scholarly journals Aproksimasi Numerik Belah Dua dan Newton-Raphson pada Estimasi Parameter Distribusi Weibul

CAUCHY ◽  
2013 ◽  
Vol 2 (4) ◽  
pp. 193
Author(s):  
Indira P Kinasih
Keyword(s):  
Weibull Distribution ◽  
Numerical Approximation ◽  
Shape Parameter ◽  
Likelihood Function ◽  
Life Time ◽  
Life Distribution ◽  
Approximation Result ◽  
Failure Data ◽  
Newton Raphson ◽  
The Right

Life time distribution of warranted product, for example like automobile and photocopier is an interesting studies. Based on the fact that mostly, life distribution of warranted product is somewhat skewed to the right, this suggests that usual failure distribution such as Weibull distribution may provide a reasonable fit to the data. Related to these studies, parameter estimation is directly applicable since life distribution function is a function of parameters. There are no closed solution for Weibull likelihood function maximation. Therefore, numerical approximation could be an alternative solution. In this paper, Newton-Raphson and bisection method were employed to estimate the scale and shape parameter of Weibull distribution for photocopier failure data for since 4,5 years. Performance of those method were compared based on their approximation result and how fast they get into the solution. Data were taken from Bulmer and Eccleston (2003) research about photocopier realibility model.

A Sample Truncation Rule for Product Reliability Estimation in Multiple Censoring Data Conditions

2020 ◽  
pp. 2150010
Author(s):  
Liyang Xie ◽  
Jiaxin Song ◽  
Chenggang Li ◽  
Haiyang Li
Keyword(s):  
Weibull Distribution ◽  
Sample Size ◽  
Confidence Level ◽  
Operation Time ◽  
Location Parameter ◽  
Life Time ◽  
Reliability Estimation ◽  
Life Distribution ◽  
Life Data ◽  
The Right

This paper studies the method to estimate the location parameter of a three-parameter Weibull life distribution in the situation of multiple censoring life data available, the effect of sample size and minimal outcome on life and reliability estimation, and the policy to choose favorable data from operation records. First of all, a method to estimate the location parameter of the Weibull distribution is presented in the scenario of product probabilistic life and reliability estimation. Relationships between the estimated life distribution parameter and the right-censored life data applied is demonstrated, a rule is proposed to choose the appropriate number of censoring life data by discarding some shorter operation time records. It is illustrated that an appropriate combination of sample size and the minimum observation value (right-censored life time) is reasonable for the balance between estimation confidence level and reliability value.

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 Weibull Failure Probability Estimation Based on Zero-Failure Data

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Ping Jiang ◽  
Yunyan Xing ◽  
Xiang Jia ◽  
Bo Guo
Keyword(s):  
Weibull Distribution ◽  
Failure Probability ◽  
Development Time ◽  
Shape Parameter ◽  
Distribution Curve ◽  
Small Sample ◽  
Reliability Testing ◽  
Failure Data ◽  
Curve Method ◽  
Small Sample Sizes

Reliability testing is often carried out with small sample sizes and short duration because of increasing costs and the restriction of development time. Therefore, for highly reliable products, zero-failure data are often collected in such tests, which could not be used to evaluate reliability by traditional methods. To cope with this problem, the match distribution curve method was proposed by some researchers. The key step needed to exercise this method is to estimate the failure probability, which has yet to be solved in the case of the Weibull distribution. This paper presents a method to estimate the intervals of failure probability for the Weibull distribution by using the concavity or convexity and property of the distribution function. Furthermore, to use the method in practice, this paper proposes using the approximate value of the shape parameter determined by either engineering experience or by hypothesis testing through apvalue. The estimation of the failure probability is thus calculated using a Bayesian approach. A numerical example is presented to validate the effectiveness and robustness of the method.

Reliability Analysis and Prediction of Metro Vehicles’ Bogie Frame

2014 ◽  
Vol 590 ◽  
pp. 872-877 ◽  
Author(s):  
Yong Qin ◽  
Zhen Yu Zhang ◽  
Jing Xuan Shi
Keyword(s):  
Survival Analysis ◽  
Weibull Distribution ◽  
Reliability Analysis ◽  
Failure Rate ◽  
Life Time ◽  
Distribution Model ◽  
Life Distribution ◽  
Main Bearing ◽  
Bogie Frame ◽  
Time Problem

Frame is the main bearing component of bogie and the reliability of which directly affects the performance and safety of the locomotive. Survival analysis is used for reliability analysis of bogie frame to solve uncertain life time problem. It turns out that the best life distribution model is three-parameter Weibull distribution. A prediction model of failure rate composed of PSO-BP is came up with to predict the failure rate of bogie frame accurately.

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.

DOM Products: Activation Energy Estimation and Reliability Assessment

2013 ◽  
Vol 470 ◽  
pp. 781-784 ◽  
Author(s):  
Chien Yi Huang ◽  
Yueh Hsun Lin ◽  
Eric Huang
Keyword(s):  
Experimental Data ◽  
Activation Energy ◽  
Subjective Experience ◽  
Reliability Assessment ◽  
Life Time ◽  
Service Condition ◽  
Energy Estimation ◽  
Failure Data ◽  
Scientific Approach ◽  
Temperature Scenario

A scientific approach is proposed in this research to investigate a disk on module (DOM) product's activation energy based on experimental data that eliminates subjective experience. This study considers multiple temperature conditions to enhance the accuracy of activation energy estimation. In order to ensure the consistency of failure mode in each temperature scenario, the slopes of Weibul probability plots obtained from the failure data are calculated followed by an examination for parallelism. The estimated life time under normal service condition differs from the results obtained using the industrial standard given activation energy by approximately 42%.

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.

Statistical Inference of LZL-Type Mass Flowmeter Life Distribution Model

2010 ◽  
Vol 458 ◽  
pp. 173-178
Author(s):  
Zhen Zhou ◽  
L.N. Zhang ◽  
Y. Qin ◽  
D.Z. Ma ◽  
B. Niu
Keyword(s):  
Least Square ◽  
Distribution Model ◽  
Maintenance Policy ◽  
Life Distribution ◽  
Mass Flowmeter ◽  
Failure Data ◽  
Distribution Type ◽  
Two Parameter ◽  
Field Failure ◽  
Type Mass

Characteristics of field failure data are analyzed in this paper. The failure data and sales record of LZL-type mass flowmeter are used to infer life distribution of this conduct. The lines can be fitted in coordinates of six distribution using least square and the residual sum of squares are compared, the minimum correspond is the best distribution type. The results show that the life distribution style of this conduct is the two parameter exponential distribution, which is the base to analyze and predict failure development, research failure mechanism and draw up maintenance policy.

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