The aim of this paper is to estimate a single reliability system (R = P, Z > W) with a strength Z subjected to a stress W in a stress-strength model that follows a power Rayleigh distribution. It proposes, generates and examines eight methods and techniques for estimating distribution parameters and reliability functions. These methods are the maximum likelihood estimation(MLE), the exact moment estimation (EMME), the percentile estimation (PE), the least-squares estimation (LSE), the weighted least squares estimation (WLSE) and three shrinkage estimation methods (sh1) (sh2) (sh3). We also use the mean square error (MSE) Bias and the mean absolute percentage error (MAPE) to compare the estimation methods. Both theoretical c

In this paper, we present a comparison of double informative priors which are assumed for the parameter of inverted exponential distribution.To estimate the parameter of inverted exponential distribution by using Bayes estimation ,will be  used two different kind of information in the Bayes estimation; two different priors have been selected for the parameter of inverted exponential distribution. Also assumed Chi-squared - Gamma distribution, Chi-squared - Erlang distribution, and- Gamma- Erlang distribution as double priors. The results are the derivations of these estimators under the squared error loss function with three different double priors.

Additionally Maximum likelihood estimation method

In this paper, two parameters for the Exponential distribution were estimated using the
Bayesian estimation method under three different loss functions: the Squared error loss function,
the Precautionary loss function, and the Entropy loss function. The Exponential distribution prior
and Gamma distribution have been assumed as the priors of the scale γ and location δ parameters
respectively. In Bayesian estimation, Maximum likelihood estimators have been used as the initial
estimators, and the Tierney-Kadane approximation has been used effectively. Based on the MonteCarlo
simulation method, those estimators were compared depending on the mean squared errors (MSEs).The results showed that the Bayesian esti

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

The question of estimation took a great interest in some engineering, statistical applications, various applied, human sciences, the methods provided by it helped to identify and accurately the many random processes.

In this paper, methods were used through which the reliability function, risk function, and estimation of the distribution parameters were used, and the methods are (Moment Method, Maximum Likelihood Method), where an experimental study was conducted using a simulation method for the purpose of comparing the methods to show which of these methods are competent in practical application This is based on the observations generated from the Rayleigh logarithmic distribution (RL) with sample sizes

This deals with estimation of Reliability function and one shape parameter (?) of two- parameters Burr – XII , when ?(shape parameter is known) (?=0.5,1,1.5) and also the initial values of (?=1), while different sample shze n= 10, 20, 30, 50) bare used. The results depend on empirical study through simulation experiments are applied to compare the four methods of estimation, as well as computing the reliability function . The results of Mean square error indicates that Jacknif estimator is better than other three estimators , for all sample size and parameter values

The m-consecutive-k-out-of-n: F linear and circular system consists of n sequentially connected components; the components are ordered on a line or a circle; it fails if there are at least m non-overlapping runs of consecutive-k failed components. This paper proposes the reliability and failure probability functions for both linearly and circularly m-consecutive-k-out-of-n: F systems. More precisely, the failure states of the system components are separated into two collections (the working and the failure collections); where each one is defined as a collection of finite mutual disjoint classes of the system states. Illustrative example is provided.

The two parameters of Exponential-Rayleigh distribution were estimated using the maximum likelihood estimation method (MLE) for progressively censoring data. To find estimated values for these two scale parameters using real data for COVID-19 which was taken from the Iraqi Ministry of Health and Environment, AL-Karkh General Hospital. Then the Chi-square test was utilized to determine if the sample (data) corresponded with the Exponential-Rayleigh distribution (ER). Employing the nonlinear membership function (s-function) to find fuzzy numbers for these parameters estimators. Then utilizing the ranking function transforms the fuzzy numbers into crisp numbers. Finally, using mean square error (MSE) to compare the outcomes of the survival

This paper is interested in comparing the performance of the traditional methods to estimate parameter of exponential distribution (Maximum Likelihood Estimator, Uniformly Minimum Variance Unbiased Estimator) and the Bayes Estimator in the case of data to meet the requirement of exponential distribution and in the case away from the distribution due to the presence of outliers (contaminated values). Through the employment of simulation (Monte Carlo method) and the adoption of the mean square error (MSE) as criterion of statistical comparison between the performance of the three estimators for different sample sizes ranged between small, medium and large        (n=5,10,25,50,100) and different cases (wit

Exponential distribution is one of most common distributions in studies and scientific researches with wide application in the fields of reliability, engineering and in analyzing survival function therefore the researcher has carried on extended studies in the characteristics of this distribution.

In this research, estimation of survival function for truncated exponential distribution in the maximum likelihood  methods and Bayes first and second method, least square method and Jackknife dependent in the first place on the maximum likelihood method, then on Bayes first method then comparing then using simulation, thus to accomplish this task, different size samples have been adopted by the searcher us