Statistical lifetime modeling

Application of Accelerated Testing and Statistical Lifetime Modeling to Membrane Electrode Assembly Development... 

Accelerated testing and statistical lifetime modeling are important tools in the development of durable membrane electrode assemblies (MEAs). There are several reasons for using accelerated tests and three of the main reasons are listed here ... 

Utilizing tools such as accelerated tests and statistical lifetime modeling allow for early estimates of durability. There are three basic types of accelerated tests (1) screening tests are appropriate for measuring incremental improvements in component... 

The mean squared energies (A ( o)) are of course also determined by the intermolecular potentials. The duration of the collision or the lifetime of the collision complex will be of primary importance. The statistical collision model assumes a statistical distribution of the energies of all oscillators in A and M during collision. If before collision A is highly excited but M is not excited, this results in very effective energy transfer. With the statistical theory of reaction rates as discussed in section 1.8 one can easily calculate for this model values of (AE ( o)>. see e.g. ref. 97. One finds in general V kT, and so = 1 in equation (1.55). Details of (AE (Eg)) for this model are... 

A very powerful idea behind Bayesian inference is that statistical inference is simply updating a previous knowledge, assessed by a prior distribution. The obtained posterior distribution, which encodes the current state of knowledge, can be sequentially updated by adding more and more data. To exemphfy this idea, let us consider a very simple problem the Bayesian assessment of an exponential lifetime model, of failure rate X ... 

As a commercial product, the failure or reliability information of the fuel cell under typical operation eonditions should be included. Basically, the durability of the fuel cell is not defined by a single lifetime test. Lifetimes at variable stresses are always statistical distributions. The detailed scheme of a typical statistical accelerated lifetime model is illustrated in Figure 1.14 [45,46]. 

S. Leigh Phoenix, Modeling the statistical lifetime of glass fiber/polymer matrix composites in tension. Composite Structures, 48(l-3) 19-29,2000. 

The following example is based on a risk assessment of di(2-ethylhexyl) phthalate (DEHP) performed by Arthur D. Little. The experimental dose-response data upon which the extrapolation is based are presented in Table II. DEHP was shown to produce a statistically significant increase in hepatocellular carcinoma when added to the diet of laboratory mice (14). Equivalent human doses were calculated using the methods described earlier, and the response was then extrapolated downward using each of the three models selected. The results of this extrapolation are shown in Table III for a range of human exposure levels from ten micrograms to one hundred milligrams per day. The risk is expressed as the number of excess lifetime cancers expected per million exposed population. 

The percolation model, which can be applied to any disordered system, is used for an explanation of the charge transfer in semiconductors with various potential barriers [4, 14]. The percolation threshold is realized when the minimum molar concentration of the other phase is sufficient for the creation of an infinite impurity cluster. The classical percolation model deals with the percolation ways and is not concerned with the lifetime of the carriers. In real systems the lifetime defines the charge transfer distance and maximum value of the possible jumps. Dynamic percolation theory deals with such case. The nonlinear percolation model can be applied when the statistical disorder of the system leads to the dependence of the system s parameters on the electrical field strength. 

Using the so-called planar libration-regular precession (PL-RP) approximation, it is possible to reduce the double integral for the spectral function to a simple integral. The interval of integration is divided in the latter by two intervals, and in each one the integrands are substantially simplified. This simplification is shown to hold, if a qualitative absorption frequency dependence should be obtained. Useful simple formulas are derived for a few statistical parameters of the model expressed in terms of the cone angle (5 and of the lifetime x. A small (3 approximation is also considered, which presents a basis for the hybrid model. The latter is employed in Sections IV and VIII, as well as in other publications (VIG). 

The formulas for the statistical characteristics are given as a generalization of the expressions obtained in Section IE. These characteristics depend now on three model parameters angular well width p, mean lifetime x, and the reduced well depth u = Uo/(kBT), where fcB is the Boltzmann constant and T is the temperature. 

When the EPA considered exposures to insecticide residues in the home they identified at least six possible sources and routes these are given in Table 2.6. Their original approach apportioned the acceptable daily intake (ADI) between the various routes but it soon became clear that this was unrealistic because an individual was unlikely to be exposed via all routes on any one day. The EPA s present strategy is to develop an approach called micro-exposure event modelling. Micro-exposure event modelling is based on statistical data on the frequencies and levels of contamination of food, water, etc. and on behavioural information about the frequency of use of lawn/pet/timber treatments, etc. The combined data are assembled in a probabilistic model called LIFELINE which is able to predict the frequency and level of exposure to a group of hypothetical individuals over their lifetime.12 The model is also able to take account of the relative proportions of different types of accommodation, the incidence of pet ownership or any other data that will affect real levels of exposure. The output from the LIFELINE model allows the exposures of individuals in a population to be modelled over any interval from a single occasion to a lifetime. 

Essentially, the problem falls into two parts. Firstly, the calculation of the multi-body reaction potential surface and secondly, the determination of the properties of the reaction products from the knowledge of the potential surface. The reverse process of inverting experimental data to yield a potential energy surface is more complicated and has rarely been attempted. The calculation of potential surfaces and of product distributions may be carried out at various levels of sophistication using classical, semi-classical or full quantum mechanical treatments. Gross features of the reaction potential surfaces may be related to various product properties by simplistic model calculations. Statistical theories may also be used in cases where the lifetime of the collision is long enough to justify their use. 

The formation of a stable product is a two-step process O + O2 - O3 O3 + M -> O3 + M. After the formation of the vibrationally excited molecule, the subsequent redistribution of the energy among its vibrational-rotational modes proceeds at some finite rate and may be incomplete during the typical lifetime of the molecule. This non-statistical concept was used to model the laboratory data with a mathematically introduced non-statistical factor rj. A value of 1.18 for rf matches the observations well. 

S. L. Phoenix, P. Schwartz, and H. H. Robinson, IV, Statistics for the Strength and Lifetime in Creep-Rupture of Model Carbon/Epoxy Composites, Composites Science and Technology, 32, 81-120 (1988). 

Within the last 25 years of X-ray spectroscopy on fusion devices, the theory of He-like ions has been developed to an impressive precision. The spectra can be modeled with deviations not more than 10% on all lines. For the modeling, only parameters with physical meaning and no additional approximation factors are required. Even the small effects due to recombination of H-like atoms, which contribute only a few percent to the line intensity, can be used to explain consistently the recombination processes and hence the charge state distribution in a hot plasma. The measurements on fusion devices such as tokamaks or stellarators allow the comparison to the standard diagnostics for the same parameters. As these diagnostics are based on different physical processes, they provide sensitive tests for the atomic physics used for the synthetic spectra. They also allow distinguishing between different theoretical approaches to predict the spectra of other elements within the iso-electronic series. The modeling of the X-ray spectra of astronomical objects or solar flares, which are now frequently explored by X-ray satellite missions, is now more reliable. In these experiments, the statistical quality of the spectra is limited due to the finite observation time or the lifetime of... 

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