2000 Advanced Flight Systems Program creates many unprecedented challenges for us.
This is a continuation of the report “Effects of Hand Soldering MIL-PRF-55365 Tantalum Capacitors,” which discusses the parametric effects of convection reflow soldering, JPL standard hand soldering, and optimized hand soldering on solid tantalum capacitors. The current focus is determining the long-term reliability effects of the various soldering techniques. Unfortunately, the 100-piece sample size chosen for the highly accelerated life tests was too small to reliably determine the effects of the different soldering techniques on the lifespan of the parts. In hindsight, this likely could have been predicted based on the large alphas and small betas of the Weibull failure distributions discovered during the scouting trials. Now that the effects of inadequate sample size are better understood, an opportunity exists to not only discover whether there are real differences in the reliability associated with the various soldering techniques, but also the potential to discover the voltage acceleration model and the temperature acceleration effect for these capacitors. It is recommended that the testing be repeated with a more appropriate sample size to capture this useful information.
Generally, it has been documented that the wearing of engine parts forms a failure distribution which can be approximated by a function developed by Weibull. The purpose here is to examine to what extent the Weibull distribution approximates failure data for designated engine parts of the Space Shuttle Main Engine (SSME). The current testing certification requirements will be examined in order to establish confidence levels. An examination of the failure history of SSME parts/assemblies (turbine blades, main combustion chamber, or high pressure fuel pump first stage impellers) which are limited in usage by time or starts will be done by using updated Weibull techniques. Efforts will be made by the investigator to predict failure trends by using Weibull techniques for SSME parts (turbine temperature sensors, chamber pressure transducers, actuators, and controllers) which are not severely limited by time or starts.
The Federal Aviation Administration has embarked on an historic task of modernizing and significantly improving the national air transportation system. One system that uses the Global Positioning System (GPS) to determine aircraft navigational information is called the Wide Area Augmentation System (WAAS). This paper describes a reliability assessment of one candidate system architecture for the WAAS. A unique aspect of this study regards the modeling and solution of a candidate system that allows a novel cold sparing scheme. The cold spare is a WAAS communications satellite that is fabricated and launched after a predetermined number of orbiting satellite failures have occurred and after some stochastic fabrication time transpires. Because these satellites are complex systems with redundant components, they exhibit an increasing failure rate with a Weibull time to failure distribution. Moreover, the cold spare satellite build-time is Weibull and upon launch is considered to be a good-as-new system with an increasing failure rate and a Weibull time to failure distribution as well. The reliability model for this system is non-Markovian because three distinct system clocks are required: the time to failure of the orbiting satellites, the build time for the cold spare, and the time to failure for the launched spare satellite. A powerful dynamic fault tree modeling notation and Monte Carlo simulation technique with importance sampling are shown to arrive at a reliability prediction for a 10 year mission.
Recent developments in reliability modeling and computer technology have made it practical to use the Weibull time to failure distribution to model the system reliability of complex fault-tolerant computer-based systems. These system models are becoming increasingly popular in space systems applications as a result of mounting data that support the decreasing Weibull failure distribution and the expectation of increased system reliability. This presentation introduces the new reliability modeling developments and demonstrates their application to a novel space system application. The application is a proposed guidance, navigation, and control (GN&C) system for use in a long duration manned spacecraft for a possible Mars mission. Comparisons to the constant failure rate model are presented and the ramifications of doing so are discussed.
The Weibull weak-link theory allows for the computation of distribution functions for both the fracture location and the applied far-field stress. Several authors have suggested using the fracture location information from tests to infer Weibull parameters, and others have used the predictive capabilities of the theory to calculate average fracture locations for brittle bodies. By a simple set of example calculations, it is shown that the fracture location distribution function is distinctly more sensitive to perturbations in the stress state than the fracture stress distribution function is. In general, the average fracture location is more subject to stress perturbations than the average fracture stress. The results indicate that care must be exercised in applying fracture location theory.
The nuclear-grade (low-impurity) graphite needed for the fuel element and moderator material for next-generation (Gen IV) reactors displays large scatter in strength and a nonlinear stress-strain response from damage accumulation. This response can be characterized as quasi-brittle. In this expanded review, relevant statistical failure models for various brittle and quasi-brittle material systems are discussed with regard to strength distribution, size effect, multiaxial strength, and damage accumulation. This includes descriptions of the Weibull, Batdorf, and Burchell models as well as models that describe the strength response of composite materials, which involves distributed damage. Results from lattice simulations are included for a physics-based description of material breakdown. Consideration is given to the predicted transition between brittle and quasi-brittle damage behavior versus the density of damage (level of disorder) within the material system. The literature indicates that weakest-link-based failure modeling approaches appear to be reasonably robust in that they can be applied to materials that display distributed damage, provided that the level of disorder in the material is not too large. The Weibull distribution is argued to be the most appropriate statistical distribution to model the stochastic-strength response of graphite.
A three-bay, space, cantilever truss is probabilistically evaluated using the computer code NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) to identify and quantify the uncertainties and respective sensitivities associated with corresponding uncertainties in the primitive variables (structural, material, and loads parameters) that defines the truss. The distribution of each of these primitive variables is described in terms of one of several available distributions such as the Weibull, exponential, normal, log-normal, etc. The cumulative distribution function (CDF's) for the response functions considered and sensitivities associated with the primitive variables for given response are investigated. These sensitivities help in determining the dominating primitive variables for that response.
A probabilistic finite element program is used to perform probabilistic analysis of a materially nonlinear structure. The program used in this study is NESSUS (Numerical Evaluation of Stochastic Structure Under Stress), under development at Southwest Research Institute. The cumulative distribution function (CDF) of the radial stress of a thick-walled cylinder under internal pressure is computed and compared with the analytical solution. In addition, sensitivity factors showing the relative importance of the input random variables are calculated. Significant plasticity is present in this problem and has a pronounced effect on the probabilistic results. The random input variables are the material yield stress and internal pressure with Weibull and normal distributions, respectively. The results verify the ability of NESSUS to compute the CDF and sensitivity factors of a materially nonlinear structure. In addition, the ability of the Advanced Mean Value (AMV) procedure to assess the probabilistic behavior of structures which exhibit a highly nonlinear response is shown. Thus, the AMV procedure can be applied with confidence to other structures which exhibit nonlinear behavior.
Stratocumulus cloud fields in the FIRE IFO region are analyzed using LANDSAT Thematic Mapper imagery. Structural properties such as cloud cell size distribution, cell horizontal aspect ratio, fractional coverage and fractal dimension are determined. It is found that stratocumulus cloud number densities are represented by a power law. Cell horizontal aspect ratio has a tendency to increase at large cell sizes, and cells are bi-fractal in nature. Using LANDSAT Multispectral Scanner imagery for twelve selected stratocumulus scenes acquired during previous years, similar structural characteristics are obtained. Cloud field spatial organization also is analyzed. Nearest-neighbor spacings are fit with a number of functions, with Weibull and Gamma distributions providing the best fits. Poisson tests show that the spatial separations are not random. Second order statistics are used to examine clustering.
A reliability analysis for predicting the statistical distribution of time to fatigue crack initiation for aircraft structures in service is presented. The present analysis utilizes the statistical data of the specimen fatigue tests, the full-scale structure tests, and the statistical dispersion of aircraft service loads. The statistical distribution of the time to fatigue crack initiation of the full-scale structure under laboratory loading spectrum is assumed to be Weibull. The service loads for gust turbulences are modeled as Poisson processes for transport-type aircraft, while the maneuver loads are modeled as compound Poisson processes for fighter and training aircraft. It is found that the statistical distribution of time to fatigue crack initiation for aircraft structures in service is not Weibull and that the prediction on the basis of the Weibull distribution is unconservative, in particular in the early service time.
A new method to determin an optimal retry policy and for use in retry of fault characterization is presented. An optimal retry policy for a given fault characteristic, which determines the maximum allowable retry durations to minimize the total task completion time was derived. The combined fault characterization and retry decision, in which the characteristics of fault are estimated simultaneously with the determination of the optimal retry policy were carried out. Two solution approaches were developed, one based on the point estimation and the other on the Bayes sequential decision. The maximum likelihood estimators are used for the first approach, and the backward induction for testing hypotheses in the second approach. Numerical examples in which all the durations associated with faults have monotone hazard functions, e.g., exponential, Weibull and gamma distributions are presented. These are standard distributions commonly used for modeling analysis and faults.
In this paper a modified importance sampling technique for improving the convergence of Importance Sampling is given. By using this approach to estimate low false alarm rates in radar simulations, the number of Monte Carlo runs can be reduced significantly. For one-dimensional exponential, Weibull, and Rayleigh distributions, a uniformly minimum variance unbiased estimator is obtained. For Gaussian distribution the estimator in this approach is uniformly better than that of previously known Importance Sampling approach. For a cell averaging system, by combining this technique and group sampling, the reduction of Monte Carlo runs for a reference cell of 20 and false alarm rate of lE-6 is on the order of 170 as compared to the previously known Importance Sampling approach.
The structure of thermally sprayed coatings consists of lamellae which are oriented parallel to the substrate surface. The lamellae separate and fracture by distinctive mechanisms which are reflected in the failure morphology, and these may be described as adhesive (between the coating and substrate), cohesive (within the coating), or mixed mode. There is a large variability in the failure stress for any nominally identical group of coatings. A lower bound for the fracture toughness of alumina coatings can be calculated as 0.2 MNm exp -3/2. The coating strength values may also be treated as belonging to the statistical distribution of the Weibull function. The Weibull modulus of the coating strength varied from 1.4 to 3.8. This analysis infers that the flaw size within coatings is highly variable and that the flaws are nonuniformly dispersed. The present work focuses on the question of whether tensile adhesion tests are an appropriate testing method for thermally sprayed materials.
A reliability-based optimization methodology has been developed to design the raked wing tip of the Boeing 767-400 extended range airliner made of composite and metallic materials. Design is formulated for an accepted level of risk or reliability. The design variables, weight and the constraints became functions of reliability. Uncertainties in the load, strength and the material properties, as well as the design variables, were modeled as random parameters with specified distributions, like normal, Weibull or Gumbel functions. The objective function and constraint, or a failure mode, became derived functions of the risk-level. Solution to the problem produced the optimum design with weight, variables and constraints as a function of the risk-level. Optimum weight versus reliability traced out an inverted-S shaped graph. The center of the graph corresponded to a 50 percent probability of success, or one failure in two samples. Under some assumptions, this design would be quite close to the deterministic optimum solution. The weight increased when reliability exceeded 50 percent, and decreased when the reliability was compromised. A design could be selected depending on the level of risk acceptable to a situation. The optimization process achieved up to a 20-percent reduction in weight over traditional design.
This project included both research and education objectives. The goal of this project was to advance innovative research and education objectives in theoretical and computational probabilistic structural analysis, reliability, and life prediction for improved reliability and safety of structural components of aerospace and aircraft propulsion systems. Research and education partners included Glenn Research Center (GRC) and Southwest Research Institute (SwRI) along with the University of Texas at San Antonio (UTSA). SwRI enhanced the NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) code and provided consulting support for NESSUS-related activities at UTSA. NASA funding supported three undergraduate students, two graduate students, a summer course instructor and the Principal Investigator. Matching funds from UTSA provided for the purchase of additional equipment for the enhancement of the Advanced Interactive Computational SGI Lab established during the first year of this Partnership Award to conduct the probabilistic finite element summer courses. The research portion of this report presents the cumulation of work performed through the use of the probabilistic finite element program, NESSUS, Numerical Evaluation and Structures Under Stress, and an embedded Material Strength Degradation (MSD) model. Probabilistic structural analysis provided for quantification of uncertainties associated with the design, thus enabling increased system performance and reliability. The structure examined was a Space Shuttle Main Engine (SSME) fuel turbopump blade. The blade material analyzed was Inconel 718, since the MSD model was previously calibrated for this material. Reliability analysis encompassing the effects of high temperature and high cycle fatigue, yielded a reliability value of 0.99978 using a fully correlated random field for the blade thickness. The reliability did not change significantly for a change in distribution type except for a change in distribution from Gaussian to Weibull for the centrifugal load. The sensitivity factors determined to be most dominant were the centrifugal loading and the initial strength of the material. These two sensitivity factors were influenced most by a change in distribution type from Gaussian to Weibull. The education portion of this report describes short-term and long-term educational objectives. Such objectives serve to integrate research and education components of this project resulting in opportunities for ethnic minority students, principally Hispanic. The primary vehicle to facilitate such integration was the teaching of two probabilistic finite element method courses to undergraduate engineering students in the summers of 1998 and 1999.
The robustness of reliability predictions based on the exponential failure law is investigated under possible deviations within the Weibull family of failure distributions. Regions of robustness are provided for series systems of N identical components, N = 1(1)15; i.e., regions in the space of the Weibull shape parameter, within which one may safely use the exponential prediction procedure and have no more than a prespecified error.
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.