This study aims to investigate the estimation of the parameters of the inverse exponential Rayleigh distribution using the Maximum Likelihood Estimation (MLE) and Ranked Set Sampling (RSS) methods, on account of their importance in modeling across lifespan and reliability data. The model is used on empirical data representing the fracture stress of carbon fibers for both single and saturated fibers, in order to determine the accuracy of the estimation methods in given applications. In addition, the classical model is expanded to a fuzzy model to focus on inherent uncertainty in real-world applications. This is realized by designing fuzzy numbers using Shih-skewed membership functions, which offer greater flexibility in illustrating asymmetry in the data. Yager algorithms are used to transform fuzzy values into crisp and clear estimates. At the end, the key distributional functions, consisting of the probability density function, cumulative distribution function, survival function, and hazard function, are derived and analyzed under both classical and fuzzy approaches. Finally, the accuracy of the estimation methods is tested with the Mean Squared Error (MSE), where the result suggests that the RSS method excels the MLE method, in particular when paired with fuzzy techniques, yielding more precise estimation in the face of uncertainty.
The Boltzmann transport equation is solved by using two- terms approximation for pure gases and mixtures. This method of solution is used to calculate the electron energy distribution function and electric transport parameters were evaluated in the range of E/N varying from . 172152110./510.VcmENVcm
The electron energy distribution function of CF4 gas is nearly Maxwellian at (1,2)Td, and when E/N increase the distribution function is non Maxwellian. Also, the mixtures are have different energy values depending on transport energy between electron and molecule through the collisions. Behavior of electrons transport parameters is nearly from the experimental results in references. The drift velocity of electron in carbon tetraflouride i
In this paper, we used maximum likelihood method and the Bayesian method to estimate the shape parameter (θ), and reliability function (R(t)) of the Kumaraswamy distribution with two parameters l , θ (under assuming the exponential distribution, Chi-squared distribution and Erlang-2 type distribution as prior distributions), in addition to that we used method of moments for estimating the parameters of the prior distributions. Bayes
We have studied Bayesian method in this paper by using the modified exponential growth model, where this model is more using to represent the growth phenomena. We focus on three of prior functions (Informative, Natural Conjugate, and the function that depends on previous experiments) to use it in the Bayesian method. Where almost of observations for the growth phenomena are depended on one another, which in turn leads to a correlation between those observations, which calls to treat such this problem, called Autocorrelation, and to verified this has been used Bayesian method.
The goal of this study is to knowledge the effect of Autocorrelation on the estimation by using Bayesian method. F
... Show MoreThe process of evaluating business processes, complex, repetition of procurement processes, need for raw materials and frequency of demand, which makes dealing with suppliers in the evaluation process, making the need for a process intervention in the process. Lighter on the other hand.
Many Iraqi companies suffer from problems related to suppliers, and cases of administrative and financial corruption are often raised regarding this type of contract and from this reality the necessity of researching this problem and trying to develop some solutions to reduce its impact on the companies' work, by using a method that works according to the standards adopted in Evaluation and selection of the supplier in the
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One of the important things provided by fuzzy model is to identify the membership functions. In the fuzzy reliability applications with failure functions of the kind who cares that deals with positive variables .There are many types of membership functions studied by many researchers, including triangular membership function, trapezoidal membership function and bell-shaped membership function. In I research we used beta function. Based on this paper study classical method to obtain estimation fuzzy reliability function for both series and parallel systems.
The way used to estimate the fuzzy reliability differs according to the nature of the information of failure time which has been dealt in this research.The information of failure times has no probable distribution to explain it , in addition it has fuzzy quality.The research includes fuzzy reliability estimation of three periods ,the first one from 1986 to 2013,the second one from 2013 to 2033 while the third one from 2033 to 2066 .Four failure time have been chosen to identify the membership function of fuzzy trapezoid represented in the pervious years after taking in consideration the estimation of most researchers, proffional geologists and the technician who is incharge of maintaining of Mosul Dam project. B
... Show MoreInferential methods of statistical distributions have reached a high level of interest in recent years. However, in real life, data can follow more than one distribution, and then mixture models must be fitted to such data. One of which is a finite mixture of Rayleigh distribution that is widely used in modelling lifetime data in many fields, such as medicine, agriculture and engineering. In this paper, we proposed a new Bayesian frameworks by assuming conjugate priors for the square of the component parameters. We used this prior distribution in the classical Bayesian, Metropolis-hasting (MH) and Gibbs sampler methods. The performance of these techniques were assessed by conducting data which was generated from two and three-component mixt
... Show MoreIn this paper ,the problem of point estimation for the two parameters of logistic distribution has been investigated using simulation technique. The rank sampling set estimator method which is one of the Non_Baysian procedure and Lindley approximation estimator method which is one of the Baysian method were used to estimate the parameters of logistic distribution. Comparing between these two mentioned methods by employing mean square error measure and mean absolute percentage error measure .At last simulation technique used to generate many number of samples sizes to compare between these methods.