Search results for "weibull distribution"
showing 10 items of 42 documents
Weibull Prediction Limits for a Future Number of Failures Under Parametric Uncertainty
2012
In this paper, we present an accurate procedure, called “within-sample prediction of order statistics,” to obtain prediction limits for the number of failures that will be observed in a future inspection of a sample of units, based only on the results of the first in-service inspection of the same sample. The failure-time of such units is modeled with a two-parameter Weibull distribution indexed by scale and shape parameters β and δ, respectively. It will be noted that in the literature only the case is considered when the scale parameter β is unknown, but the shape parameter δ is known. As a rule, in practice the Weibull shape parameter δ is not known. Instead it is estimated subjectively …
Probabilistic description of traffic breakdowns
2001
We analyze the characteristic features of traffic breakdown. To describe this phenomenon we apply to the probabilistic model regarding the jam emergence as the formation of a large car cluster on highway. In these terms the breakdown occurs through the formation of a certain critical nucleus in the metastable vehicle flow, which enables us to confine ourselves to one cluster model. We assume that, first, the growth of the car cluster is governed by attachment of cars to the cluster whose rate is mainly determined by the mean headway distance between the car in the vehicle flow and, may be, also by the headway distance in the cluster. Second, the cluster dissolution is determined by the car …
Unbiased Simultaneous Prediction Limits on Observations in Future Samples
2013
This paper provides procedures for constructing unbiased simultaneous prediction limits on the observations or functions of observations of all of k future samples using the results of a previous sample from the same underlying distribution belonging to invariant family. The results have direct application in reliability theory, where the time until the first failure in a group of several items in service provides a measure of assurance regarding the operation of the items. The simultaneous prediction limits are required as specifications on future life for components, as warranty limits for the future performance of a specified number of systems with standby units, and in various other app…
Study of the reliability of internal combustion engines by application of a Weibull model in bands
2009
The performance of 1,6 l four-valve Otto cycle engines is examined in this paper from the point of view of excessive consumption of lubricating oil. Three failure bands were recognized, at low, medium, and high distance traveled, each one obtained from a sample of 15 vehicles. A “Weibull model in bands” was applied; we obtained a satisfactory result from the point of view of reliability and applied the method to several types of motor vehicle. FMEA analysis of a sample permitted identification of the principal causes of unevenness in cylinder surfaces and an evaluation of the methods of machining required to correct this unevenness. Finishing of cylinders with a flexible smoothing tool is a…
Advanced fragmentation stage of oxide coating on polymer substrate under biaxial tension
2005
Crack patterns of 100-nm-thick silicon oxide coating on polypropylene film subjected to equibiaxial stress loading are studied experimentally. The loading is achieved by means of a bulging cell mounted under an optical microscope with stepwise pressurization of film specimens. The evolution of the coating fragment area distribution at relatively high strains is modeled using Weibull statistics to describe the coating strength. The fragment area distribution at an advanced fragmentation stage is shown to scale with the average fragment area, the latter being a power function of the applied biaxial strain.
Ultimate strain and deformability of elementary flax fibres
2011
Flax fibres possess high specific strength and stiffness, and thus are competitive in terms of mechanical properties with the traditional reinforcing fibres used in polymer-matrix composite materials. The mechanical properties of fibres have considerable variability that needs to be characterized and allowed for in the analysis of mechanical response of composites. In this study, the distribution of ultimate strain of elementary flax fibres and its dependence on gauge length is considered. The applicability of the modified Weibull distribution, used for fibre strength, to fibre ultimate strain is evaluated. A simplified relation of ultimate strain and fibre strength distributions is propos…
Booms, Busts and normal times in the housing market
2015
We assess the existence of duration dependence in the likelihood of an end in housing booms, busts, and normal times. Using data for 20 industrial countries and a continuous-time Weibull duration model, we find evidence of positive duration dependence suggesting that housing market cycles have become longer over the last decades. Then, we extend the baseline Weibull model and allow for the presence of a change-point in the duration dependence parameter.We show that positive duration dependence is present in booms and busts that last less than 26 quarters, but that does not seem to be the case for longer phases of the housing market cycle. For normal times, no evidence of change-points is fo…
Generating survival times to simulate Cox proportional hazards models
2005
Simulation studies present an important statistical tool to investigate the performance, properties and adequacy of statistical models in pre-specified situations. One of the most important statistical models in medical research is the proportional hazards model of Cox. In this paper, techniques to generate survival times for simulation studies regarding Cox proportional hazards models are presented. A general formula describing the relation between the hazard and the corresponding survival time of the Cox model is derived, which is useful in simulation studies. It is shown how the exponential, the Weibull and the Gompertz distribution can be applied to generate appropriate survival times f…
Bayesian analysis of a disability model for lung cancer survival
2016
Bayesian reasoning, survival analysis and multi-state models are used to assess survival times for Stage IV non-small-cell lung cancer patients and the evolution of the disease over time. Bayesian estimation is done using minimum informative priors for the Weibull regression survival model, leading to an automatic inferential procedure. Markov chain Monte Carlo methods have been used for approximating posterior distributions and the Bayesian information criterion has been considered for covariate selection. In particular, the posterior distribution of the transition probabilities, resulting from the multi-state model, constitutes a very interesting tool which could be useful to help oncolog…
RNA viruses as complex adaptive systems
2004
RNA viruses have high mutation rates and so their populations exist as dynamic and complex mutant distributions. It has been consistently observed that when challenged with a new environment, viral populations adapt following hyperbolic-like kinetics: adaptation is initially very rapid, but then slows down as fitness reaches an asymptotic value. These adaptive dynamics have been explained in terms of populations moving towards the top of peaks on rugged fitness landscapes. Fitness fluctuations of varying magnitude are observed during adaptation. Often the presence of fluctuations in the evolution of physical systems indicates some form of self-organization, or where many components of the s…