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All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Estimating Weibull parameters for composite materials.

This paper deals with the statistical analysis of strength and fracture of materials in general, with application to fiber composites. The 'weakest link' model is considered in a fairly general form, and the resulting equations are demonstrated by using a Weibull distribution for flaws. This distribution appears naturally in a variety of problems, and therefore additional attention is devoted to analysis and statistical estimation connected with this distribution. Special working charts are included to facilitate interpretation of observed data and estimation of parameters. Implications of the size effect are considered for various kinds of flaw distributions. The paper describes failure and damage in a fiber-reinforced systems.

Robinson, E. Y.↗
NASA NTRS1973

Bayesian estimation of life parameters in the Weibull distribution.

Development of a Bayesian analysis of the scale and shape parameters in the Weibull distribution and the corresponding reliability function with respect to the usual life-testing procedures. For the scale parameter theta, Bayesian estimates of theta and reliability are obtained for the uniform, exponential, and inverted gamma prior probability densities. Bhattacharya's results (1967) for the one-parameter exponential life-testing distribution are reduced to a special case of these results. A fully Bayesian analysis of both the scale and shape parameters is developed by assuming independent prior distributions; since in the latter case, analytical tractability is not possible, Bayesian estimates are obtained through a conjunction of Monte Carlo simulation and numerical-integration techniques. In both cases, a computer simulation is carried out, and a comparison is made between the Bayesian and the corresponding minimum-variance unbiased, or maximum likelihood, estimates. As expected, the Bayesian estimates are superior.

Canavos, G. C.↗
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 NTRS1989

Transmission overhaul and replacement predictions using Weibull and renewel theory

A method to estimate the frequency of transmission overhauls is presented. This method is based on the two-parameter Weibull statistical distribution for component life. A second method is presented to estimate the number of replacement components needed to support the transmission overhaul pattern. The second method is based on renewal theory. Confidence statistics are applied with both methods to improve the statistical estimate of sample behavior. A transmission example is also presented to illustrate the use of the methods. Transmission overhaul frequency and component replacement calculations are included in the example.

Savage, M.↗
NASA NTRS1989

Transmission overhaul and replacement predictions using Weibull and renewal theory

A method to estimate the frequency of transmission overhauls is presented. This method is based on the two-parameter Weibull statistical distribution for component life. A second method is presented to estimate the number of replacement components needed to support the transmission overhaul pattern. The second method is based on renewal theory. Confidence statistics are applied with both methods to improve the statistical estimate of sample behavior. A transmission example is also presented to illustrate the use of the methods. Transmission overhaul frequency and component replacement calculations are included in the example.

Savage, M.↗
NASA NTRS1996

Least Squares Best Fit Method for the Three Parameter Weibull Distribution: Analysis of Tensile and Bend Specimens with Volume or Surface Flaw Failure

Material characterization parameters obtained from naturally flawed specimens are necessary for reliability evaluation of non-deterministic advanced ceramic structural components. The least squares best fit method is applied to the three parameter uniaxial Weibull model to obtain the material parameters from experimental tests on volume or surface flawed specimens subjected to pure tension, pure bending, four point or three point loading. Several illustrative example problems are provided.

Gross, Bernard↗
NASA NTRS2002

Predictive Failure of Cylindrical Coatings Using Weibull Analysis

Rotating, coated wiping rollers used in a high-speed printing application failed primarily from fatigue. Two coating materials were evaluated: a hard, cross-linked, plasticized polyvinyl chloride (PVC) and a softer, plasticized PVC. A total of 447 tests was conducted with these coatings in a production facility. The data were evaluated using Weibull analysis. The softer coating produced more than twice the life of the harder cross-linked coating and reduced the wiper replacement rate by two-thirds, resulting in minimum production interruption.

Vlcek, Brian L.↗
NASA NTRS1971

Table for estimating parameters of Weibull distribution

Table yields best linear invariant /BLI/ estimates for log of reliable life under censored life tests, permitting reliability estimations in failure analysis of items with multiple flaws. These BLI estimates have uniformly smaller expected loss than Gauss-Markov best linear unbiased estimates.

Mann, N. R.↗
NASA NTRS1986

Stratified processes to analyze SSME parts and subsystems using Weibull methodology

Due to the various parts found in a Space Shuttle Main Engine (SSME), analyzation of every part is not feasible or needed. Based on previous mathematical modeling experience of high velocity cryogenic equipment, the environmental traits of location of the part, temperature range, fluid velocity, pressure range, and elevation variation of fluid flow as being significant factors were determined. Six parts categories were developed. The part categories are: (1) fuel turbomachinery, (2) oxidizer, (3) combustion devices, (4) valves, (5) ducts, and (6) lines. Due to a suspicion that superficial failure modes exist, six status codes were developed. The codes are: (1) part is in service presently, (2) part is out-of-service due to its own failure, (3) part is out-of-service due to engine (or some other part failure), (4) part is out-of-service because it's retired/obsolete (time related), (5) never fired-scrapped due to own problem or part is store, and (6) part is out-of-service for repair. It was suggested that to properly model failure behavior of SSME parts that: (1) significant factors contributing to failure must be examined, (2) relatively precision based on real life data must be examined, and (3) alternative definitions of failure must be initialized by the engineers.

Gray, Lou Allen Bell↗
NASA NTRS2016

The Effect of Roughness Model on Scattering Properties of Ice Crystals.

We compare stochastic models of microscale surface roughness assuming uniform and Weibull distributions of crystal facet tilt angles to calculate scattering by roughened hexagonal ice crystals using the geometric optics (GO) approximation. Both distributions are determined by similar roughness parameters, while the Weibull model depends on the additional shape parameter. Calculations were performed for two visible wavelengths (864 nm and 410 nm) for roughness values between 0.2 and 0.7 and Weibull shape parameters between 0 and 1.0 for crystals with aspect ratios of 0.21, 1 and 4.8. For this range of parameters we find that, for a given roughness level, varying the Weibull shape parameter can change the asymmetry parameter by up to about 0.05. The largest effect of the shape parameter variation on the phase function is found in the backscattering region, while the degree of linear polarization is most affected at the side-scattering angles. For high roughness, scattering properties calculated using the uniform and Weibull models are in relatively close agreement for a given roughness parameter, especially when a Weibull shape parameter of 0.75 is used. For smaller roughness values, a shape parameter close to unity provides a better agreement. Notable differences are observed in the phase function over the scattering angle range from 5deg to 20deg, where the uniform roughness model produces a plateau while the Weibull model does not.

Weibull density functions↗
NASA NTRS2001

Effect of Roller Profile on Cylindrical Roller Bearing Life Prediction: Comparison of Bearing Life Theories - Part 1

Four rolling-element bearing life theories were chosen for analysis and compared for a simple roller-race geometry model. The life theories were those of Weibull; Lundberg and Palmgren; Ioannides and Harris; and Zaretsky. The analysis without a fatigue limit of Ioannides and Harris is identical to the Lundberg and Palmgren analysis, and the Weibull analysis is similar to that of Zaretsky if the exponents are chosen to be identical. The resultant predicted life a each stress condition not only depends on the life equation used but also on the Weibull slope assumed. The least variation in predicted life with Weibull slope comes with the Zaretsky equation. Except for a Weibull slope of 1.11, at which the Weibull equation predicts the highest lives, the highest lives are predicted for the Zaretsky equation. For Weibull slopes of 1.5 and 2, both the Lundherg-Palmgren and Ioannides-Harris (where tau(sub u) = 0) equations predict lower lives than the ANSI/ABMA/ISO standard. Based upon the Hertz stresses for line contact, the accepted load-life exponent of 10/3 results in a maximum Hertz stress-life exponent equal to 6.6. This value is inconsistent with that experienced in the field. The assumption of as shear stress fatigue limit tau(sub u) results in Hertz stress-life exponents greater than are experimentally verifiable.

Poplawski, Joseph V.↗
NASA NTRS2013

Rolling Bearing Life Prediction, Theory, and Application

A tutorial is presented outlining the evolution, theory, and application of rolling-element bearing life prediction from that of A. Palmgren, 1924; W. Weibull, 1939; G. Lundberg and A. Palmgren, 1947 and 1952; E. Ioannides and T. Harris, 1985; and E. Zaretsky, 1987. Comparisons are made between these life models. The Ioannides-Harris model without a fatigue limit is identical to the Lundberg-Palmgren model. The Weibull model is similar to that of Zaretsky if the exponents are chosen to be identical. Both the load-life and Hertz stress-life relations of Weibull, Lundberg and Palmgren, and Ioannides and Harris reflect a strong dependence on the Weibull slope. The Zaretsky model decouples the dependence of the critical shear stress-life relation from the Weibull slope. This results in a nominal variation of the Hertz stress-life exponent. For 9th- and 8th-power Hertz stress-life exponents for ball and roller bearings, respectively, the Lundberg- Palmgren model best predicts life. However, for 12th- and 10th-power relations reflected by modern bearing steels, the Zaretsky model based on the Weibull equation is superior. Under the range of stresses examined, the use of a fatigue limit would suggest that (for most operating conditions under which a rolling-element bearing will operate) the bearing will not fail from classical rolling-element fatigue. Realistically, this is not the case. The use of a fatigue limit will significantly overpredict life over a range of normal operating Hertz stresses. Since the predicted lives of rolling-element bearings are high, the problem can become one of undersizing a bearing for a particular application.

Zaretsky, Erwin V.↗