Comparison of Some of Estimation methods of Stress-Strength Model: R = P(Y < X < Z)

Abstract

In this study, the stress-strength model R = P(Y &lt; X &lt; Z) is discussed as an important parts of reliability system by assuming that the random variables follow Invers Rayleigh Distribution. Some traditional estimation methods are used to estimate the parameters namely; Maximum Likelihood, Moment method, and Uniformly Minimum Variance Unbiased estimator and Shrinkage estimator using three types of shrinkage weight factors. As well as, Monte Carlo simulation are used to compare the estimation methods based on mean squared error criteria.

Comparison Various Estimation Methods for R = P (Y1 < X < Y2) Utilizing Restricted Generalized Weibull Distribution

“…The key idea is that it is possible to reduce the amount of squared errors between the imposed simple values and estimated value; [6].…”

“…In this context, the statistical implications were calculated to compare the performance of the offered estimators. Following is how a Monte Carlo simulation was employed in this situation; [6,16,17].…”

“…When the stresses Y 1 and Y 2 and the strength X have inverse Rayleigh distribution, Raheem, S.H., Kalaf, B.A., and Salman, A.N. in 2021, compare the estimation of R = (Y 1 < X < Y 2 ); [6].…”

Enhanced Support Vector Machine Methods Using Stochastic Gradient Descent and Its Application to Heart Disease Dataset

“…Eq (1) is linear in terms of the new space that ɸ (x) maps the data to non-linear in the space, see Figure 3. The most common kernels are: linear, polynomial, sigmoid or Multi-Layer Perceptron (MLP) and Gaussian or Radial Basis Function (RPF) [11][12][13]. Their expressions are as follows: we define the kernel function as K(𝑥 𝑖 , 𝑥 𝑗 ) =< ɸ(𝑥 𝑖 ), ɸ(𝑥 𝑗 ) >= ɸ(𝑥 𝑖 ) 𝑇 ɸ(𝑥 𝑗 ) where ɸ is a mapping from input space to output space, see Figure 4.…”

Estimation of a Parallel Stress-strength Model Based on the Inverse Kumaraswamy Distribution

“…It is found to be helpful in situations where the reliability of a component or system is defined by the probability that a random variable of strength is more significant than a random variable (stress). At the same time, it makes intuitive sense that a component is deemed to have failed when its strength is lower than the applied stress [2][3]. Several researchers studied various lifetime distributions of the parallel system reliability in stress-strength model.…”