Further theoretical results and a comparison between two methods for approximating eigenvalues of perturbed covariance matrices

Covariance matrices, or in general matrices of sums of squares and cross-products, are used as input in many multivariate analyses techniques. The eigenvalues of these matrices play an important role in the statistical analysis of data including estimation and hypotheses testing. It has been recognized that one or few observations can exert an undue influence on the eigenvalues of a covariance matrix. The relationship between the eigenvalues of the covariance matrix computed from all data and the eigenvalues of the perturbed covariance matrix (a covariance matrix computed after a small subset of the observations has been deleted) cannot in general be written in closed-form. Two methods for approximating the eigenvalues of a perturbed covariance matrix have been suggested by Hadi (1988) and Wang and Nyquist (1991) for the case of a perturbation by a single observation. In this paper we improve on these two methods and give some additional theoretical results that may give further insight into the problem. We also compare the two improved approximations in terms of their accuracies.     

A method for computing the autocovariance of renewal processes

In this paper we derive formulae for the autocovariance functions of renewal and renewal reward processes. The derivation is based on a Poissonization technique of a renewal process. The formulae are expressed in the form of Laplace transforms. In some cases we may invert the Laplace transforms analytically, but in general we have to invert them numerically.     

Goodness-of-Fit Tests Based on Correcting Moments of Entropy Estimators

In this article, we consider the entropy estimator introduced by Alizadeh Noughabi and Arghami (2010) and derive the nonparametric distribution function corresponding to our estimator as a piece-wise uniform distribution. We use the results to introduce goodness-of-fit tests for the normal and the exponential distributions. The critical values and powers for some alternatives are obtained by simulation. The powers of the proposed tests under various alternatives are compared with the competitors.     

A critical investigation of Industry 4.0 in manufacturing: theoretical operationalisation framework

Increasing global competition on product quality and production costs, and the need for flexibility in production petition for transformed production processes which enable high level of connectivity and integration between business processes and systems. Much of the conventional computer- integrated efforts and advanced manufacturing technologies are limited in scope and restricted to only some organisational areas. Such limited scope, which stems from limited connectivity and integration between manufacturing and enterprise systems, confines the achievement of full potential of these systems within manufacturing. Industry 4.0, characterised by computing developments, can create a platform for addressing integration challenge through enabling comprehensive connectivity. Hence, this paper, through following deductive research paradigm and using systems theory as the theoretical base, aims to investigate recent academic research and industrial reports in the area of Industry 4.0 and smart manufacturing to provide detailed insights on execution of Industry 4.0, and to propose a theoretical framework for operationalisation of Industry 4.0 in manufacturing.     

Empirical likelihood ratio-based goodness-of-fit test for the logistic distribution

The logistic distribution has been used to model growth curves in survival analysis and biological studies. In this article, we propose a goodness-of-fit test for the logistic distribution based on the empirical likelihood ratio. The test is constructed based on the methodology introduced by Vexler and Gurevich [17 A. Vexler and G. Gurevich, Empirical likelihood ratios applied to goodness-of-fit tests based on sample entropy, Comput. Stat. Data Anal. 54 (2010), pp. 531–545. doi: 10.1016/j.csda.2009.09.025[Crossref], [Web of Science ®] , [Google Scholar]]. In order to compute the test statistic, parameters of the distribution are estimated by the method of maximum likelihood. Power comparisons of the proposed test with some known competing tests are carried out via simulations. Finally, an illustrative example is presented and analyzed.     

Monitoring two-stage processes with a profile at the second stage

In the multistage processes, quality of a process or a product at each stage is related to the previous stage(s). This property is referred to as a cascade property. Sometimes, quality of a process is characterized by a profile. In this paper, we consider a two-stage process with a normal quality characteristic in the first stage and a simple linear regression profile in the second stage. Then we propose two methods to monitor quality characteristics in both stages. The performance of the proposed two methods is evaluated through a numerical example in terms of average run length criterion.     

Testing exponentiality based on Kullback—Leibler information for progressively Type II censored data

In many life-testing and reliability experiments, data are often censored in order to reduce the cost and time associated with testing and since the conventional Type-I and Type-II censoring schemes are not flexible enough, progressive censoring is developed by researchers. In this article, we develop a general goodness of fit test by using a new estimate of Kullback–Leibler information based on progressively Type-II censored data. Consistency and other properties of the proposed test are shown. Then, we use the proposed test statistic to test for exponentiality based on progressively Type-II censored data. The power values of the proposed test under different progressively Type-II censoring schemes are computed, through Monte Carlo simulations. It is observed that the proposed test is quite powerful in compared with the test proposed by Balakrishnan et al. (2007 Balakrishnan, N., Habibi Rad, A., and Arghami, N. R. (2007). Testing exponentiality based on Kullback–Leibler information with progressively type-II censored data. IEEE Transactions on Reliability 56:301–307. [Google Scholar]). Two real datasets from progressive censoring literature are finally presented for illustrative purpose.     

Accountability in a state of liminality: Iranian students’ experiences in American airports

This paper studies the lived experience of Iranian students upon arrival at American airports. By using two concepts of liminality and accountability, I examine how Iranian students walk the gauntlet of US airports, and study the influences of the treatment they receive at airports on their perceptions of the US. Empirically, I draw on 15 in-depth qualitative interviews with eight Iranian students at a Southern university in the US. The paper posits that multiple layers of liminality surface and intensify in airports as a threshold where international travelers can see both ways, behind and before them, while belonging to neither one. The requirement to be an ‘accountable other’ adds up to the contingencies of the situation. Theoretically, this paper puts the politics of mobility in the colonial context and claims that legal recognition will not result in integration when negative discourses around the civilizational other regards their mobility as a threat and challenges their social recognition.     

Preservation properties for the Laplace transform ordering of residual lives

Several preservation results for the Laplace transform ordering of residual lives (Lt−rl) are given. In particular, we show that theTt−rl-order is preserved under convolutions, mixtures and weak convergence. Some examples of interest in reliability theory are also presented.     

A sustainable supply chain network considering lot sizing with quantity discounts under disruption risks: centralized and decentralized models

This study proposes a framework for the main parties of a sustainable supply chain network considering lot-sizing impact with quantity discounts under disruption risk among the first studies. The proposed problem differs from most studies considering supplier selection and order allocation in this area. First, regarding the concept of the triple bottom line, total cost, environmental emissions, and job opportunities are considered to cover the criteria of sustainability. Second, the application of this supply chain network is transformer production. Third, applying an economic order quantity model lets our model have a smart inventory plan to control the uncertainties. Most significantly, we present both centralized and decentralized optimization models to cope with the considered problem. The proposed centralized model focuses on pricing and inventory decisions of a supply chain network with a focus on supplier selection and order allocation parts. This model is formulated by a scenario-based stochastic mixed-integer non-linear programming approach. Our second model focuses on the competition of suppliers based on the price of products with regard to sustainability. In this regard, a Stackelberg game model is developed. Based on this comparison, we can see that the sum of the costs for both levels is lower than the cost without the bi-level approach. However, the computational time for the bi-level approach is more than for the centralized model. This means that the proposed optimization model can better solve our problem to achieve a better solution than the centralized optimization model. However, obtaining this better answer also requires more processing time. To address both optimization models, a hybrid bio-inspired metaheuristic as the hybrid of imperialist competitive algorithm (ICA) and particle swarm optimization (PSO) is utilized. The proposed algorithm is compared with its individuals. All employed optimizers have been tuned by the Taguchi method and validated by an exact solver in small sizes. Numerical results show that striking similarities are observed between the results of the algorithms, but the standard deviations of PSO and ICA–PSO show better behavior. Furthermore, while PSO consumes less time among the metaheuristics, the proposed hybrid metaheuristic named ICA–PSO shows more time computations in all small instances. Finally, the provided results confirm the efficiency and the performance of the proposed framework and the proposed hybrid metaheuristic algorithm.