• Journal of Biosystems Engineering
• /
• 제11권1호
• /
• pp.76-85
• /
• 1986

This study was intended to examine the failure characteristics and breakdowns of the head-fed type combines generally used on farms. The failure distribution was assumed to follow Weibull distribution function and the Weibull parameters of the major parts, units and combine as whole were estimated by using the data collected in a survey. A computer program for the estimation of the Weibull parameter was developed. Monte Carlo method was used in predicting the time between failures. The results of study may be summarized as follows: 1. The number of failures per combine was 4.83 times per year and 0.3 times per hectare of combines of different ages. 2. According to the Kolmogorov-Smirnov test method, it was proved that the Weibull distribution function is well fitted to the characteristics of the failure and breakdowns of combines. 3. Weibull parameters of failure distribution of the combine as a whole were estimated to give the shape parameter ${\beta}$=1.3089 and the scale parameter ${\alpha}$=105.2409. The combining area with 80% reliability was 1.1 ha, and the probability of operating the combine without any failure for a year, was $2.76{\times}10^{-4}$. 4. The mean time between failures (MTBF) of the combines was predicted to be 3.2 ha of operation, which corresponds to 32 hours of operation.

• 전기학회논문지P
• /
• 제66권1호
• /
• pp.33-37
• /
• 2017

This paper describes the modeling of the failure rate estimation technique for applying the asset management technique to electric power facilities. There are many modeling techniques to estimate the failure rate. In this paper, the characteristics of the normal distribution, exponential distribution, weibull distribution, and piecewise linear functions are discussed. When evaluating reliability, the evaluation may be less meaningful if the sample data is insufficient. Therefore, Weibull distribution and piecewise linear function are adopted as the most suitable functions for estimating the failure rate of power facilities and the resulting failure rate function is derived.

• Journal of the Korean Data and Information Science Society
• /
• 제28권3호
• /
• pp.659-668
• /
• 2017

The inverse Weibull distribution (IWD) can be readily applied to a wide range of situations including applications in medicines, reliability and ecology. It is generally known that the lifetimes of test items may not be recorded exactly. In this paper, therefore, we consider the maximum likelihood estimation (MLE) and Bayes estimation of the entropy of a IWD under generalized progressive hybrid censoring (GPHC) scheme. It is observed that the MLE of the entropy cannot be obtained in closed form, so we have to solve two non-linear equations simultaneously. Further, the Bayes estimators for the entropy of IWD based on squared error loss function (SELF), precautionary loss function (PLF), and linex loss function (LLF) are derived. Since the Bayes estimators cannot be obtained in closed form, we derive the Bayes estimates by revoking the Tierney and Kadane approximate method. We carried out Monte Carlo simulations to compare the classical and Bayes estimators. In addition, two real data sets based on GPHC scheme have been also analysed for illustrative purposes.

• International Journal of Reliability and Applications
• /
• 제9권2호
• /
• pp.153-165
• /
• 2008

This paper discusses the reliability equivalences of a series-parallel system. The system components are assumed to be independent and identical. The failure rates of the system components are functions of time and follow Weibull distribution. Three different methods are used to improve the given system reliability. The reliability equivalence factor is obtained using the reliability function. The fractiles of the original and improved systems are also obtained. Numerical example is presented to interpret how to utilize the obtained results.

• 한국수자원학회:학술대회논문집
• /
• 한국수자원학회 2016년도 학술발표회
• /
• pp.201-201
• /
• 2016

The asymptotic extreme value distributions of maxima are a natural choice when designing against future extreme events like flood peaks or wave heights, given a stationary time series. The generalized extreme value distribution (GEV) is often utilised in this context because it is seen as a convenient single expression for extreme event analysis. However, the GEV has a drawback because the location of the distribution bound relative to the data is a discontinuous function of the GEV shape parameter. That is, for annual maxima approximated by the Gumbel distribution, the data is also consistent with a GEV distribution with an upper bound (no lower bound) or a GEV distribution with a lower bound (no upper bound). A more consistent single extreme value expression for design purposes is proposed as the Weibull distribution of smallest extremes, as applied to transformed annual maxima. The Weibull distribution limit holds here for sufficiently large sample sizes, irrespective of the extreme value domain of attraction applicable to the untransformed maxima. The Gumbel, Type 2, and Type 3 extreme value distributions thus become redundant, together with the GEV, because in reality there is only a single asymptotic extreme value distribution required for design purposes - the Weibull distribution of minima as applied to transformed maxima. An illustrative synthetic example is given showing transformed maxima from the normal distribution approaching the Weibull limit much faster than the untransformed sample maxima approach the normal distribution Gumbel limit. Some New Zealand examples are given with the Weibull distribution being applied to reciprocal transformations of annual flood maxima, where the untransformed maxima follow apparently different extreme value distributions.

• Communications for Statistical Applications and Methods
• /
• 제24권5호
• /
• pp.519-531
• /
• 2017

We consider goodness-of-fit test statistics for Weibull distributions when data are randomly censored and the parameters are unknown. Koziol and Green (Biometrika, 63, 465-474, 1976) proposed the $Cram\acute{e}r$-von Mises statistic's randomly censored version for a simple hypothesis based on the Kaplan-Meier product limit of the distribution function. We apply their idea to the other statistics based on the empirical distribution function such as the Kolmogorov-Smirnov and Liao and Shimokawa (Journal of Statistical Computation and Simulation, 64, 23-48, 1999) statistics. The latter is a hybrid of the Kolmogorov-Smirnov, $Cram\acute{e}r$-von Mises, and Anderson-Darling statistics. These statistics as well as the Koziol-Green statistic are considered as test statistics for randomly censored Weibull distributions with estimated parameters. The null distributions depend on the estimation method since the test statistics are not distribution free when the parameters are estimated. Maximum likelihood estimation and the graphical plotting method with the least squares are considered for parameter estimation. A simulation study enables the Liao-Shimokawa statistic to show a relatively high power in many alternatives; however, the null distribution heavily depends on the parameter estimation. Meanwhile, the Koziol-Green statistic provides moderate power and the null distribution does not significantly change upon the parameter estimation.

• Communications for Statistical Applications and Methods
• /
• 제22권4호
• /
• pp.333-348
• /
• 2015

In this paper, we study a generalization of the modified Weibull distribution. The generalization follows the recent work of Cordeiro et al. (2013) and is based on a class of exponentiated generalized distributions that can be interpreted as a double construction of Lehmann. We introduce a class of exponentiated generalized modified Weibull (EGMW) distribution and provide a list of some well-known distributions embedded within the proposed distribution. We derive some mathematical properties of this class that include ordinary moments, generating function and order statistics. We propose a maximum likelihood method to estimate model parameters and provide simulation results to assess the model performance. Real data is used to illustrate the usefulness of the proposed distribution for modeling reliability data.

• Communications for Statistical Applications and Methods
• /
• 제23권5호
• /
• pp.363-383
• /
• 2016

The Weibull family of lifetime distributions play a fundamental role in reliability engineering and life testing problems. This paper investigates the potential usefulness of transmuted new generalized Weibull (TNGW) distribution for modeling lifetime data. This distribution is an important competitive model that contains twenty-three lifetime distributions as special cases. We can obtain the TNGW distribution using the quadratic rank transmutation map (QRTM) technique. We derive the analytical shapes of the density and hazard functions for graphical illustrations. In addition, we explore some mathematical properties of the TNGW model including expressions for the quantile function, moments, entropies, mean deviation, Bonferroni and Lorenz curves and the moments of order statistics. The method of maximum likelihood is used to estimate the model parameters. Finally the applicability of the TNGW model is presented using nicotine in cigarettes data for illustration.

• Communications for Statistical Applications and Methods
• /
• 제30권2호
• /
• pp.191-213
• /
• 2023

Unit distributions are frequently used in probability theory and statistics to depict meaningful variables having values between zero and one. Using convenient transformation, the unit inverse exponentiated weibull (UIEW) distribution, which is equally useful for modelling data on the unit interval, is proposed in this study. Quantile function, moments, incomplete moments, uncertainty measures, stochastic ordering, and stress-strength reliability are among the statistical properties provided for this distribution. To estimate the parameters associated to the recommended distribution, well-known estimation techniques including maximum likelihood, maximum product of spacings, least squares, weighted least squares, Cramer von Mises, Anderson-Darling, and Bayesian are utilised. Using simulated data, we compare how well the various estimators perform. According to the simulated outputs, the maximum product of spacing estimates has lower values of accuracy measures than alternative estimates in majority of situations. For two real datasets, the proposed model outperforms the beta, Kumaraswamy, unit Gompartz, unit Lomax and complementary unit weibull distributions based on various comparative indicators.

• Wind and Structures
• /
• 제21권2호
• /
• pp.203-221
• /
• 2015

Wind speed is the most important parameter in the design and study of wind energy conversion systems. The weibull distribution is commonly used for wind energy analysis as it can represent the wind variations with an acceptable level of accuracy. In this study, the wind data for 11 cities in Iran have been analysed over a period of one year. The Goodness of fit test is used for testing data fit to weibull distribution. The results show that this data fit to weibull function very well. The scale and shape factors are two parameters of the weibull distribution that depend on the area under study. The kinds of numerical methods commonly used for estimating weibull parameters are reviewed. Their performance for the cities under study was compared according to root mean square and wind energy errors. The result of the study reveals the empirical, modified maximum likelihood estimate of wind speed with minimum error. Also, that the moment and modified maximum likelihood are the best methods for estimating the energy production of wind turbines.