Study on Sequential Compliance Method Influenced by Shape Parameter of Weibull Distribution

2011 ◽  
Vol 189-193 ◽  
pp. 4361-4364 ◽  
Author(s):  
Hong Liang Lou ◽  
Xing Lin Li ◽  
Xian Zhao Xu ◽  
Yang Ping Zhang ◽  
Zhong Hua Yu
Keyword(s):  
Weibull Distribution ◽  
Shape Parameter ◽  
Weibull Distributions ◽  
Simulation Test ◽  
Consumer’S Risk ◽  
Producer’S Risk ◽  
Rejection Probability

When sequential compliance method is used for Weibull distributions, the shape parameter is usually considered to be fixed. However, because of the life of products are determined by many factors, the shape parameter is variational in practice, that is to say, the shape parameter in the criterions is different from that in the practice. In this paper, the changes of acceptance and rejection probability are researched by the influence of shape parameter changes. Finally, by means of simulation test, changes on the shape parameter affecting on the probability of acceptance and rejection are quantitatively analyzed. As a result, the larger the gap on the shape parameter in the criterions and in the practice is, the larger the gap on the producer’s risk and the consumer’s risk.

Study of Sequential Sampling Method for Weibull Distribution

2011 ◽  
Vol 291-294 ◽  
pp. 2195-2198 ◽  
Author(s):  
Xian Zhao Xu ◽  
Hong Liang Lou ◽  
Xing Lin Li
Keyword(s):  
Weibull Distribution ◽  
Sampling Method ◽  
Shape Parameter ◽  
Sequential Sampling ◽  
Acceptance Probability ◽  
Distribution Shape ◽  
Rejection Probability

When sequential sampling method based on MTTF is applied to weibull distribution, shape parameter is considered to be fixed. But, shape parameter in criterions or references is different from that in practice. According to sequential sampling method, with the shape parameter changing, changes of acceptance probability and rejection probability are studied. Finally, the result of simulation evaluating shows that the method of sequential sampling method is feasible and reasonable.

scholarly journals Investigation of Feller-Buncher Performance Using Weibull Distribution

Forests ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 284
Author(s):  
Ebru Bilici
Keyword(s):  
Weibull Distribution ◽  
Shape Parameter ◽  
B Value ◽  
Productivity Analysis ◽  
Volume Data ◽  
Estimation Model ◽  
Distribution Method ◽  
Timber Volume ◽  
C Value ◽  
The Right

With the advancement of technology in forestry, the utilization of advanced machines in forest operations has been increasing in the last decades. Due to their high operating costs, it is crucial to select the right machinery, which is mostly done by using productivity analysis. In this study, a productivity estimation model was developed in order to determine the timber volume cut per unit time for a feller-buncher. The Weibull distribution method was used to develop the productivity model. In the study, the model of the theoretical (estimated) volume distributions obtained with the Weibull probability density function was generated. It was found that the c value was 1.96 and the b value was 0.58 (i.e., b is the scale parameter, and c is the shape parameter). The model indicated that the frequency of the volume data had moved away from 0 as the shape parameter of the Weibull distribution increased. Thus, it was revealed that the shape parameter gives preliminary information about the distribution of the volume frequency. The consistency of the measured timber volume with the estimated timber volume strongly indicated that this approach can be effectively used by decision makers as a key tool to predict the productivity of a feller-buncher used in harvesting operations.

Germination of Aristida armata Under Constant and Alternating Temperatures and Its Analysis With the Cumulative Weibull Distribution as a Model

1987 ◽  
Vol 35 (5) ◽  
pp. 581 ◽  
Author(s):  
RF Brown
Keyword(s):  
Weibull Distribution ◽  
Shape Parameter ◽  
Germination Rate ◽  
Coefficient Of Determination ◽  
Its Analysis ◽  
Minimal Distortion ◽  
Different Temperatures ◽  
Fitted Function ◽  
Extremes Of Temperature

Germination of Aristida armata was compared at different temperatures on a thermogradient plate. Temperatures ranged from 10°C to 50°C with day/night differentials of 0, 5, 10 and 15°C. Alternating temperatures improved overall germination, particularly at the extremes of temperature. Average temperatures of 35°C and higher were fatal to many seeds. Day temperatures of 17.5°C and lower inhibited germination but did not prevent subsequent germination under warmer conditions. There was little variation in the rate of germination with incubation under constant temperatures. Under alternating temperatures, maximum germination occurred at lower temperatures than those under which germination rate was greatest. A four-parameter cumulative Weibull distribution was used to summarise cumulative germination. The distribution has the general form: Y = M(1-exp[- {k(t - I)}c]), where Y is the total germination at time t, M is the final total germination, k is germination rate, I is the interval between the start of incubation and the start of germination, and c is a shape parameter. In nearly all cases, the fitted function had a coefficient of determination greater than 0.98. The Weibull distribution allows reconstruction of the original germination data with minimal distortion and its use is recommended for both the analysis and modelling of germination responses.

International trade distributions and their relation with random fragmentation processes

2021 ◽  
Author(s):  
R. Bustos-Guajardo
Keyword(s):  
International Trade ◽  
Shape Parameter ◽  
Size Distributions ◽  
Weibull Distributions ◽  
Traded Goods ◽  
Power Law Decay ◽  
Approximate Power ◽  
Almost All ◽  
Data Log ◽  
Fragmentation Processes

A study of the distribution of the value of traded goods under the Harmonized System is presented. The ramifications of this classification system are found to exhibit an approximate power law decay, indicating complexity and self-organization in the nomenclature of traded merchandises. For almost all countries with available data, log-values of annually imported and exported goods are well described by three-parameter Weibull distributions. This distribution commonly appears in particles size distributions, suggesting a connection between random fragmentation processes and the mechanisms behind the international trade of merchandises. Analysis of the resulting values for the fitting parameters from 1995 to 2018 shows a nearly constant linear relationship between the parameters of the Weibull distributions, so that, for each country, the distribution of log-values can be approximately characterized by a single shape parameter [Formula: see text]. The empirical findings of this paper suggest that specialization on trading a constant set of goods prevents the values of all traded merchandises from growing/decreasing simultaneously.

On the use of the Weibull distribution in modeling and describing diameter distributions of clonal eucalypt stands

2020 ◽  
Vol 50 (10) ◽  
pp. 1050-1063 ◽  
Author(s):  
Luciane Naimeke Schmidt ◽  
Mateus Niroh Inoue Sanquetta ◽  
John Paul McTague ◽  
Gilson Fernandes da Silva ◽  
Clayton Vieira Fraga Filho ◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Goodness Of Fit ◽  
Cumulative Distribution ◽  
Growth And Yield ◽  
Likelihood Method ◽  
Weibull Distributions ◽  
Recovery Method ◽  
Stand Attributes ◽  
Parameter Prediction ◽  
Diameter Distributions

Weibull distributions have been widely used to describe tree stem diameter distributions. However, there is a scarcity of studies that suggest the best Weibull formulation. The parameters of the Weibull distribution are usually predicted by either the parameter prediction method (PPM) or the parameter recovery method (PRM), although other methods have been proposed. Thus, this study aimed to evaluate the performance of eight Weibull formulations and compare methods of parameter prediction to describe diameter distributions of clonal eucalypt stands in Brazil. Data originated from remeasurements of 56 plots at ages 3, 5, and 6 years. Weibull distributions were fitted using the maximum likelihood method and evaluated in a goodness-of-fit indicators ranking. The right-truncated two-parameter formulation showed the best results and was used to evaluate the methods of parameter prediction. Stand attributes showed a strong relationship with shape and scale parameters. Regression models were developed and resulted in accurate estimates using PPM. PRM used a growth and yield system to estimate the stand attributes, followed by the moment-based method. The modified cumulative distribution function regression (CDFR) approach was also evaluated, and it presented the poorest results. Although the PPM showed excellent results, PRM is recommended in older stands with inventory because it implicitly promotes compatibility among stand attributes.

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