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The purpose of this paper is to find the proper statistical distribution function, which can cover the failure time of a single machine or a group of machines. To this end, an innovative program is written in an Excel software, capable of assessing at least six statistical distribution functions. This research study intends to show the advantages of applying statistical distribution functions in an integrated model format to create or increase productive reliability machines. Productive reliability is a simultaneous combination of efficiency and effectiveness in reliability.

The method of theoretical research methodology comprises data collection tools, reference books and articles in addition to exploiting written reports of the Iranian Center for Defence’s Standards. The practical research method includes deploying and assessing the proposed model for a selected machine (in this case a computerized numerical control machine).

A comprehensive program in an Excel software having the capability of assessing at least six statistical distribution functions was developed to find the most efficient option for covering the failure times of each machine in the shortest time with the highest precision. This is regarded as the most important achievement of the present study. Furthermore, the advantages of applying the developed model are discussed and a large group of which have direct influences on the productivity of equipment reliability.

The originality of the research was ascertained by managers and experts working in maintenance issues at the different levels of the Defense Industries Organization.

Constructing and evaluating behavioral science models is a complex process. Decisions must be made about which variables to include, which variables are related to each other, the functional forms of the relationships, and so on. The last 10 years have seen a substantial extension of the range of statistical tools available for use in the construction process. The progress in tool development has been accompanied by the publication of handbooks that introduce the methods in general terms (Arminger et al., 1995; Tinsley & Brown, 2000a). Each chapter in these handbooks cites a wide range of books and articles on specific analysis topics.

Solar power forecasting will have a significant impact on the future of large-scale renewable energy plants. Predicting photovoltaic power generation depends heavily on climate conditions, which fluctuate over time. In this research, we propose a hybrid model that combines machine-learning methods with Theta statistical method for more accurate prediction of future solar power generation from renewable energy plants. The machine learning models include long short-term memory (LSTM), gate recurrent unit (GRU), AutoEncoder LSTM (Auto-LSTM) and a newly proposed Auto-GRU. To enhance the accuracy of the proposed Machine learning and Statistical Hybrid Model (MLSHM), we employ two diversity techniques, i.e. structural diversity and data diversity. To combine the prediction of the ensemble members in the proposed MLSHM, we exploit four combining methods: simple averaging approach, weighted averaging using linear approach and using non-linear approach, and combination through variance using inverse approach. The proposed MLSHM scheme was validated on two real-time series datasets, that sre Shagaya in Kuwait and Cocoa in the USA. The experiments show that the proposed MLSHM, using all the combination methods, achieved higher accuracy compared to the prediction of the traditional individual models. Results demonstrate that a hybrid model combining machine-learning methods with statistical method outperformed a hybrid model that only combines machine-learning models without statistical method.

Gender inequality in paid work persists, in the form of a gender wage gap, occupational sex segregation and a “glass ceiling” for women, despite substantial institutional change in recent decades. Two classes of explanations that have been offered as partial explanations of persistent gender inequality include economic theories of statistical discrimination and social psychological theories of status-based discrimination. Despite the fact that the two theories offer explanations for the same phenomena, little effort has been made to compare them, and practitioners of one theory are often unfamiliar with the other. In this article, we assess both theories. We argue that the principal difference between the two theories lies in the mechanism by which discrimination takes place: discrimination in statistical models derives from an informational bias, while discrimination in status models derives from a cognitive bias. We also consider empirical assessments of both explanations, and find that while research has generally been more supportive of status theories than statistical theories, statistical theories have been more readily evoked as explanations for gender inequalities in the paid labor market. We argue that status theories could be more readily applied to understanding gender inequality by adopting the broader conception of performance favored by statistical discrimination theories. The goal is to build on the strong empirical base of status characteristic theory, but draw on statistical discrimination theories to extend its ability to explain macro level gender inequalities.

For numerical treatment of resin‐containing systems and forecasting of their properties, certain models of branching are needed. In this review, existing theoretical models of systems containing branched structures (polymers, aggregates, etc.) are analyzed and compared. The criteria of selection of the optimal theoretical model comprise chemical and physical problems available for solution, simplicity of such solution, connection between theoretically forecasted and experimental results, and the time needed for computing. It is concluded that, according to these criteria, the optimal (between existing models) is the statistical polymer method.

The purpose of this paper is to establish three modeling methods (physical model, statistical model, and artificial neural network (ANN) model) and use it to predict the fiber diameter of spunbonding nonwovens from the process parameters.

The results show the physical model is based on the inherent physical principles, it can yield reasonably good prediction results and provide insight into the relationship between process parameters and fiber diameter.

By analyzing the results of the physical model, the effects of process parameters on fiber diameter can be predicted. The ANN model has good approximation capability and fast convergence rate, it can provide quantitative predictions of fiber diameter and yield more accurate and stable predictions than the statistical model.

The effects of process parameters on fiber diameter are also determined by the ANN model. Excellent agreement is obtained between these two modeling methods.

The intent of this paper is to discuss the use of statistical mathematics in property valuation and the wider question concerning the role of mathematics in the field of economics.

This paper reviews the evolution of the application of mathematics, including statistics in economics and drawing conclusions about applicability and effectiveness of quantitative modelling in property valuation.

This paper discusses the future use of statistical models in valuation and the need to recognise the relationships between market participants and the increasingly complex environment, and their impact on value. This would suggest adopting modelling techniques from behavioural economics.

This paper highlights the difference between quantitative and qualitative models and discusses the role that each can play in property valuation.

This paper provides insights on the development of statistical modelling and discusses the application of the same in property valuation.

The purpose of this paper is to investigate the economic‐statistical design of EWMA charts with variable sampling intervals (VSIs) under non‐normality to reduce the process production cycle cost and improve the statistical performance of control charts. The objective is to minimize the cost function by adjusting the control chart parameters which suffice for the statistical restriction.

First, using the Burr distribution to approximate various non‐normal distributions, the economic‐statistical model of the VSI EWMA charts under non‐normality can be developed. Further, the genetic algorithms will be used to search for the optimal values of parameters of the VSI EWMA charts under non‐normality. Finally, a sensitivity analysis is carried out to investigate the effect of model parameters and statistical restriction on the solution of the economic‐statistical design.

The result of sensitivity analysis shows that a large lower bound of average time to signal when the process is in control increases the control limit coefficient, no model parameter significantly affects the short sampling intervals, and so on.

The economic‐statistical design method proposed in this paper can improve the statistical performance of economic design of control charts and the general idea can be applied to other VSI control charts.

Driven by the development in sensing techniques and information and communications technology, and their applications in the manufacturing system, data-driven quality control methods play an essential role in the quality improvement of assembly products. This paper aims to review the development of data-driven modeling methods for process monitoring and fault diagnosis in multi-station assembly systems. Furthermore, the authors discuss the applications of the methods proposed and present suggestions for future studies in data mining for quality control in product assembly.

This paper provides an outline of data-driven process monitoring and fault diagnosis methods for reduction in variation. The development of statistical process monitoring techniques and diagnosis methods, such as pattern matching, estimation-based analysis and artificial intelligence-based diagnostics, is introduced.

A classification structure for data-driven process control techniques and the limitations of their applications in multi-station assembly processes are discussed. From the perspective of the engineering requirements of real, dynamic, nonlinear and uncertain assembly systems, future trends in sensing system location, data mining and data fusion techniques for variation reduction are suggested.

This paper reveals the development of process monitoring and fault diagnosis techniques, and their applications in variation reduction in multi-station assembly.

The purpose of this paper considers optimal input signal design for flutter model parameters identification, as input signal is the first step during the whole identification process. According to the constructed flutter stochastic model with observed noises, separable least squares identification and set membership identification are proposed to identify those unknown model parameters for statistical noise and unknown but bounded noise, respectively. The common trace operation with respect to the asymptotic variance matrix is minimized to solve the power spectral for the optimal input signal in the framework of statistical noise. Moreover, for the unknown bout bounded noise, the radius of information, corresponding to the established parameter uncertainty interval, is minimized to give the optimal input signal.

First, model identification for aircraft flutter is reviewed as one problem of parameter identification and this aircraft flutter model corresponds to one stochastic model, whose input signal and output are corrupted by external noises. Second, for aircraft flutter statistical model with statistical noise, separable least squares identification is proposed to identify the unknown model parameters, then the optimal input signal is designed to satisfy one given performance function. Third, for aircraft flutter model with unknown but bounded noise, set membership identification is proposed to solve the parameter set for each unknown model parameter. Then, the optimal input signal is designed by applying the idea of the radius of information with unknown but bounded noise.

This aircraft flutter model corresponds to one stochastic model, whose input signal and output are corrupted by external noises. Then identification strategy and optimal input signal design are studied for aircraft flutter model parameter identification with statistical noise and unknown but bounded noise, respectively.

To the best knowledge of the authors, this problem of the model parameter identification for aircraft flutter was proposed by their previous work, and they proposed many identification strategies to identify these model parameters. This paper proposes two novel identification strategies and opens a new subject about optimal input signal design for statistical noise and unknown noise, respectively.