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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.

Haitun has recently shown that empirical distributions are of two types—‘Gaussian’ and ‘Zipfian’—characterized by the presence or absence of moments. Gaussian‐type distributions arise only in physical contexts: Zipfian only in social contexts. As the whole of modern statistical theory is based on Gaussian distributions, Haitun thus shows that its application to social statistics, including cognitive statistics, is ‘inadmissible’. A new statistical theory based on ‘Zipfian’ distributions is therefore needed for the social sciences. Laplace's notorious ‘law of succession’, which has evaded derivation by classical probability theory, is shown to be the ‘Zipfian’ frequency analogue of the Bradford law. It is argued that these two laws together provide the most convenient analytical instruments for the exploration of social science data. Some implications of these findings for the quantitative analysis of information systems are briefly discussed.

That part of human behaviour which is not rigidly determined by external constraints can be considered as a sequence of more or less free choices. One can talk of a choice only if it is one of several alternatives, and of a free choice only in so far as it is not determined by conditions over which the individuals have no control. Moreover, we recognise an alternative only if it is actually elected by at least a fraction of a population. This leads to the concept of statistical freedom. Postulates are formulated which must be satisfied by any numerical measures of statistical freedom, and certain mathematical expressions are proposed which are shown to conform to these postulates. Statistical freedom has two fundamental features, which appear as factors in its numerical measure: diversity and independence. The measures of diversity and independence are derived in the first place front a certain model of society, but once they are obtained, the model is discarded, and the statistical coefficients are justified by their mathematical properties. Safeguards against arbitrary manipulation of statistical material are discussed, and the potential use of the new measures is illustrated by application to the problem of choice of profession.

The purpose of this paper is to indicate trade characteristics of Foreign direct investment (FDI) inflows in China and examine the dynamic interaction between FDI inflows and China’s international trade through empirical analysis.

At first, this paper builds the probability distribution model (Poisson and negative binomial (NB)) to capture the characteristics of spatial distribution of all kinds of FDI firms in Chinese cities and provinces based on count data, so as to indicate the potentials for further introducing FDI inflows in China; Second, this paper investigates the effects of trade on FDI firms inflows based on probability regress model (Binary Logit, Tobit, NB, Poisson, zero inflated negative binomial) and shows how international trade accelerates the different kinds of FDI firms to agglomerate in Eastern, Middle and Western region by the endowments of factors; third, this paper empirically examines the magnitude and characteristics of trade effects generated by FDI inflows by building dynamic panel model based on continuous data.

First, statistical tests of probability distribution model based on count data show that there are characteristics of spatial agglomeration of FDI firms such as manufacture firm, R & D firm, managing and marketing firm and total sectors, which obey NB distribution as whole; Second, this study indicate that FDI inflows have strong positive effects on the international trade in China’s provinces and on China’s regional trade, and that most of foreign firms in China are export oriented being strongly characterized as labor-intensive industries, especially, contributions of FDI to imports are greater than the contributions of FDI to exports in China’s Middle and Western trade, and the growth of FDI trade in China’s trade volume has been strong over the past years; third, the empirical results of models based on count data and continuous data indicate that FDI inflows have significantly positive relationship with international trade, that is, the relationship between FDI and international trade in the case of China is the characteristics with complement and imports substituting relationship.

Because of mixed data set for FDI inflows of processing and assembling trade and production-oriented FDI, efficiency-seeking and knowledge or technology – intensive FDI inflows in the past 36 years, the paper only investigate characteristics of FDI inflows in China before the turning point of financial crisis, but it is important for capturing the whole picture of trade characteristics of FDI inflows in China.

The derived quantitative results imply that there are still greater potentials for further introducing FDI inflows in China, and decision-maker should make policy of introducing FDI inflows which are favorable to supporting innovative activities and economic agglomeration, and preferably encourage efficiency-seeking and export-oriented FDI inflows so as enhance quality and efficiency of economic growth, which are also helpful to accelerate upgrade of Chinese industry and gradually shorten gap of growth among Eastern, Middle and Western region.

FDI inflows in China not only stimulate the remarkable growth of bilateral trade between host country and home country, but also promote the growth of international trade between China and the rest of the world. Thus, policies of bilateral or multilateral free-trade and investment area should be encouraged, which will be also favorable to promote the growth and welfare in all the regions.

This paper demonstrates that spatial distributions of FDI firms in Chinese cities and provinces obey NB probability distribution pattern, and puts forward the methodology of model based on count data and continuous data. Besides, this paper quantitatively indicates trade characteristics of FDI inflows in China as well as the dynamic interaction between FDI inflows and China’s international trade.

Undertakes a comparative study of the statistical capability of three spreadsheets which are commonly used in the business sector. The spreadsheets considered are Lotus 1‐2‐3, Microsoft Excel and Quattro Pro. Considers five areas of statistical analysis regularly used by business decision makers (rather than specialist personnel). In order to obtain an objective measure of the statistical provision of each spreadsheet, comparison has also been made with dedicated statistical software regularly used by business decision makers, namely MINITAB. By making this comparison, argues that the spreadsheet is not only a tool for analysis, but also for presentation. Moreover, considers that two spreadsheets in particular, namely Excel and Quattro Pro, offer a user‐friendly statistical provision which should be sufficient for most business decision makers.

The purpose of this paper is to investigate hazards for minor users while they are exposed to social networks. In particular, it provides the statistical relationship of these hazards with the exposure time as well as the amount of published personal information.

An experiment was conducted that has revealed a huge number of personal information exposed by users of social network applications. Moreover, a significant amount of suspicious activity against minors has been recorded. Experimental data led to the hypothesis that online hazards can be modeled with known statistical distributions. In order to examine this hypothesis, survival analysis techniques, which involve the estimation of certain functions that reflect the relation of a disastrous event with time, were applied.

The results show that the incoming hazards for minor female profiles follow the Logistic distribution, while the corresponding hazards for minor male profiles follow the Normal distribution.

The findings of this work are crucial for developing an effective system for automated grooming recognition in real time by optimizing the detection threshold as a function of time. Thus, the threshold sensitivity can be appropriately adjusted such that lower frequencies of occurrence lead to lower threshold sensitivities, and higher frequencies of occurrence lead to higher threshold sensitivities.

Analytic and computational techniques for evaluating reliability functions and data are described. Estimation and goodness‐of‐fit tests using graphical methods and interactive procedures are presented, based on several alternative distributions.

In acceptance sampling, the hypergeometric operating characteristic (OC) function (so called type-A OC) is used to be approximated by the binomial or Poisson OC function, which actually reduce computational effort, but do not provide suffcient approximation results. The purpose of this paper is to examine binomial- and Poisson-type approximations to the hypergeometric distribution, in order to find a simple but accurate approximation that can be successfully applied in acceptance sampling.

The authors present a new binomial-type approximation for the type-A OC function, and derive its properties. Further, the authors compare this approximation via an extensive numerical study with other common approximations in terms of variation distance and relative efficiency under various conditions on the parameters including limiting cases.

The introduced approximation generates best numerical results over a wide range of parameter values, and ensures arithmetic simplicity of the binomial distribution and high accuracy to meet requirements regarding acceptance sampling problems. Additionally, it can considerably reduce the computational effort in relation to the type-A OC function and therefore is strongly recommended for calculating sampling plans.

The newly presented approximation provides a remarkably close fit to the type-A OC function, is discrete and needs no correction for continuity, and is skewed in the same direction by roughly the same amount as the exact OC. Due to less factorials, this OC in general involves lower powers than the type-A OC function. Moreover, the binomial-type approximation is easy to fit to the conventional statistical computing packages.

Bamboo scrimber is a new natural fiber-reinforced composite material in the modern industry. In this paper, the strength characteristics of this material were chosen as the object of study.

First, axial tensile fracture experiments were conducted on different test specimens to determine the corresponding strength data. Then three commonly used distribution models were applied to analyze the relationship between the strength and survival rate.

The results show that the tensile data demonstrate obvious dispersion. In addition, the three-parameter Weibull model fits the data best and may be used as the fundamental model for future analysis.

Special statistical analysis research of the bamboo material experimental results has rarely been discovered. This paper provides a solid foundation for better understanding the mechanism of the bamboo scrimber strength phenomenon.

The purpose of this paper is to compare four life data models, namely the exponential and the Weibull models, and their corresponding generalized versions, q-exponential and q-Weibull models, by means of one practical application.

Application of the models to a practical example (a welding station), with estimation of parameters by the use of the least squares method, and the Akaike Information Criterion (AIC).

The data of the example considered in this paper is divided into three regimes, decreasing, constant and increasing failure rate, and the q-Weibull model describes the bathtub curve displayed by the data with a single set of parameters.

The simplicity and flexibility of the q-Weibull model may be very useful for practitioners of reliability analysis, and its benefits surpasses the inconvenience of the additional parameter, as AIC shows.

The q-Weibull model is compared in detail with other three models, through the analysis of one example that clearly exhibits a bathtub curve, and it is shown that it can describe the whole time range with a single set of parameters.