Determining the shape parameter of a Weibull distribution from mechanical damage models

2002 ◽  
Author(s):  
F. Guerin ◽  
B. Dumon ◽  
R. Hambli
Keyword(s):  
Weibull Distribution ◽  
Shape Parameter ◽  
Mechanical Damage ◽  
Damage Models

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.

scholarly journals Mechanical Damage Assessment for Pneumatic Control Valves Based on a Statistical Reliability Model

Sensors ◽  
2021 ◽  
Vol 21 (10) ◽  
pp. 3307
Author(s):  
Nirbhay Mathur ◽  
Vijanth Sagayan Asirvadam ◽  
Azrina Abd Aziz
Keyword(s):  
Weibull Distribution ◽  
Reliability Assessment ◽  
Mechanical Damage ◽  
Control Valve ◽  
Reliability Models ◽  
Statistical Reliability ◽  
Processing Plants ◽  
Simulated Process ◽  
Pneumatic Control Valves ◽  
Log Normal

A reliability assessment is an important tool used for processing plants, since the facility consists of many loops and instruments attached and operated based on other availability; thus, a statistical model is needed to visualize the reliability of its operation. The paper focuses on the reliability assessment and prediction based on the existing statistical models, such as normal, log-normal, exponential, and Weibull distribution. This paper evaluates and visualizes the statistical reliability models optimized using MLE and considers the failure mode caused during a simulated process control operation. We simulated the failure of the control valve caused by stiction running with various flow rates using a pilot plant, which depicted the Weibull distribution as the best model to estimate the simulated process failure.

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.

scholarly journals Computation of history-dependent mechanical damage of axonal fiber tracts in the brain: towards tracking sub-concussive and occupational damage to the brain

2018 ◽  
Author(s):  
Jesse I. Gerber ◽  
Harsha T. Garimella ◽  
Reuben H. Kraft
Keyword(s):  
Fiber Bundle ◽  
Brain Injuries ◽  
Mechanical Response ◽  
Head Injuries ◽  
Mechanical Damage ◽  
Tissue Level ◽  
Internal Damage ◽  
Damage Models ◽  
Axonal Fiber ◽  
The Brain

ABSTRACTFinite element models are frequently used to simulate traumatic brain injuries. However, current models are unable to capture the progressive damage caused by repeated head trauma. In this work, we propose a method for computing the history-dependent mechanical damage of axonal fiber bundle tracts in the brain. Through the introduction of multiple damage models, we provide the ability to link consecutive head impact simulations, so that potential injury to the brain can be tracked over time. In addition, internal damage variables are used to degrade the mechanical response of each axonal fiber bundle element. As a result, the stiffness of the aggregate tissue decreases as damage evolves. To counteract this degenerative process, we have also introduced a preliminary healing model that reverses the accumulated damage, based on a user-specified healing duration. Using two detailed examples, we demonstrate that damage produces a significant decrease in fiber stress, which ultimately propagates to the tissue level and produces a measurable decrease in overall stiffness. These results suggest that damage modeling has the potential to enhance current brain simulation techniques and lead to new insights, especially in the study of repetitive head injuries.

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.

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