Results for “Weibull parameters” — Page 8

DOE OSTI2024

Inferring Reliability Model Parameters from Expert Opinion

Here, we propose a method for constructing bathtub models of reliability from opinion. The method is intended for reliability studies early in the design and prototyping of a new system, before data concerning reliability has become available. A stylized bathtub curve is presented for soliciting best engineering judgement from technical experts. By pooling these stylized curves, we produce data that can be used to infer parameters for a piece-wise Weibull model of reliability. A numerical example demonstrates the practicality of the method while also highlighting potential pitfalls when working with subjective data.

42 ENGINEERING↗

NASA NTRS1992

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.↗

NASA NTRS2011

Reliability Based Design for a Raked Wing Tip of an Airframe

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.

Patnaik, Surya N.↗

NASA NTRS1997

Estimation of Slow Crack Growth Parameters for Constant Stress-Rate Test Data of Advanced Ceramics and Glass by the Individual Data and Arithmetic Mean Methods

The two estimation methods, individual data and arithmetic mean methods, were used to determine the slow crack growth (SCG) parameters (n and D) of advanced ceramics and glass from a large number of room- and elevated-temperature constant stress-rate ('dynamic fatigue') test data. For ceramic materials with Weibull modulus greater than 10, the difference in the SCG parameters between the two estimation methods was negligible; whereas, for glass specimens exhibiting Weibull modulus of about 3, the difference was amplified, resulting in a maximum difference of 16 and 13 %, respectively, in n and D. Of the two SCG parameters, the parameter n was more sensitive to the estimation method than the other. The coefficient of variation in n was found to be somewhat greater in the individual data method than in the arithmetic mean method.

Choi, Sung R.↗

NASA NTRS1990

A case study of the Thunderstorm Research International Project storm of July 11, 1978. I - Analysis of the data base

The data obtained at the time of the Thunderstorm Research International Project storm at the Kennedy Space Center on July 11, 1978 are analyzed in a model-independent manner. The data base included data from three Doppler radars, a lightning detection and ranging system and a network of 25 electric field mills, and rain gages. Electric field measurements were used to analyze the charge moments transferred by lightning flashes, and the data were fitted to Weibull distributions; these were used to estimate statistical parameters of the lightning for both intracloud and cloud-to-ground flashes and to estimate the fraction of the flashes which were below the observation threshold. The displacement and the conduction current densities were calculated from electric field measurements between flashes. These values were used to derive the magnitudes and the locations of dipole and monopole generators by least squares fitting the measured Maxwell current densities to the displacement-dominated equations.

Nisbet, John S.↗

NASA NTRS1992

An application of synthetic seismicity in earthquake statistics - The Middle America Trench

The way in which seismicity calculations which are based on the concept of fault segmentation incorporate the physics of faulting through static dislocation theory can improve earthquake recurrence statistics and hone the probabilities of hazard is shown. For the Middle America Trench, the spread parameters of the best-fitting lognormal or Weibull distributions (about 0.75) are much larger than the 0.21 intrinsic spread proposed in the Nishenko Buland (1987) hypothesis. Stress interaction between fault segments disrupts time or slip predictability and causes earthquake recurrence to be far more aperiodic than has been suggested.

Ward, Steven N.↗

NASA NTRS2003

Bayesian estimation of dose thresholds

An example is described of Bayesian estimation of radiation absorbed dose thresholds (subsequently simply referred to as dose thresholds) using a specific parametric model applied to a data set on mice exposed to 60Co gamma rays and fission neutrons. A Weibull based relative risk model with a dose threshold parameter was used to analyse, as an example, lung cancer mortality and determine the posterior density for the threshold dose after single exposures to 60Co gamma rays or fission neutrons from the JANUS reactor at Argonne National Laboratory. The data consisted of survival, censoring times and cause of death information for male B6CF1 unexposed and exposed mice. The 60Co gamma whole-body doses for the two exposed groups were 0.86 and 1.37 Gy. The neutron whole-body doses were 0.19 and 0.38 Gy. Marginal posterior densities for the dose thresholds for neutron and gamma radiation were calculated with numerical integration and found to have quite different shapes. The density of the threshold for 60Co is unimodal with a mode at about 0.50 Gy. The threshold density for fission neutrons declines monotonically from a maximum value at zero with increasing doses. The posterior densities for all other parameters were similar for the two radiation types.

NASA Discipline Radiation Health↗

NASA NTRS2005

The Influence of Roughness on Gear Surface Fatigue

Gear working surfaces are subjected to repeated rolling and sliding contacts, and often designs require loads sufficient to cause eventual fatigue of the surface. This research provides experimental data and analytical tools to further the understanding of the causal relationship of gear surface roughness to surface fatigue. The research included evaluations and developments of statistical tools for gear fatigue data, experimental evaluation of the surface fatigue lives of superfinished gears with a near-mirror quality, and evaluations of the experiments by analytical methods and surface inspections. Alternative statistical methods were evaluated using Monte Carlo studies leading to a final recommendation to describe gear fatigue data using a Weibull distribution, maximum likelihood estimates of shape and scale parameters, and a presumed zero-valued location parameter. A new method was developed for comparing two datasets by extending the current methods of likelihood-ratio based statistics. The surface fatigue lives of superfinished gears were evaluated by carefully controlled experiments, and it is shown conclusively that superfinishing of gears can provide for significantly greater lives relative to ground gears. The measured life improvement was approximately a factor of five. To assist with application of this finding to products, the experimental condition was evaluated. The fatigue life results were expressed in terms of specific film thickness and shown to be consistent with bearing data. Elastohydrodynamic and stress analyses were completed to relate the stress condition to fatigue. Smooth-surface models do not adequately explain the improved fatigue lives. Based on analyses using a rough surface model, it is concluded that the improved fatigue lives of superfinished gears is due to a reduced rate of near-surface micropitting fatigue processes, not due to any reduced rate of spalling (sub-surface) fatigue processes. To complete the evaluations, surface inspection were completed. The surface topographies of the ground gears changed substantially due to running, but the topographies of the superfinished gears were essentially unchanged with running.

Krantz, Timothy↗

NASA NTRS2012

Emperical Tests of Acceptance Sampling Plans

Acceptance sampling is a quality control procedure applied as an alternative to 100% inspection. A random sample of items is drawn from a lot to determine the fraction of items which have a required quality characteristic. Both the number of items to be inspected and the criterion for determining conformance of the lot to the requirement are given by an appropriate sampling plan with specified risks of Type I and Type II sampling errors. In this paper, we present the results of empirical tests of the accuracy of selected sampling plans reported in the literature. These plans are for measureable quality characteristics which are known have either binomial, exponential, normal, gamma, Weibull, inverse Gaussian, or Poisson distributions. In the main, results support the accepted wisdom that variables acceptance plans are superior to attributes (binomial) acceptance plans, in the sense that these provide comparable protection against risks at reduced sampling cost. For the Gaussian and Weibull plans, however, there are ranges of the shape parameters for which the required sample sizes are in fact larger than the corresponding attributes plans, dramatically so for instances of large skew. Tests further confirm that the published inverse-Gaussian (IG) plan is flawed, as reported by White and Johnson (2011).

White, K. Preston, Jr.↗

NASA NTRS2014

Assessing the Effect of Spaceflight on the Propensity for Astronauts to Develop Disk Herniation

BACKGROUND: A previous study [1] reported that the instantaneous risk of developing a Herniated Nucleus Pulposus (HNP) was higher in astronauts who had flown at least one mission, as compared with those in the corps who had not yet flown. However, the study only analyzed time to HNP after the first mission (if any) and did not account for the possible effects of multiple missions. While many HNP's occurred well into astronauts' careers or in some cases years after retirement, the higher incidence of HNPs relatively soon after completion of space missions appears to indicate that spaceflight may lead to an increased risk of HNP. The purpose of this study was to support the Human System Risk Board assessment of back pain, evaluate the risk of injury due to dynamic loads, and update the previous dataset which contained events up to December 31, 2006. METHODS: Data was queried from the electronic medical record and provided by the Lifetime Surveillance of Astronaut Health. The data included all 330 United States astronauts from 1959 through February 2014. Cases were confirmed by Magnetic Resonance Imaging, Computerized Tomography, Myelography, operative findings, or through clinical confirmation with a neurologist or neurosurgeon. In this analysis, astronauts who had an HNP at selection into the corps or had an HNP diagnosis prior to their first flight were excluded. The statistical challenges in using the available data to separate effects of spaceflight from those associated with general astronaut training and lifestyle on propensity to develop HNPs are many. The primary outcome is reported date of first HNP (if any), which at best is only an approximation to the actual time of occurrence. To properly analyze this data with a survival analysis model, one must also know the "exposure" time - i.e. how long each astronaut has been at risk for developing an HNP. If an HNP is reported soon after a mission, is it mission caused or general? If the former, exposure time should be counted from the time of landing (assuming the risk of HNP occurring during a mission is zero). If the latter, exposure time should be counted from the time of selection; however we can't directly know which one to use. In our analysis we take both of these possibilities into account with a competing risks model, wherein two distinct stochastic processes are going on: TG = time to HNP (general) and TS = time to HNP (spaceflight). Under this type of model, whichever of these occurs first is what we observe; in other words we don't observe TG or TS, only min(TG, TS). Here, we parameterized the model in terms of separate Weibull hazard functions for each process and estimated all parameters using maximum likelihood. In addition, we allowed for a "cured fraction" - i.e. the possibility that some astronauts may never develop an HNP. RESULTS: Results will include a depiction of the competing hazard functions as well as a probability curve for the relative likelihood that an HNP reported at a given time after a mission is actually mission caused. Other factors, such as dwell time in microgravity and vehicle landing environment will be explored. An overall assessment as to whether spaceflight truly exacerbates HNP risk will be made.

Feiveson, A. H.↗

DOE OSTI2022

Accelerated statistical failure analysis of multifidelity TRISO fuel models

Statistical nuclear fuel failure analysis is critical for the design and development of advanced reactor technologies. Although Monte Carlo Sampling (MCS) is a standard method of statistical failure analysis for fuels, the low failure probabilities of some advanced fuel forms and the correspondingly large number of required model evaluations limit its application to low-fidelity (e.g., 1-D) fuel models. In this paper, we present four other statistical methods for fuel failure analysis in Bison, considering tri-structural isotropic (TRISO)-coated particle fuel as a case study. The statistical methods considered are Latin hypercube sampling (LHS), adaptive importance sampling (AIS), subset simulation (SS), and the Weibull theory. Using these methods, we analyzed both 1-D and 2-D representations of TRISO models to compute failure probabilities and the distributions of fuel properties that result in failures. The results of these methods compare well across all TRISO models considered. Overall, SS and the Weibull theory were deemed the most efficient, and can be applied to both 1-D and 2-D TRISO models to compute failure probabilities. Moreover, since SS also characterizes the distribution of parameters that cause TRISO failures, and can consider failure modes not described by the Weibull criterion, it may be preferred over the other methods. Finally, a discussion on the efficacy of different statistical methods of assessing nuclear fuel safety is provided.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS2021

Effect of High Temperature Storage on AC Characteristics of Polymer Tantalum Capacitors

Replacement of MnO2 with conductive polymers as cathode materials in chip tantalum capacitors allows for a substantial reduction of the equivalent series resistance (ESR), improvement of frequency characteristics, and elimination of the possibility of ignition during failures. One of the drawbacks of chip polymer tantalum capacitors (CPTCs) is a relatively poor long-term stability at high temperatures. In this work, variations of capacitance, dissipation factor, and ESR in different types of capacitors including automotive grade parts from three manufacturers have been monitored during storage at temperatures from 100 ºC to 175 ºC for up to 18,000 hours. Results show that ESR is the most and capacitance the least sensitive to degradation parameter. Times to parametric failures have been simulated using a Weibull-Arrhenius model that allowed for assessments of activation energies of the degradation and prediction of times to failure at the use temperature. Degradation of CPTCs was explained by thermo-oxidative processes in conductive polymers that result in exponential increasing of the resistivity with time of ageing. This process starts after a certain incubation period that depends on packaging materials and design and corresponds to the time that is necessary to form delamination between the encapsulating molding compound and lead frame. The effectiveness of the existing qualification procedures to assure stable operation of CPTCs is discussed.

Alexander A Teverovsky↗

NASA NTRSDate not supplied

Effect of High Temperature Storage on AC Characteristics of Polymer Tantalum Capacitors

Replacement of MnO2 with conductive polymers as cathode materials in chip tantalum capacitors allows for a substantial reduction of the equivalent series resistance (ESR), improvement of frequency characteristics, and elimination of the possibility of ignition during failures. One of the drawbacks of chip polymer tantalum capacitors (CPTCs) is a relatively poor long-term stability at high temperatures. In this work, variations of capacitance, dissipation factor, and ESR in different types of capacitors including automotive grade parts from three manufacturers have been monitored during storage at temperatures from 100 ºC to 175 ºC for up to 18,000 hours. Results show that ESR is the most and capacitance the least sensitive to degradation parameter. Times to parametric failures have been simulated using a Weibull-Arrhenius model that allowed for assessments of activation energies of the degradation and prediction of times to failure at the use temperature. Degradation of CPTCs was explained by thermo-oxidative processes in conductive polymers that result in exponential increasing of the resistivity with time of ageing. This process starts after a certain incubation period that depends on packaging materials and design and corresponds to the time that is necessary to form delamination between the encapsulating molding compound and lead frame. The effectiveness of the existing qualification procedures to assure stable operation of CPTCs is discussed.

Aging↗

NASA NTRSDate not supplied

Effect of High Temperature Storage on AC Characteristics of Polymer Tantalum Capacitors

Replacement of MnO2 with conductive polymers as cathode materials in chip tantalum capacitors allows for a substantial reduction of the equivalent series resistance (ESR), improvement of frequency characteristics, and elimination of the possibility of ignition during failures. One of the drawbacks of chip polymer tantalum capacitors (CPTCs) is a relatively poor long-term stability at high temperatures. In this work, variations of capacitance, dissipation factor, and ESR in different types of capacitors including automotive grade parts from three manufacturers have been monitored during storage at temperatures from 100 ºC to 175 ºC for up to 18,000 hours. Results show that ESR is the most and capacitance the least sensitive to degradation parameter. Times to parametric failures have been simulated using a Weibull-Arrhenius model that allowed for assessments of activation energies of the degradation and prediction of times to failure at the use temperature. Degradation of CPTCs was explained by thermo-oxidative processes in conductive polymers that result in exponential increasing of the resistivity with time of ageing. This process starts after a certain incubation period that depends on packaging materials and design and corresponds to the time that is necessary to form delamination between the encapsulating molding compound and lead frame. The effectiveness of the existing qualification procedures to assure stable operation of CPTCs is discussed.

Aging↗

NASA NTRS1991

Structural reliability analysis of laminated CMC components

For laminated ceramic matrix composite (CMC) materials to realize their full potential in aerospace applications, design methods and protocols are a necessity. The time independent failure response of these materials is focussed on and a reliability analysis is presented associated with the initiation of matrix cracking. A public domain computer algorithm is highlighted that was coupled with the laminate analysis of a finite element code and which serves as a design aid to analyze structural components made from laminated CMC materials. Issues relevant to the effect of the size of the component are discussed, and a parameter estimation procedure is presented. The estimation procedure allows three parameters to be calculated from a failure population that has an underlying Weibull distribution.

Duffy, Stephen F.↗

NASA NTRS1991

Structural reliability analysis of laminated CMC components

For laminated ceramic matrix composite (CMC) materials to realize their full potential in aerospace applications, design methods and protocols are a necessity. The time independent failure response of these materials is focussed on and a reliability analysis is presented associated with the initiation of matrix cracking. A public domain computer algorithm is highlighted that was coupled with the laminate analysis of a finite element code and which serves as a design aid to analyze structural components made from laminated CMC materials. Issues relevant to the effect of the size of the component are discussed, and a parameter estimation procedure is presented. The estimation procedure allows three parameters to be calculated from a failure population that has an underlying Weibull distribution.

Duffy, Stephen F.↗

NASA NTRS2005

Estimation of ZnSe Slow-Crack-Growth Properties for Design of the Flow Enclosure Accommodating Novel Investigations in Combustion of Solids (FEANICS) Windows

This report reviews some of the literature on the fracture strength, fracture toughness, and crack growth properties of chemical-vapor-deposited ZnSe. The literature was reviewed to determine if the existing data on ZnSe is adequate to design windows for the Flow Enclosure Accommodating Novel Investigations in Combustion of Solids (FEANICS) project. Unfortunately, most of the published reports do not give all of the necessary design parameters despite having measured the data to do so. Further, the original data is not available. The data tabulated herein was determined by digitizing plots in original reprints of the publications. Based on the published data, an estimate of the slow-crack-growth parameters for small cracks in 100 percent humidity was made. For 100 percent humidity, the slow-crack-growth parameters n and A for small crack (or single crystal) failure were estimated. Weibull moduli estimated from bending of beams and circular plates ranged from 4 to 9, while fracture strengths ranged from 29 MPa in water to 72 MPa in dry nitrogen. Fracture toughness measurements yielded ranges, with the lower values representing failure from small flaws within grains and the larger values representing macroscopic cracks. Much of the data analyzed exhibited significant scatter, and the standard deviations were very large.

Salem, Jonathan A.↗

NASA NTRS2021

Effect of High Temperature Storage on AC Characteristics of Polymer Tantalum Capacitors

Replacement of MnO2 with conductive polymers as cathode materials in chip tantalum capacitors allows for a substantial reduction of the equivalent series resistance (ESR), improvement of frequency characteristics, and elimination of the possibility of ignition during failures. One of the drawbacks of chip polymer tantalum capacitors (CPTCs) is a relatively poor long-term stability at high temperatures. In this work, variations of capacitance, dissipation factor, and ESR in different types of capacitors including automotive grade parts from three manufacturers have been monitored during storage at temperatures from 100 ºC to 175 ºC for up to 18,000 hours. Results show that ESR is the most and capacitance the least sensitive parameter to degradation. Times to parametric failures have been simulated using a Weibull-Arrhenius model that allowed for assessments of activation energies of the degradation and prediction of times to failure at the use temperature. Degradation of CPTCs was explained by thermo-oxidative processes in conductive polymers that result in exponential increase of the resistivity with time of aging. This process starts after a certain incubation period that depends on packaging materials and design and corresponds to the time that is necessary to form delamination between the encapsulating molding compound and lead frame. The effectiveness of the existing qualification procedures to assure stable operation of CPTCs is discussed.

high temperature storage (HTS)↗