Reliability modeling and analysis of mixture of exponential distributions using artificial neural network

Abstract

In recent years, statisticians have become more and more interested in the study of mixture models, especially in the last decade, without adequately considering the difficulty of modeling the reliability measures of mixture models using artificial neural networks. In this study, in which artificial neural networks and mixed model reliability criteria are analyzed, various reliability parameters are calculated considering different scenarios. In order to estimate the obtained numerical reliability parameters, a multilayer artificial neural network model has been developed. Seven different reliability parameter values have been obtained from the artificial neural network model designed with four input parameters. The prediction values obtained from the artificial neural network model developed with five neurons in the hidden layer have been compared with numerical data, and the performance of the model has been analyzed comprehensively. The mean squared error (MSE) value for the network model has been calculated as 1.98E‐08 and the R value as 0.99991. The results clearly revealed that the artificial neural network model developed using data from the appropriate statistical model is an excellent tool that can be used to estimate reliability measures.

Comparative study of artificial neural network versus parametric method in COVID-19 data analysis

“…Data optimization and suitable grouping set employed in the progression of ANN models is one of the hyperparameters which directly affects prediction behavior of the model [53] . 70% of the data employed in the MLP network designed with a total of 59 datasets are grouped for training model, 15% for the confirmation phase and 15% for the testing phase [54] , [55] , [56] . In the hidden and output layers of the neural network, Tan-Sig and Purelin transfer functions are utilized respectively.…”

Reliability Analysis Based on Mixture of Lindley Distributions with Artificial Neural Network

“…Mean squared error (MSE), coefficient of determination (R) and margin of deviation (MoD) values were used for performance analysis. The formulas used in the calculation of the performance parameters are given below [52][53][54][55][56]…”

“…Mean squared error (MSE), coefficient of determination (R) and margin of deviation (MoD) values were used for performance analysis. The formulas used in the calculation of the performance parameters are given below [ 52–56 ] $$\begin{equation} \text{MSE}=\frac{1}{N}\sum _{i=1}^{N}{\left(Z_{\exp {\left(i\right)} }-Z_{\text{ANN}{\left(i\right)} }\right)} ^{2} \end{equation}$$ $$\begin{equation} R=\sqrt {1-\frac{\sum _{i=1}^{N}{\left(Z_{\exp {\left(i\right)} }-Z_{\text{ANN}{\left(i\right)} }\right)} ^{2}}{\sum _{i=1}^{N}{\left(Z_{\exp {\left(i\right)} }\right)} ^{2}}} \end{equation}$$ $$\begin{equation} \text{MoD}{\left(\%\right)} ={\left[ \frac{Z_{\exp }-Z_{\text{ANN}}}{Z_{\exp }}\right]} \times 100 \end{equation}$$…”

Increasing the Efficiency of a Control System for Detecting the Type and Amount of Oil Product Passing through Pipelines Based on Gamma-Ray Attenuation, Time Domain Feature Extraction, and Artificial Neural Networks

“…To increase productivity and increase speed in neural network training, available data should be optimized. There are various optimization methods that can be used according to the type and nature of available data [ 49 , 50 , 51 , 52 , 53 ]. In this research, in order to optimize the data, all the input and output data were transferred to a range between 0 and 1, and after training the network, the output data were returned to their original state.…”