scholarly journals Study of the modified Weibull function to analyze reliability in engineering components that fail and are repairable

2021 ◽  
Vol 1981 (1) ◽  
pp. 012011
Author(s):  
E Espinel-Blanco ◽  
E Flórez-Solano ◽  
J Arévalo-Rueda
Keyword(s):  
Weibull Function ◽  
Modified Weibull

Modelling the phytotoxicity of aluminum, cadmium, copper, manganese, nickel, and zinc using the Weibull frequency distribution

1991 ◽  
Vol 69 (2) ◽  
pp. 359-367 ◽  
Author(s):  
Gregory J. Taylor ◽  
Kenneth J. Stadt ◽  
Mark R. T. Dale
Keyword(s):  
Frequency Distribution ◽  
Maximum Growth ◽  
Metal Stress ◽  
Weibull Function ◽  
Mathematical Function ◽  
Growth Data ◽  
Toxicity Threshold ◽  
Copper Manganese ◽  
Modified Weibull ◽  
Dose Responses

The toxic effects of aluminum, cadmium, copper, manganese, nickel, and zinc stress on root growth of Triticum aestivum were modelled using a modified version of the Weibull frequency distribution. The modified Weibull function is a continuous, nonlinear mathematical function that provides direct estimates of several important biological parameters, including maximum growth, minimum growth, growth response, toxicity threshold, and maximum unit toxicity. The function was fit to experimental data using standard nonlinear regression techniques. Despite variation among metals in the characteristics of observed dose responses, the Weibull function provided a close fit for each of the metals tested (0.96 ≤ R2 ≤ 0.99). Estimates of maximum unit toxicities indicated that cadmium was most toxic to T. aestivum (152% growth reduction (GR)/(μmol∙L)), followed by copper (19.0% GR/(μmol∙L)), nickel (3.9% GR/(μmol∙L)), aluminum (1.3% GR/(μmol∙L)), zinc (0.5% GR/(μmol∙L)), and manganese (0.2% GR/((μmol∙L)). Estimated toxicity thresholds also indicated that cadmium was most toxic. Cadmium showed the lowest threshold for metal injury (0.02 μM), followed by copper (3.4 μM), nickel (11 μM), aluminum (18 μM), manganese (37 μM), and zinc (45 μM). The shift in the relative position of Mn and Zn suggests that unit toxicity and the toxicity threshold may be independent measures of the response of plants to metal stress. These experiments clearly demonstrate the utility of the Weibull function in modelling the response of plants to metal stress. Furthermore, the ability of the function to model primary growth data directly provides a suitable technique for investigation of potential interactions between phytotoxic metals. Key words: dose response, modelling, metal stress, toxicity threshold, unit toxicity.

Modeling the potential for boron amelioration of aluminum toxicity using the Weibull function

1994 ◽  
Vol 72 (8) ◽  
pp. 1187-1196 ◽  
Author(s):  
Gregory J. Taylor ◽  
Sheila M. Macfie
Keyword(s):  
Aluminum Toxicity ◽  
Acid Soils ◽  
Triticum Aestivum L ◽  
Solution Culture ◽  
Al Toxicity ◽  
Plant Performance ◽  
Boron Toxicity ◽  
Weibull Function ◽  
Experimental Conditions ◽  
Modified Weibull

Several recent reports have suggested that boron (B) may alleviate the toxic effects of aluminum (Al) on plant growth, providing improved plant performance on acid soils. To test this hypothesis, an Al-sensitive cultivar of Triticum aestivum L. (cv. Neepawa) was grown in solution culture with 10 concentrations of Al (0–300 μM), in the presence of deficient (0 μM), sufficient (6 μM), luxury (75 μM), or toxic (750 μM) concentrations of B. The effects of both Al and B on the response of roots and leaves to Al was accurately modeled (R2 < 0.99) using a modified Weibull function. Comparison of best fit function parameters for the response to Al under varying conditions of B supply failed to reveal any evidence of B amelioration of Al toxicity. The combined effects of Al and B were adequately explained by a multiplicative model. Although formation of stable Al-borate complexes could occur in growth solutions under our experimental conditions, varying the supply of B had little effect on accumulation of Al in roots and leaves. In contrast, increasing Al concentrations in solution resulted in increased immobilization of B in roots and decreased accumulation of B in leaves. Growth of plants with elevated B supply resulted in higher concentrations of B in roots and leaves without improving growth. We suggest that previous reports of B amelioration of Al toxicity must reflect the unique characteristics of soil-based media, and (or) differences among species in internal requirements for B and the effects of Al on B nutrition. Key words: amelioration, aluminum, boron, toxicity, Weibull function, wheat.

Preliminary Evaluation of a Weibull Function for Fitting Slow-Component Eye Velocity over the Time Course of Caloric-Induced Nystagmus

1989 ◽  
Vol 32 (3) ◽  
pp. 681-687 ◽  
Author(s):  
C. Formby ◽  
B. Albritton ◽  
I. M. Rivera
Keyword(s):  
Time Course ◽  
Slow Component ◽  
Weibull Function ◽  
Preliminary Evaluation ◽  
Mathematical Function ◽  
Before And After ◽  
Best Fitting ◽  
Eye Velocity ◽  
Fitting Parameters ◽  
Weibull Equation

We describe preliminary attempts to fit a mathematical function to the slow-component eye velocity (SCV) over the time course of caloric-induced nystagmus. Initially, we consider a Weibull equation with three parameters. These parameters are estimated by a least-squares procedure to fit digitized SCV data. We present examples of SCV data and fitted curves to show how adjustments in the parameters of the model affect the fitted curve. The best fitting parameters are presented for curves fit to 120 warm caloric responses. The fitting parameters and the efficacy of the fitted curves are compared before and after the SCV data were smoothed to reduce response variability. We also consider a more flexible four-parameter Weibull equation that, for 98% of the smoothed caloric responses, yields fits that describe the data more precisely than a line through the mean. Finally, we consider advantages and problems in fitting the Weibull function to caloric data.

A Blind Spot in the Use of the Weibull Function for Modeling Diameter Distributions

2020 ◽  
Author(s):  
Adrian Norman Goodwin
Keyword(s):  
Lower Bound ◽  
Blind Spot ◽  
Forest Growth ◽  
Growth And Yield ◽  
Diameter Distribution ◽  
Absolute Difference ◽  
Weibull Function ◽  
Distribution Models ◽  
Difference Statistic ◽  
Diameter Distributions

Abstract Diameter distribution models based on probability density functions are integral to many forest growth and yield systems, where they are used to estimate product volumes within diameter classes. The three-parameter Weibull function with a constrained nonnegative lower bound is commonly used because of its flexibility and ease of fitting. This study compared Weibull and reverse Weibull functions with and without a lower bound constraint and left-hand truncation, across three large unthinned plantation cohorts in which 81% of plots had negatively skewed diameter distributions. Near-optimal lower bounds for the unconstrained Weibull function were negative for negatively skewed data, and the left-truncated Weibull using these bounds was 14.2% more accurate than the constrained Weibull, based on the Kolmogorov-Smirnov statistic. The truncated reverse Weibull fit dominant tree distributions 23.7% more accurately than the constrained Weibull, based on a mean absolute difference statistic. This work indicates that a blind spot may have developed in plantation growth modeling systems deploying constrained Weibull functions, and that left-truncation of unconstrained functions could substantially improve model accuracy for negatively skewed distributions.

Modeling and experimental study on the mechanical behavior of glass/basalt fiber metal laminates after thermal cycling

2021 ◽  
pp. 105678952199873
Author(s):  
Mehdi Abdollahi Azghan ◽  
F Bahari-Sambran ◽  
Reza Eslami-Farsani
Keyword(s):  
Thermal Cycling ◽  
Glass Fibers ◽  
Basalt Fiber ◽  
Tensile Modulus ◽  
Alloy Sheet ◽  
Experimental Results ◽  
Weibull Function ◽  
Basalt Fibers ◽  
Thermal Stabilities ◽  
Fiber Metal

In the present study, the effect of thermal cycling and stacking sequence on the tensile behavior of fiber metal laminate (FML) composites containing glass and basalt fibers was investigated. To fabricate the FML samples, fibers reinforced epoxy composite were sandwiched between two layers of 2024-T3 aluminum alloy sheet. 55 thermal cycles were implemented at a temperature range of 25–115°C for 6 min. The tensile tests were carried out after the thermal cycling procedure, and the results were compared with non-thermal cycling specimens. Scanning electron microscopy (SEM) was employed for the characterization of the damage mechanisms. The FMLs containing four basalt fibers’ layers showed higher values of tensile strength, modulus, and energy absorption. On the other hand, the lowest strength and fracture energy were found in the asymmetrically stacked sample containing basalt and glass fibers, due to weak adhesion between composite components (basalt and glass fibers). The lowest tensile modulus was found in the sample containing glass fibers that was due to the low modulus of the glass fibers compared to basalt fibers. In the case of the samples exposed to thermal cycling, the highest and the lowest thermal stabilities were observed in basalt fibers samples and asymmetrically stacked samples, respectively. In accordance with the experimental results, a non-linear damage model using the Weibull function and tensile modulus was employed to predict the stress-strain relationship. The simulated strain–strain curves presented an appropriate agreement with the experimental results.

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