Search NASA⌕ Search

SEARCH · Search NASA

Results for “Weibull Probability”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Producibility of fibrous refractory composite insulation, FRCI 40-20

Fibrous Refractory Composite Insulation (FRCI) is a NASA-developed, second generation, reusable heat-shield material that comprises a mixture of aluminoborosilicate fibers, silica fibers, and silicon carbide. Under NASA contract, a program was conducted to demonstrate the capability for manufacturing FRCI 40-20 billets. A detailed fabrication procedure was written and validated by testing specimens from the first two billets. The material conformed to NASA requirements for density, tensile strength, modulus of rupture, thermal expansion, cristobalite content, and uniformity. Twenty-four billets were prepared to provide 20 deliverable articles. Production billets were checked for density, modulus of rupture, cristobalite content, and uniformity. Billet density ranged from 309.48 to 332.22 kg/cu m (19.32 to 20.74 lb/cu ft) and modulus of rupture from 4690 to 10,140 kPa (680 to 1470 psi). Cristobalite content was less than 1 percent. A Weibull analysis of modulus-of-rupture data indicated a 1.5 percent probability for failure below the specified strength of 4480 kPa (650 psi).

Strauss, E. L.↗
NASA NTRS1986

A Monte Carlo study of Weibull reliability analysis for space shuttle main engine components

The incorporation of a number of additional capabilities into an existing Weibull analysis computer program and the results of Monte Carlo computer simulation study to evaluate the usefulness of the Weibull methods using samples with a very small number of failures and extensive censoring are discussed. Since the censoring mechanism inherent in the Space Shuttle Main Engine (SSME) data is hard to analyze, it was decided to use a random censoring model, generating censoring times from a uniform probability distribution. Some of the statistical techniques and computer programs that are used in the SSME Weibull analysis are described. The methods documented in were supplemented by adding computer calculations of approximate (using iteractive methods) confidence intervals for several parameters of interest. These calculations are based on a likelihood ratio statistic which is asymptotically a chisquared statistic with one degree of freedom. The assumptions built into the computer simulations are described. The simulation program and the techniques used in it are described there also. Simulation results are tabulated for various combinations of Weibull shape parameters and the numbers of failures in the samples.

Abernethy, K.↗
NASA NTRS1986

Some design considerations for ceramic components in heat engine applications

The design methodology for brittle material structures which is being developed and used at the Lewis Research Center for sizing ceramic components in heat engine applications is reviewed. Theoretical aspects of designing with structural ceramics are discussed, and a general purpose reliability program for predicting fast fracture response due to volume distributed flaws is described. Statistical treatment of brittle behavior, based on the Weibull model, is reviewed and its advantages, as well as drawbacks, are listed. A mechanistic statistical fracture theory, proposed by Batdorf to overcome the Weibull model limitations and based on Griffith fracture mechanics, is summarized. Failure probability predictions are made for rotating annular Si3N4 disks using various fracture models, and the results are compared to actual failure data. The application of these design methods to Government funded ceramics engine demonstration programs is surveyed. The uncertainty in observed component performance emphasizes the need for proof testing and improved nondestructive evaluation to guarantee adequate structural integrity.

Gyekenyesi, John P.↗
NASA NTRS1988

Design and development of ceramic components

The development of the AGT 100 turbine components in structural ceramic materials is described. Development is defined as the complete and iterative cycle from design, analysis, test, and design refinement culminating in successful demonstration of the design requirements. The components are analyzed by a linear elastic probabilistic approach, which involves finite element (three- and/or two-dimensional) simulation of the component combined with a Weibull characterization of the brittle ceramic material strength distribution to calculate a probability of survival for the component in the operating environment. Component test failure investigation has resulted in design modifications, and an improvement in component reliability has been demonstrated. Engine testing (over 570 h to date) continues to assess design/development of structural ceramic components.

Holtman, R. L.↗
NASA NTRSDate not supplied

Lower neck injury criteria for THOR and Hybrid III dummies in rear impact

The objectives of the study are to derive lower-neck-injury probability curves under rear impact loading from matched pair Hybrid III and THOR dummy tests. Methods: Twelve whole-body and 15 isolated head-neck rear-impact sled tests were conducted using the 2 dummies. They were positioned on a rigid seat that was attached to an acceleration sled. The dummies were positioned with the head parallel to the ground, torso against the seat back, and legs stretched such that there was no axial rotation. The acceleration pulse matched the previous in-house human cadaver tests. The 6-axis lower-neck load cell was used in both dummies. For the isolated rear-impact tests,the head-neck was excised from the dummies, and the lower-neck load cell was mounted to the top of the sled with the head parallel to the ground and such that the acceleration vector was in the rear impact mode. Lower-neck loads and lower-neck-injury criteria (LNij) were obtained using the load cell data and survival analysis to develop injury-assessment-risk values and curves for both dummies. The LNij criteria were determined for both dummies using the intercept value corresponding to the 90% probability level for the forces and moments. Results: The log normal and Weibull distributions were the optimal distributions for the Hybrid III and THOR devices. At the 50% risk level, the mean LNij of 1.1 and NCIS was 0.77 for the Hybrid III, and 1.5 NCIS was 0.30 for the THOR device. The quality indices were in the fair range and good range for the 2 dummies, respectively, at this risk level. Conclusions: The lower-neck-based IARCs and IARVs serve as the first dataset for injury assessments, and the THOR may be a better test device for assessing injures in rear impact environments.

Narayan Yoganandan↗
NASA NTRS1990

Reliability analysis of a structural ceramic combustion chamber

The Weibull modulus, fracture toughness and thermal properties of a silicon nitride material used to make a gas turbine combustor were experimentally measured. The location and nature of failure origins resulting from bend tests were determined with fractographic analysis. The measured Weibull parameters were used along with thermal and stress analysis to determine failure probabilities of the combustor with the CARES design code. The effect of data censoring, FEM mesh refinement, and fracture criterion were considered in the analysis.

Salem, Jonathan A.↗
NASA NTRS1991

A statistical comparison of two carbon fiber/epoxy fabrication techniques

A statistical comparison of the compression strengths of specimens that were fabricated by either a platen press or an autoclave were performed on IM6/3501-6 carbon/epoxy composites of 16-ply (0,+45,90,-45)(sub S2) lay-up configuration. The samples were cured with the same parameters and processing materials. It was found that the autoclaved panels were thicker than the platen press cured samples. Two hundred samples of each type of cure process were compression tested. The autoclaved samples had an average strength of 450 MPa (65.5 ksi), while the press cured samples had an average strength of 370 MPa (54.0 ksi). A Weibull analysis of the data showed that there is only a 30 pct. probability that the two types of cure systems yield specimens that can be considered from the same family.

Hodge, A. J.↗
NASA NTRS1991

Reliability analysis of a structural ceramic combustion chamber

The Weibull modulus, fracture toughness and thermal properties of a silicon nitride material used to make a gas turbine combustor were experimentally measured. The location and nature of failure origins resulting from bend tests were determined with fractographic analysis. The measured Weibull parameters were used along with thermal and stress analysis to determine failure probabilities of the combustor with the CARES design code. The effect of data censoring, FEM mesh refinement, and fracture criterion were considered in the analysis.

Salem, Jonathan A.↗
NASA NTRS1991

Statistical structural analysis of rotor impact ice shedding

The statistical characteristics of impact ice shear strength are analyzed, with emphasis placed on the most probable shear strength and statistical distribution of an ice deposit. Several distribution types are considered: the Weibull, two-parameter Weibull, and exponential distributions, as well as the Gumbell distribution of the smallest extreme and the Gumbell distribution of the largest extreme. It is concluded that the Weibull distribution yields the best results; however, the expected life, shape parameter, and scale parameter should be determined separately for each case of varying wind speed and droplet size. The theoretical predictions of shear stresses in a specific rotating ice shape are compared, and it is noted that when the effects of lift are added to the theoretical model and the interference is calculated with a new mean and standard deviation, the probability of ice shed is computed as 36.64 pct.

Kellacky, C. J.↗
NASA NTRS2014

A Multiscale Progressive Failure Modeling Methodology for Composites that Includes Fiber Strength Stochastics

A multiscale modeling methodology was developed for continuous fiber composites that incorporates a statistical distribution of fiber strengths into coupled multiscale micromechanics/finite element (FE) analyses. A modified two-parameter Weibull cumulative distribution function, which accounts for the effect of fiber length on the probability of failure, was used to characterize the statistical distribution of fiber strengths. A parametric study using the NASA Micromechanics Analysis Code with the Generalized Method of Cells (MAC/GMC) was performed to assess the effect of variable fiber strengths on local composite failure within a repeating unit cell (RUC) and subsequent global failure. The NASA code FEAMAC and the ABAQUS finite element solver were used to analyze the progressive failure of a unidirectional SCS-6/TIMETAL 21S metal matrix composite tensile dogbone specimen at 650 degC. Multiscale progressive failure analyses were performed to quantify the effect of spatially varying fiber strengths on the RUC-averaged and global stress-strain responses and failure. The ultimate composite strengths and distribution of failure locations (predominately within the gage section) reasonably matched the experimentally observed failure behavior. The predicted composite failure behavior suggests that use of macroscale models that exploit global geometric symmetries are inappropriate for cases where the actual distribution of local fiber strengths displays no such symmetries. This issue has not received much attention in the literature. Moreover, the model discretization at a specific length scale can have a profound effect on the computational costs associated with multiscale simulations.models that yield accurate yet tractable results.

Generalized Method of Cells↗
NASA NTRS2017

Rolling-Bearing Service Life Based on Probable Cause for Removal: A Tutorial

In 1947 and 1952, Gustaf Lundberg and Arvid Palmgren developed what is now referred to as the Lundberg-Palmgren Model for Rolling Bearing Life Prediction based on classical rolling-element fatigue. Today, bearing fatigue probably accounts for less than 5 percent of bearings removed from service for cause. A bearing service life prediction methodology and tutorial indexed to eight probable causes for bearing removal, including fatigue, are presented, which incorporate strict series reliability; Weibull statistical analysis; available published field data from the Naval Air Rework Facility; and 224,000 rolling-element bearings removed for rework from commercial aircraft engines.

Life prediction↗
DOE OSTI2025

Evaluating design safety margins in the American Society of Mechanical Engineers graphite core components design-by-analysis assessments

Graphite is an important material being used for core components in next-generation high-temperature gas-cooled nuclear reactors. The selection of graphite grade for a specific Designer is a complex task, dependent on reactor conditions, component functionality, and required reliability. The American Society of Mechanical Engineers (ASME) provides two semi-probabilistic design-by-analysis assessments to evaluate graphite core components against design reliability targets. The simplified assessment uses a 2-parameter Weibull distribution to describe the graphite grade’s tensile-strength distribution to establish component stress limits. The full assessment uses the 3-parameter Weibull distribution and a modified Weakest-Link Theory approach to calculate a component design probability of failure. The paper defines recommended assessment rules, which are the as-written simplified assessment and the full assessment with parameter lower bounds, the modulus update with threshold reduction, and the 2027 grouping rules. Code rules are applied to three grades: 2114, IG-110, and NBG-18. The baseline margin calculation is developed using the experimental tensile dogbone specimen. Percent margin is defined as the percent reduction in the median experimental load to obtain the allowable load per ASME assessments. Under the recommended rules, the SRC–1 margin in the simplified assessment ranged from 40.2 % to 52.7 % among the grades in this study and from 36.1 % to 49.8 % in the full assessment. The full assessment only decreases the margins by 2.5–4.5 % for the SRC-1 components and 0–1.5 % for the SRC-2 components for this baseline case. Margin is inversely related to material median strength (i.e., the strongest grade, 2114, has the lowest margin).

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1992

Design prediction for long term stress rupture service of composite pressure vessels

Extensive stress rupture studies on glass composites and Kevlar composites were conducted by the Lawrence Radiation Laboratory beginning in the late 1960's and extending to about 8 years in some cases. Some of the data from these studies published over the years were incomplete or were tainted by spurious failures, such as grip slippage. Updated data sets were defined for both fiberglass and Kevlar composite stand test specimens. These updated data are analyzed in this report by a convenient form of the bivariate Weibull distribution, to establish a consistent set of design prediction charts that may be used as a conservative basis for predicting the stress rupture life of composite pressure vessels. The updated glass composite data exhibit an invariant Weibull modulus with lifetime. The data are analyzed in terms of homologous service load (referenced to the observed median strength). The equations relating life, homologous load, and probability are given, and corresponding design prediction charts are presented. A similar approach is taken for Kevlar composites, where the updated stand data do show a turndown tendency at long life accompanied by a corresponding change (increase) of the Weibull modulus. The turndown characteristic is not present in stress rupture test data of Kevlar pressure vessels. A modification of the stress rupture equations is presented to incorporate a latent, but limited, strength drop, and design prediction charts are presented that incorporate such behavior. The methods presented utilize Cartesian plots of the probability distributions (which are a more natural display for the design engineer), based on median normalized data that are independent of statistical parameters and are readily defined for any set of test data.

Robinson, Ernest Y.↗
NASA NTRS1987

Weibull Distribution From Interval Inspection Data

Most likely failure sequence assumed. Memorandum discusses application of Weibull distribution to statistics of failures of turbopump blades. Is generalization of well known exponential random probability distribution and useful in describing component-failure modes including aging effects. Parameters found from experimental data by method of maximum likelihood.

Rheinfurth, Mario H.↗
NASA NTRS1988

Life and reliability of rotating disks

In aerospace applications, an engineer must be especially cognizant of size and weight constraints which affect design decisions. Although designing at or below the material fatigue limit may be desirable in most industrial applications, in aerospace application it is almost mandatory to design certain components for a finite life at an acceptable probability of survival. Zaretsky outlined such a methodology based in part on the work of W. Weibull (1939, 1951) and G. Lundberg and A. Palmgren (1947a, 1947b, 1952). It is the objective of this work to apply the method of Zaretsky (1987) to statistically predict the life of a generic solid disk with and without bolt holes; determine the effect of disk design variables, thermal loads, and speed on relative life; and develop a generalized equation for determining disk life by incorporating only these variables.

Zaretsky, Erwin V.↗
NASA NTRS2009

Bayes Analysis and Reliability Implications of Stress-Rupture Testing a Kevlar/Epoxy COPV using Temperature and Pressure Acceleration

Composite Overwrapped Pressure Vessel (COPVs) that have survived a long service time under pressure generally must be recertified before service is extended. Sometimes lifetime testing is performed on an actual COPV in service in an effort to validate the reliability model that is the basis for certifying the continued flight worthiness of its sisters. Currently, testing of such a Kevlar49(registered TradeMark)/epoxy COPV is nearing completion. The present paper focuses on a Bayesian statistical approach to analyze the possible failure time results of this test and to assess the implications in choosing between possible model parameter values that in the past have had significant uncertainty. The key uncertain parameters in this case are the actual fiber stress ratio at operating pressure, and the Weibull shape parameter for lifetime; the former has been uncertain due to ambiguities in interpreting the original and a duplicate burst test. The latter has been uncertain due to major differences between COPVs in the data base and the actual COPVs in service. Any information obtained that clarifies and eliminates uncertainty in these parameters will have a major effect on the predicted reliability of the service COPVs going forward. The key result is that the longer the vessel survives, the more likely the more optimistic stress ratio is correct. At the time of writing, the resulting effect on predicted future reliability is dramatic, increasing it by about one nine , that is, reducing the probability of failure by an order of magnitude. However, testing one vessel does not change the uncertainty on the Weibull shape parameter for lifetime since testing several would be necessary.

Phoenix, S. Leigh↗
NASA NTRS2009

Bayes Analysis and Reliability Implications of Stress-Rupture Testing a Kevlar/Epoxy COPV Using Temperature and Pressure Acceleration

Composite Overwrapped Pressure Vessels (COPVs) that have survived a long service time under pressure generally must be recertified before service is extended. Flight certification is dependent on the reliability analysis to quantify the risk of stress rupture failure in existing flight vessels. Full certification of this reliability model would require a statistically significant number of lifetime tests to be performed and is impractical given the cost and limited flight hardware for certification testing purposes. One approach to confirm the reliability model is to perform a stress rupture test on a flight COPV. Currently, testing of such a Kevlar49 (Dupont)/epoxy COPV is nearing completion. The present paper focuses on a Bayesian statistical approach to analyze the possible failure time results of this test and to assess the implications in choosing between possible model parameter values that in the past have had significant uncertainty. The key uncertain parameters in this case are the actual fiber stress ratio at operating pressure, and the Weibull shape parameter for lifetime; the former has been uncertain due to ambiguities in interpreting the original and a duplicate burst test. The latter has been uncertain due to major differences between COPVs in the database and the actual COPVs in service. Any information obtained that clarifies and eliminates uncertainty in these parameters will have a major effect on the predicted reliability of the service COPVs going forward. The key result is that the longer the vessel survives, the more likely the more optimistic stress ratio model is correct. At the time of writing, the resulting effect on predicted future reliability is dramatic, increasing it by about one "nine," that is, reducing the predicted probability of failure by an order of magnitude. However, testing one vessel does not change the uncertainty on the Weibull shape parameter for lifetime since testing several vessels would be necessary.

Phoenix, S. Leigh↗