This study introduces a time-dependent fuzzy multi-objective reliability redundancy allocation problem (TF-MORRAP) for the n-stage (level) series–parallel system. System reliability maximization and system cost minimization according to time by optimizing the redundant components counting at every stage of the system is the main objective of this study. This optimization is done by satisfying the entropy constraints with limited redundant components at every stage and in the whole system. The reliability and cost of every component are represented as triangular fuzzy numbers (TFN) to handle the uncertainty of input information of the system. According to time, the component reliability and cost decrease by some factor of their previous existing value. This factor follows the change in the length of radius of the inverse logarithmic spiral with respect to angle which is regarded as time here. The proposed problem is analyzed by using an over-speed protection system of a gas turbine. We compare the membership values of optimal solutions obtained by using two well-known techniques namely non-dominated sorting genetic algorithm-II (NSGA-II) and a multi-objective particle swarm optimization algorithm called NF-MOPSO. Various performances of the algorithms are compared to solve the aforementioned problem by using some performance metrics. NF-MOPSO shows the high satisfaction level of objective functions and better performance than NSGA-II.

The main goal of this paper is to solve a fuzzy multi-objective reliability redundancy allocation problem (MORRAP) for xj -out-of- mj series-parallel system. We consider that system reliability and system cost are two conflicting objectives. Due to the incompleteness and uncertainty of input information, we formulate the objectives by considering the reliability and cost of each component as a triangular fuzzy number (TFN). Here, the fuzzy multi-objective optimization problem of system reliability and cost is analyzed simultaneously using our proposed fuzzy rank-based multi-objective particle swarm optimization (FRMOPSO) algorithm. Comparing the results of FRMOPSO with standard particle swarm optimization (PSO), we see that better optimum reliability and cost have been achieved in the FRMOPSO technique. To illustrate the effectiveness of our proposed technique, we consider the problem of the over-speed protection system of gas turbines containing two mutually conflicting reliability and cost objectives with entropy and several other constraints. We present graphically the effect of optimum system reliability and cost with respect to the percentage change of different parameters. We also compare the convergence rate of FRMOPSO with PSO. Our proposed algorithm shows better results.

This article proposes a modified ranking technique for generalized interval type-2 trapezoidal fuzzy numbers. For demonstrating uncertainty and managing imprecision in decision-making information, interval type-2 fuzzy sets are beneficial. The proposed ranking methodology resolves the difficulty of multi-criteria group decision-making on sustainable urban conveyance. Additionally, the proposed ranking approach considers all crucial aspects of transportation sustainability, including the effectiveness of durable transportation systems from economic, social, and ecological perspectives in multi-criteria group decision-making scenarios. The new ranking methodology yields superior outcomes for choosing sustainable urban transportation options. In the numerical part, studies compared the proposed ranking approach to other methods currently used for various MCDM techniques.

This paper proposes an artificial neural network ANN based software reliability model trained by novel particle swarm optimization PSO algorithm for enhanced forecasting of the reliability of software. The proposed ANN is developed considering the fault generation phenomenon during software testing with the fault complexity of different levels. We demonstrate the proposed model considering three types of faults residing in the software. We propose a neighborhood based fuzzy PSO algorithm for competent learning of the proposed ANN using software failure data. Fitting and prediction performances of the neighborhood fuzzy PSO based proposed neural network model are compared with the standard PSO based proposed neural network model and existing ANN based software reliability models in the literature through three real software failure data sets. We also compare the performance of the proposed PSO algorithm with the standard PSO algorithm through learning of the proposed ANN. Statistical analysis shows that the neighborhood fuzzy PSO based proposed neural network model has comparatively better fitting and predictive ability than the standard PSO based proposed neural network model and other ANN based software reliability models. Faster release of software is achievable by applying the proposed PSO based neural network model during the testing period.

In this paper, an artificial neural network (ANN)-based dynamic weighted combination model trained by novel particle swarm optimization (PSO) algorithm is proposed for software reliability prediction. Different software reliability growth models (SRGMs) are merged based on the weights derived by the learning algorithm of the proposed ANN. To avoid trapping in local minima during training of the ANN, we propose a neighborhood-based adaptive PSO (NAPSO) algorithm for learning of the proposed ANN in order to find global optimal weights. We conduct the experiments on real software failure data sets for validation of the proposed dynamic weighted combination model (PDWCM). Fitting performance and predictability of the proposed PSO-based neural network are compared with the conventional PSO-based neural network (CPSO) and existing ANN-based software reliability models. We also compare the performance of the proposed PSO algorithm with the CPSO algorithm through learning of the proposed ANN. Empirical results indicate that the proposed PSO and CPSO-based neural network present fairly accurate fitting and prediction capability than the other existing ANN-based software reliability models. Moreover, the proposed PSO-based neural network is most promising for the purpose of software fault prediction since it shows comparatively better fitting and prediction performance results than the other models.

In this paper, we propose a multi-layer feedforward artificial neural network (ANN) based logistic growth curve model (LGCM) for software reliability estimation and prediction. We develop the ANN by designing different activation functions for the hidden layer neurons of the network. We explain the ANN from the mathematical viewpoint of logistic growth curve modeling for software reliability. We also propose a neuro-genetic approach for the ANN based LGCM by optimizing the weights of the network using proposed genetic algorithm (GA). We first train the ANN using back-propagation algorithm (BPA) to predict software reliability. After that, we use the proposed GA to train the ANN by globally optimizing the weights of the network. The proposed ANN based LGCM is compared with the traditional Non-homogeneous Poisson process (NHPP) based software reliability growth models (SRGMs) and ANN based software reliability models. We present the comparison between the two training algorithms when they are applied to train the proposed ANN to predict software reliability. The applicability of the different approaches is explained through three real software failure data sets. Experimental results demonstrate that the proposed ANN based LGCM has better fitting and predictive capability than the other NHPP and ANN based software reliability models. It is also noted that when the proposed GA is employed as the learning algorithm to the ANN, the proposed ANN based LGCM gives more fitting and prediction accuracy i.e. the proposed neuro-genetic approach to the LGCM provides utmost predictive validity. Proposed model can be applied during software testing time to get better software reliability estimation and prediction than the other traditional NHPP and ANN based software reliability models.

Traditional parametric software reliability growth models (SRGMs) are based on some assumptions or distributions and none such single model can produce accurate prediction results in all circumstances. Non-parametric models like the artificial neural network (ANN) based models can predict software reliability based on only fault history data without any assumptions. In this paper, initially we propose a robust feedforward neural network (FFNN) based dynamic weighted combination model (PFFNNDWCM) for software reliability prediction. Four well-known traditional SRGMs are combined based on the dynamically evaluated weights determined by the learning algorithm of the proposed FFNN. Based on this proposed FFNN architecture, we also propose a robust recurrent neural network (RNN) based dynamic weighted combination model (PRNNDWCM) to predict the software reliability more justifiably. A real-coded genetic algorithm (GA) is proposed to train the ANNs. Predictability of the proposed models are compared with the existing ANN based software reliability models through three real software failure data sets. We also compare the performances of the proposed models with the models that can be developed by combining three or two of the four SRGMs. Comparative studies demonstrate that the PFFNNDWCM and PRNNDWCM present fairly accurate fitting and predictive capability than the other existing ANN based models. Numerical and graphical explanations show that PRNNDWCM is promising for software reliability prediction since its fitting and prediction error is much less relative to the PFFNNDWCM. © 2014 Elsevier B.V.

In this paper, we propose a non-homogeneous Poisson process (NHPP) based software reliability growth model (SRGM) in the presence of modified imperfect debugging and fault generation phenomenon. The testing team may not be able to remove a fault perfectly on observation of a failure due to the complexity of software systems and incomplete understanding of software, and the original fault may remain, or get replaced by another fault causing error generation. We have proposed an exponentially increasing fault content function and constant fault detection rate. The total fault content of the software for our proposed model increases rapidly at the beginning of the testing process. It grows gradually at the end of the testing process because of increasing efficiency of the testing team with testing time. We use the maximum likelihood estimation method to estimate the unknown parameters of the proposed model. The applicability of our proposed model and comparisons with established models in terms of goodness of fit and predictive validity have been presented using five known software failure data sets. Experimental results show that the proposed model gives a better fit to the real failure data sets and predicts the future behavior of software development more accurately than the traditional SRGMs. © 2014 World Scientific Publishing Company.

This research paper presents a multi-objective reliability redundancy allocation problem for optimum system reliability and system cost with limitation on entropy of the system which is very essential for effective sustainability. Both crisp and interval-valued system parameters are considered for better realization of the model in more realistic sense. We propose that the system cost of the redundancy allocation problem depends on reliability of the components. A subpopulation and entropy based region reducing genetic algorithm (GA) with Laplace crossover and power mutation is proposed to determine the optimum number of redundant components at each stage of the system. The approach is demonstrated through the case study of a break lining manufacturing plant. A comprehensive study is conducted for comparing the performance of the proposed GA with the single-population based standard GA by evaluating the optimum system reliability and system cost with the optimum number of redundant components. Set of numerical examples are provided to illustrate the effectiveness of the redundancy allocation model based on the proposed optimization technique. We present a brief discussion on change of the system using graphical phenomenon due to the changes of parameters of the system. Comparative performance studies of the proposed GA with the standard GA demonstrate that the proposed GA is promising to solve the reliability redundancy optimization problem providing better optimum system reliability. © 2014 Elsevier Ltd. All rights reserved.

In this paper, we propose a non-homogeneous Poisson process (NHPP) based S-shaped software reliability growth model (SRGM) in presence of imperfect debugging with a new exponentially increasing fault content function and S-shaped fault detection rate. We develop the fault content function considering learning capability of testing team during software development process. Fault content increases rapidly at the beginning of testing process while it grows gradually at the end of testing process due to increasing efficiency of testing team with testing time. We use maximum likelihood estimation (MLE) method to estimate model parameters. Applicability of the proposed model has been presented by comparing with established models in terms of goodness of fit and predictive validity using two software failure data sets. Experimental results show that the proposed model gives better fit to real failure data sets and predicts future failure behaviour of software development accurately than established models. Copyright © 2013 Inderscience Enterprises Ltd.