Weibull method

The Weibull approach, although useful when comparing fibres, does not take account of the failure mechanism. On the other hand, the deterministic theory of LEFM overcomes some of the limitations of the Weibull method but is applicable only when the initial crack geometry is known. There are intermediate cases where the crack geometry is known but not its precise location, as, for example, inner circular cracks located randomly. In these circumstances, LEFM can provide answers to questions such as what is the maximum rupture stress for a postulated maximum defect size of unknown location ... 

The appropriateness of the Weibull analysis for a partially ductile material can also be justified fundamentally. Although the Weibull method of reliability analysis is formally developed for classically brittle materials (Kelly and Macmillan, 1986), i.e. materials that fail before they can exhibit a yield point, its use can be generalised for materials that exhibit flaw sensitivity. This generalisation can be arrived at simply by examining the equation (Simon and Bunsell, 1984 Chou, 1992) which is plotted to obtain a value... 

The plotted characteristic numbers of cycles to fracture were determined by the Weibull method [21]. Each point represents a test series of ten specimens. In the diagram it can be seen clearly that fretting fatigue leads to a distinct deterioration of the specimen strength and life time. The higher the maximum Hertzian stresses the clearer the decline of the strength and life time is. 

Polyethoxylates may contain polyethylene glycols as well as ethoxylated alcohols, alkylphenols, etc. Both types of component are determined by the Weibull method [10], which has been adopted as an international standard [11], reference to which is advised. The following is an abbreviated version. The method can be used for fatty acid ethoxylates, but the ethyl acetate extract will include any free fatty acid present in the sample. 

ISO 2268 1 2 Surface active agents (non-ionic)— Determination of polyethylene glycols and non-ionic active matter (adducts)— Weibull method. International Organization for Standardization, Geneva. 

Part 4.2 Total nonionic active and polyethylene glycols— Weibull method 2268... 

The Weibull method is not suitable for determination of polypropylene glycol in propoxylates. HPLC is suitable for the analysis, using almost the same normal phase or reversed-phase conditions as for PEG determination (27). 

An alternative method is to fit the best straight line through the linearized set of data assoeiated with distributional models, for example the Normal and 3-parameter Weibull distributions, and then ealeulate the correlation coejficient, r, for eaeh (Lipson and Sheth, 1973). The eorrelation eoeffieient is a measure of the degree of (linear) assoeiation between two variables, x and y, as given by equation 4.4. 

Suppose again that both the stress and strength distributions of interest are of the Normal type, where the loading stress is given as L A (350,40) MPa and the strength distribution is S A (500, 50) MPa. The Normal distribution eannot be used with the integral transform method, but ean be approximated by the 3-parameter Weibull distribution where the CDF is in elosed form. It was determined above that the loading stress parameters for the 3-parameter Weibull distribution were ... 

Similarly, the strength parameters for the Weibull distribution ean be approximated by the same method to ... 

Mischke, C. R. 1989 Stochastic Methods in Mechanical Design Part 1 property data and Weibull parameters. In Proceedings 8th Biannual Conference on Failure Prevention and Reliability, Design Engineering of ASME, Montreal, Canada, 1-10 Sept. 

Today there are many tools available to aid in problem solving or f ure analysis. These include the Weibull Analysis, Failure Mode i Effect Analysis, and Fault Tree Analysis, to name a few. One of the m widely accepted is the Weibull analysis. This method can provide accurate engineering analysis based on extraordinary small samples [1]. 

Statistical Methods for Nonelectronic Reliability, Reliability Specifications, Special Application Methods for Reliability Prediction Part Failure Characteristics, and Reliability Demonstration Tests. Data is located in section 5.0 on Part Failure Characteristics. This section describes the results of the statistical analyses of failure data from more than 250 distinct nonelectronic parts collected from recent commercial and military projects. This data was collected in-house (from operations and maintenance reports) and from industry wide sources. Tables, alphabetized by part class/ part type, are presented for easy reference to part failure rates assuminng that the part lives are exponentially distributed (as in previous editions of this notebook, the majority of data available included total operating time, and total number of failures only). For parts for which the actual life times for each part under test were included in the database, further tables are presented which describe the results of testing the fit of the exponential and Weibull distributions. 

Cran, G. W. Graphical Estimation Methods for Weibull Distribution. Microelectronics and Reliability, Vol. 15, 1976, p. 47. 

Given next are the different methods for estimating distribution parameters on exponential, Weibull, normal, log normal, and extreme-value hazard papers. The methods are explained with the aid of simulated data from known distributions. Thus, we can judge from the hazard plots how well the hazard-plotting method does. 

These various distributions reflect the variations in reactivity of the reacting sites. Johnson and Kotz [444] discuss in detail the Weibull and other distributions which find application when conditions of strict randomness of the exponential distribution are not satisfied. From an empirical point of view, the power transformation is a practical and convenient method of introducing a degree of flexibility into a model. Gittus [445] has discussed some situations in which the Weibull distribution may be expected to find application, including nucleation and growth processes in alloy transformations. 

DuyvesteynW S, ShimoniE and LabuzaTP(2001), Determination of the end of shelf life for milk using Weibull Hazard Method , Food Science and Technology, 34, 143-148. 

In the first method a series of electrical breakdown tests is carried out at the maximum design service temperature and these data are fitted to a 3 parameter Weibull distribution... 

Joergensen K, Jacobsen L. Factorial design used for ruggedness testing of flow through cell dissolution method by means of Weibull transformed drug release profiles. Inti J Pharm 1992 88 23-29. 

Alternative methods and algorithms may be used, such as the model-independent approach to compare similarity limits derived from multi-variate statistical differences (MSD) combined with a 90% confidence interval approach for test and reference batches (21). Model-dependent approaches such as the Weibull function use the comparison of parameters obtained after curve fitting of dissolution profiles. See Chapters 8 and 9 for further discussion of these methods. 

ISO (2005). Milk Products and Milk-Based Foods—Determination of Fat Content by the Weibull-Berntrop Gravimetric Method (Standard ISO 8262-3/IDF 124-3). International Organization for Standardization, Geneva. 

The above reasoning shows that the stretched exponential function (4.14), or Weibull function as it is known, may be considered as an approximate solution of the release problem. The advantage of this choice is that it is general enough for the description of drug release from vessels of various shapes, in the presence or absence of different interactions, by adjusting the values of the parameters a and b. Monte Carlo simulation methods were used to calculate the values of the parameters a and (mainly) the exponent b [87]. 

Equation (9.32) is a linear Fredholm integral equation of the first kind. It is also known as an unfolding or deconvolution equation. One can preanalyze the data and try to solve this first-kind integral equation. Besides the complexity of this equation, there is a paucity of numerical methods for determining the unknown function / (h) [208,379] with special emphasis on methods based on the principle of maximum entropy [207,380]. The so-obtained density function may be approximated by several models, gamma, Weibull, Erlang, etc., or by phase-type distributions. 

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