Search results for "Scale parameter"
showing 10 items of 11 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 …
Finding Prediction Limits for a Future Number of Failures in the Prescribed Time Interval under Parametric Uncertainty
2012
Computing prediction intervals is an important part of the forecasting process intended to indicate the likely uncertainty in point forecasts. Prediction intervals for future order statistics are widely used for reliability problems and other related problems. 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, …
Sequential estimation of a location parameter and powers of a scale parameter from delayed observations
2013
The problem of sequentially estimating a location parameter and powers of a scale parameter is considered in the case when the observations become available at random times. Certain classes of sequential estimation procedures are derived under an invariant balanced loss function and with the observation cost determined by a convex function of the stopping time and the number of observations up to that time.
A simplified approach to estimate water retention for Sicilian soils by the Arya-Paris model
2014
Application of the Arya and Paris (AP) model to estimate the soil water retention curve requires a detailed description of the particle-size distribution (PSD) because the scale factor a, relating the pore length of an ideal soil to that of the natural one, depends on the particle size distribution parameters. For a dataset of 140 Sicilian soils that were grouped in five texture groups, the logistic and linear models were applied to evaluate a, and the water retention values predicted by the AP model were compared with the measured ones. Using the parameters proposed by Arya et al. (1999), the two models yielded similar unsystematic root mean error of estimate (RMSEu). Therefore, their pote…
Testing different approaches to characterize Burundian soils by the best procedure
2011
Abstract The Beerkan Estimation of Soil Transfer parameters (BEST) procedure seems attractive for soil hydraulic characterization but it has received little testing so far. The objective of this investigation was to test BEST with different application approaches for some soils in Burundi, where there is the need of using simple methods to characterize soils. Most (14) of the 19 sampled sites had a clay soil texture whereas texture ranged from silty clay to loam in the other cases. On average, the fitting ability of both the particle size distribution (PSD) model (mean relative error, Me ( E r ) = 2.0%) and the cumulative infiltration model ( Me ( E r ) = 2.3%) was good according to recomme…
Some Remarks on Exponential Families
1987
Abstract The following facts may serve to provide a feeling about how restrictive the assumption of an exponential family is. (a) A one-parameter exponential family in standard form with respect to Lebesgue measure is a location parameter family iff it is normal with fixed variance. (b) It is a scale parameter family iff it is gamma with fixed shape parameter. Both facts are known (see Borges and Pfanzagl 1965; Ferguson 1962; Lindley 1958) but may not have received as much attention as they deserve. Under the assumption of differentiable densities, short and elementary proofs are given.
Empirical model building based on Weibull distribution to describe the joint effect of pH and temperature on the thermal resistance of Bacillus cereu…
2002
Abstract A mathematical model based on Weibull parameters was built to describe the joint effect of temperature and pH on thermal inactivation of Bacillus cereus spores (strain INRA TZ415). The effect of these factors on Weibull model parameters ( β , 1/ α ) was also studied. Heat inactivation tests were carried out in acidified carrot broth as vegetable substrate, following a full factorial design at four levels for temperature (80, 85, 90 and 95 °C) and pH (6.2, 5.8, 5.2 and 4.7). The Weibull distribution model provided good individual fits for the different combinations of temperature–pH tested, with discrepancy factors, D f , coming close to 25% for most cases. The temperature and pH di…
Improved model based on the Weibull distribution to describe the combined effect of pH and temperature on the heat resistance of Bacillus cereus in c…
2003
The effect of pH and temperature on the thermal inactivation of different strains of Bacillus cereus was modeled. Inactivation tests were carried out in carrot broth, following a full factorial design at four levels for temperature (from 90 to 105 degrees C, depending on the strain) and pH (6.2, 5.8, 5.2, and 4.7). Individual inactivation curves were analyzed by applying the Weibull model function (with percent discrepancy close to 20% for most cases), and the effects of pH and temperature on the scale parameter (designated D(beta)) and the shape parameter (beta) were also studied. Temperature and pH did not have a significant effect on the shape parameter (beta). The effect of temperature …
An assessment of the BEST procedure to estimate the soil water retention curve: A comparison with the evaporation method
2018
The Beerkan Estimation of Soil Transfer parameters (BEST) procedure is an attractive, easy, robust, and inexpensive way for a complete soil hydraulic characterization but testing the ability of this procedure to estimate the water retention curve is necessary as relatively little information is available in the literature. In this investigation the soil water retention curve was predicted for four differently textured soils by applying three existing BEST algorithms (i.e., slope, intercept and steady) and the results compared with those measured by the standard Wind evaporation method. A sensitivity analysis of the infiltration constants, beta and gamma, was also carried out and their impac…
PD recognition by means of statistical and fractal parameters and a neural network
2000
A novel partial discharge (PD) defect identification method is described. Starting with PD data on different families of specimens, a suitable set of parameters are determined and then used as input variables to a neural network for the purpose of identifying the defects within the insulation. In this procedure the statistical Weibull analysis is performed on PD pulse amplitude histograms to obtain the scale parameter /spl alpha/ and the shape parameter /spl beta/. Thereafter, the two statistical operators (skewness and kurtosis) and two fractal parameters (fractal dimension and lacunarity) are evaluated from the PD phase on the discharge epoch histogram and from the 3 dimensional (pulse am…