Failure Density Function Research Articles

Statistical failure analysis of metallic U-10zr/HT9 fast reactor fuel pin by considering the weibull distribution and cumulative damage fraction

A statistical failure analysis is performed to obtain some insight into the rupture behavior of the metallic U-10Zr/HT-9 fast reactor fuel pins which were irradiated in X447 subassembly of EBR-II reactor. Generally, the primary factor that contributes to metallic fuel pin failure is believed to be plenum pressure buildup due to fission gas release. However, the calculated cumulative damage fraction (CDF), by considering plenum pressure buildup as the sole contributor for cladding stress, are lower than the expected value by an order of magnitude. When fuel/cladding mechanical interaction is considered in CDF calculations, the calculated values of failed pins are closer to the expected values. The remained difference may be due to the effects of temperature/stress fluctuation and neutron irradiation during operation, which are hard to be quantitatively modeled. The failure probability functions are determined in terms of CDF and burnup, respectively, based upon the known Weibull statistical failure model. The failure density function based on CDF exhibits wide distribution (shape parameter, β is ~1.5), while the function on burnup shows sharp distribution shape (β is ~17). The calculated limit on peak burnup and CDF to meet 99.99% reliability for X447 pins are 6.6 at.% and 2.2 × 10 −4, respectively. The CDF limit for 99.99% reliability is ~0.3% of their mean value to failure. The CDF based failure function agrees relatively well with the strain based failure function in literature.

Unimodality and bimodality of mixed weibull distributions

AbstractThe failure density function and probability density function of logarithmic lifetime are partially correlated. Normally, both patterns are either unimodal or else bimodal. This is not always the case. Quantitative criteria are introduced to check their correlation.

Bimodal distribution. Are you sure?

AbstractThe paper points out complicated relations between the failure density function and the probability density function of logarithmic lifetime and practical consequences.

A unimodal hazard rate function and its failure distribution

A unimodal hazard rate function is suggested to model a failure rate that has a relatively high rate of failure in the middle of expected life time. This unimodal hazard rate function has two shape parameters. One of the parameters indicates the location (time) of the mode and the other controls the height of the mode. In effect, these two parameters index the class of unimodal hazard rate functions. The reliability function and the failure density function of the unimodal hazard rate function are relatively uncomplicated and mathematically tractable. The properties of the unimodal hazard rate function and the failure density function are investigated. The maximum likelihood method is used for the inference concerning the two parameters and an example based on real data is presented. This unimodal hazard rate function is particularly useful when the time of the peak failure rate is of prime interest. The failure distribution provides a practical way of estimating the peak failure time.

Finite difference analysis of reliability optimization through sampling techniques

This paper describes qualitative and quantitative techniques for reliability sampling plans based on failure density functions (MTTF, MTBF and MTTR) as expected values and as functions of time duration ( t ). Examples are provided of how the techniques are applied in determining plans for a specified lot size. These plans are to test service life, the effectiveness of reliability and MTTF, MTBF and MTTR as expected values and as functions of t and the percentage of reliable units expected in any lot size based on consumer's and producer's risks. Some graphs are constructed from which we can investigate the required aims. Several decision plans for several specified confidence limits, and variable percentages of deterioration of components, are shown for several sample sizes and specified lot sizes. The techniques used in this research, which are based on the calculus of finite differences, on statistical simulation and on the complex stochastic process for determining the relations required, are applicable to all statistical distributions, provided that the components are statistically independent.

Critical and non-critical human error modelling in redundant systems: modified block diagram approach

Abstract Three newly developed models are presented for performing reliability analysis of redundant systems with erlangian-distributed critical and non-critical human error times. Parallel, k-out-of-n and parallel-series configurations are analysed. System reliability, mean time to failure, time-to-failure variance, failure density function formulae, and hazard rate function formulae are developed. Selective plots are shown to demonstrate the effect of varying critical and non-critical human errors.

Evolutionary reliability theory.

I am developing a new branch of reliability theory called evolutionary reliability theory that concerns the evolution of reliability in populations of systems, such as organisms, that evolve. It subsumes the standard reliability theory but has a higher dimension of time, namely, evolutionary time. In reliability theory, failure phenomena are usually classified according to the monotone properties of the hazard rate h(x) = g(x)/R(x), where h is the hazard rate, x is the age at failure, g is the failure density function, and R is the reliability, where R(x) = P(X > x). Following this method of classification, we have three kinds of evolutionary reliability phenomena: failure events that exhibit (1) a decreasing hazard rate, (2) a constant hazard rate, and (3) an increasing hazard rate. An example of (1) is the reliability of biological development—the selection forces that have evolved safeguards, such as redundancy, so that developmental errors are maintained at a tolerable level. An example of (2) is the reliability of the fully developed system as it faces random failure processes, e.g., accidents, disease, and competition, and it thus concerns the evolution of structural and functional redundancy (e.g., two kidneys and two lungs). Category (3) concerns the reliability of the system with respect to wearout (aging) and this is the main subject of this paper.

Effects of Weibull hazard rate on common cause failure analysis of reliability networks

This paper presents formulae for system mean life, variance of time to failure, hazard rate and reliability of parallel, k-out-of-n, parallel-series and bridge networks with common cause failures. The components in every configuration are assumed to be identical and characterized by a Weibull time to failure density function. The graphical plots of the system reliability and mean life gain are shown.

Component reliability under environmental stress

In this paper, the author has developed a mathematical model for the evaluation of components' reliability under the assumption that the component possesses a non-constant (variable) failure rate of the form (m/k)t m−1, which means that the failure density function follows Weibull pattern (distribution). The stress, under which component operates, has been assumed to be Maxwellian. In the end, cases when Weibull distribution reduces to exponential and Rayleigh distributions, have also been discussed.

The assessment of connector reliability : R. T. Lovelock. Microelectron. & Reliab.12, 475 (1973)

This paper describes qualitative and quantitative techniques for reliability sampling plans based on failure density functions (MTTF, MTBF and MTTR) as expected values and as functions of time duration (t). Examples are provided of how the techniques are applied in determining plans for a specified lot size. These plans are to test service life, the effectiveness of reliability and MTTF, MTBF and MTTR as expected values and as functions of t and the percentage of reliable units expected in any lot size based on consumer's and producer's risks. Some graphs are constructed from which we can investigate the required aims. Several decision plans for several specified confidence limits, and variable percentages of deterioration of components, are shown for several sample sizes and specified lot sizes. The techniques used in this research, which are based on the calculus of finite differences, on statistical simulation and on the complex stochastic process for determining the relations required, are applicable to all statistical distributions, provided that the components are statistically independent.

Reliability Physics Models

The generalized stress-strength model which is prevalent in current literature is perhaps the closest that analysts have come to a general physical model. To obtain a failure density function and associated hazard function one must assume a certain probability distribution for the part strength and a particular amplitude distribution and frequency of occurrence distribution for the part stress. If one assumes a normal strength distribution and Poisson distributed stress occurrence times with normally distributed amplitudes, then this leads to an exponential failure density function and a constant hazard. Such a model is probably best suited for situations in which the part generally lasts a long time and only seems to fail when on occasion a large stress occurs. In many situations the failure of parts seems to fit a different pattern. The part is operated at nearly a constant stress level; however, the part strength gradually deteriorates with time. As time goes on the rate of deterioration should increase sharply as wear-out is reached and cause an increase in hazard. A probabilistic model which fits this hypothesis is a constantly applied stress and a Rayleigh distributed part strength. The parameter of the Rayleigh distribution is allowed to increase in an exponential fashion with time which produces the strength deterioration effect. Basically the failure rate turns out to depend on the square of the applied stress; however, if the strength deterioration rate is allowed to be a function of the input stress, other behaviors are predicted.

A Method for Discriminating between Failure Density Functions Used in Reliability Predictions

Unless sufficient evidence to the contrary exists, the exponential distribution is often assumed as a model for the failure density function in reliability predictions. The generalized gamma distribution, with known location parameter, is a three parameter distribution which encompasses the exponential, Weibull, gamma and many others. In this paper, (i) maximum likelihood estimation for the three parameters is indicated, (ii) it is noted that these estimators are asymptotically multivariate normally distributed, and (iii) using the distribution of the estimators, probability regions for the estimators of the parameters of the generalized gamma distribution are established for large sample situations. In situations where the generalized gamma can be assumed as the correct density function, the exponential and the Weibull are special cases. A method is presented using experimental or life data for rejecting (with a known probability of false rejection) the Weibull and (or) the exponential functions when they do not appear to describe the failure density function of a unit.

A Method for Discriminating Between Failure Density Functions Used In Reliability Predictions

Unless sufficient evidence to the contrary exists, the exponential distribution is often assumed as a model for the failure density function in reliability predictions. The generalized gamma distribution, with known location parameter, is a three parameter distribution which encompasses the exponential, Weibull, gamma and many others. In this paper, (i) maximum likelihood estimation for the three parameters is indicated, (ii) it is noted that these estimators are asymptotically multivariate normally distributed, and (iii) using the distribution of the estimators, probability regions for the estimators of the parameters of the generalized gamma distribution are established for large sample situations. In situations where the generalized gamma can be assumed as the correct density function, the exponential and the Weibull are special cases. A method is presented using experimental or life data for rejecting (with a known probability of false rejection) the Weibull and (or) the exponential functions when the...