This paper discusses reliability R of the (2+1) Cascade model of inverse Weibull distribution. Reliability is to be found when strength-stress distributed is inverse Weibull random variables with unknown scale parameter and known shape parameter. Six estimation methods (Maximum likelihood, Moment, Least Square, Weighted Least Square, Regression and Percentile) are used to estimate reliability. There is a comparison between six different estimation methods by the simulation study by MATLAB 2016, using two statistical criteria Mean square error and Mean Absolute Percentage Error, where it is found that best estimator between the six estimators is Maximum likelihood estimation method.

In this research, we find the Bayesian formulas and the estimation of Bayesian expectation for product system of Atlas Company.  The units of the system have been examined by helping the technical staff at the company and by providing a real data the company which manufacturer the system.  This real data include the failed units for each drawn sample, which represents the total number of the manufacturer units by the company system.  We calculate the range for each estimator by using the Maximum Likelihood estimator.  We obtain that the expectation-Bayesian estimation is better than the Bayesian estimator of the different partially samples which were drawn from the product system after  it checked by the

Fifty-four Sprague-Dawley albino adult male rats were classified into three main groups each of 18 rats treated for a particular duration (1,2, and 4) weeks respectively. Each group was subdivided into three subgroups each of six rats treated as follows; group (1) serve as normal control, group (2, and 3) intra-peritoneal treated with TiO₂NPs (50,200) mg/kg respectively, body *weight of all rats was measured before and after the experiment, then rats were dissected at the end of each experiment and the weights of the thyroid was measured. The result showed a highly significant decrease (p<0.01) in thyroid gland weight, a highly significant increase (p<0.01) in body weights and TSH, while a highly significant decrease (p&

    Biomedical signal such as ECG is extremely important in the diagnosis of patients and is commonly recorded with a noise. Many different kinds of noise exist in biomedical environment such as Power Line Interference Noise (PLIN). Adaptive filtering is selected to contend with these defects, the adaptive filters can adjust the filter coefficient with the given filter order. The objectives of this paper are: first an application of the Least Mean Square (LMS) algorithm, Second is an application of the Recursive Least Square (RLS) algorithm to remove the PLIN. The LMS and RLS algorithms of the adaptive filter were proposed to adapt the filter order and the filter coefficients simultaneously, the performance of existing LMS

The primary aim of this paper, is to introduce the rough probability from topological view. We used the Gm-topological spaces which result from the digraph on the stochastic approximation spaces to upper and lower distribution functions, the upper and lower mathematical expectations, the upper and lower variances, the upper and lower standard deviation and the upper and lower r th moment. Different levels for those concepts are introduced, also we introduced some results based upon those concepts.

Maximum likelihood estimation method, uniformly minimum variance unbiased estimation method and minimum mean square error estimation, as classical estimation procedures, are frequently used for parameter estimation in statistics, which assuming the parameter is constant , while Bayes method assuming the parameter is random variable and hence the Bayes estimator is an estimator which minimize the Bayes risk for each value the random observable and for square error lose function the Bayes estimator is the posterior mean. It is well known that the Bayesian estimation is hardly used as a parameter estimation technique due to some difficulties to finding a prior distribution.

The interest of this paper is that

Objective: The aim of this study was to evaluate the effect of pumice, burning investment material
and black sand on the surface roughness of heat cure acrylic resin.
Methodology: Sixty specimens were prepared from pink heat cure acrylic resin, the specimens
where grouped into; 20 specimens which polished with pumice and water (control group); 20
specimens which polished with investment material (after burning it) and water; and 20 specimens
which polished with black sand and water. The average surface roughness of specimens after
polishing procedure had been determined by profilometer (surface roughness tester).
Results: Through the application of ANOVA and LSD tests, the result of this study showed that there
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