The 3-parameter Weibull distribution is used as a model for failure since this distribution is proper when the failure rate somewhat high in starting operation and these rates will be decreased with increasing time .

In practical side a comparison was made between (Shrinkage and Maximum likelihood) Estimators for parameter and reliability function using simulation , we conclude that the Shrinkage estimators for parameters are better than maximum likelihood estimators but the maximum likelihood estimator for reliability function is the better using statistical measures (MAPE)and (MSE) and for different sample sizes.

Note:- n_s : small sample ; n_m=median sample

In this paper was discussed the process of compounding two distributions using new compounding procedure which is connect a number of life time distributions ( continuous distribution ) where is the number of these distributions represent random variable distributed according to one of the discrete random distributions . Based on this procedure have been compounding zero – truncated poisson distribution with weibell distribution to produce new life time distribution having three parameter , Advantage of that failure rate function having many cases ( increasing , dicreasing , unimodal , bathtube) , and study the resulting distribution properties such as : expectation , variance , comulative function , reliability function and fa

Transforming the common normal distribution through the generated Kummer Beta model to the Kummer Beta Generalized Normal Distribution (KBGND) had been achieved. Then, estimating the distribution parameters and hazard function using the MLE method, and improving these estimations by employing the genetic algorithm. Simulation is used by assuming a number of models and different sample sizes. The main finding was that the common maximum likelihood (MLE) method is the best in estimating the parameters of the Kummer Beta Generalized Normal Distribution (KBGND) compared to the common maximum likelihood according to Mean Squares Error (MSE) and Mean squares Error Integral (IMSE) criteria in estimating the hazard function. While the pr

Entropy define as uncertainty measure has been transfared by using the cumulative distribution function and reliability function for the Burr type – xii. In the case of data which suffer from volatility to build a model the probability distribution on every failure of a sample after achieving limitations function, probabilistic distribution. Has been derived formula probability distribution of the new transfer application entropy on the probability distribution of continuous Burr Type-XII and tested a new function and found that it achieved the conditions function probability, been derived mean and function probabilistic aggregate in order to be approved in the generation of data for the purpose of implementation of simulation

        In this paper, an estimate has been made for parameters and the reliability function for Transmuted power function (TPF) distribution through using some estimation methods as proposed new technique for white, percentile, least square, weighted least square and modification moment methods. A simulation was used to generate random data that follow the (TPF) distribution on three experiments (E₁ , E₂ , E₃)  of the real values of the parameters, and with sample size (n=10,25,50 and 100) and iteration samples (N=1000), and taking reliability times (0< t < 0) . Comparisons have been made between the obtained results from the estimators using mean square error (MSE). The results showed the

The objective of the present study is to verify the actual carious lesion depth by laser
fluorescence technique using 650 nm CW diode laser in comparison with the histopathological
investigation. Five permanent molar teeth were extracted from adult individuals for different reasons
(tooth impaction, periodontal diseases, and pulp infections); their ages were ranging from 20-25 years
old. Different carious teeth with varying clinical stages of caries progression were examined. An
experimental laser fluorescence set-up was built to perform the work regarding in vitro detection and
quantification of occlusal dental caries and the determination of its actual clinical carious lesion depth by
650 nm CW diode laser (excitat

Estimation of the tail index parameter of a one - parameter Pareto model has wide important by the researchers because it has awide application in the econometrics science and reliability theorem.

Here we introduce anew estimator of ^"generalized median" type and compare it with the methods of Moments and Maximum likelihood by using the criteria, mean square error.

 The estimator of generalized median type performing best over all.

The objective of this study is to examine the properties of Bayes estimators of the shape parameter of the Power Function Distribution (PFD-I), by using two different prior distributions for the parameter θ and different loss functions that were compared with the maximum likelihood estimators. In many practical applications, we may have two different prior information about the prior distribution for the shape parameter of the Power Function Distribution, which influences the parameter estimation. So, we used two different kinds of conjugate priors of shape parameter θ of the <

The goal of this study was to investigate the protein peroxidation role by measuring serum levels of advanced oxidation protein products (AOPP) in type 2 diabetic patients with or without retinopathy and comparing them to controls to see if circulating AOPP levels can be used as a detection biomarker for DR. And see which of the two widely used antidiabetic treatment groups had the most impact on this oxidative stress marker. The groups were divided into two subgroups: 1) 70 type 2 diabetic patients (36 male, 34 female), 35 with diabetic retinopathy (DR) and 35 with no evidence of DR, and 2) non-diabetic controls (11 male, 9 female) were chosen from Ibn AL-Haitham Hospital for Ophthalmology and a Specialized Center for Endocrinology and Dia

Changes in mechanical properties of material as a result of service in different conditions can be provided by mechanical testing to assist the estimation of current internal situation of these materials, or the degree of deterioration may exist in furnaces serviced at high temperature and exceed their design life. Because of the rarity works on austenitic stainless steel material type AISI 321H, in this work, ultimate tensile strength, yield strength, elongation, hardness, and absorbed energy by impact are evaluated based on experimental data obtained from mechanical testing. Samples of tubes are extracted from furnace belong to hydrotreaterunit, also samples from un-used tube material are used to make comparisons between these properti