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The authors’ conclusions are based on mathematical derivations that are supported by computer simulations and three worked examples in applications of economics and finance. Finally, the authors provide a link to a computer program so that researchers can perform the analyses easily.

Based on a parameter estimation goal, the present work is concerned with determining the minimum sample size researchers should collect so their sample medians can be trusted as good estimates of corresponding population medians. The authors derive two solutions, using a normal approximation and an exact method.

The exact method provides more accurate answers than the normal approximation method. The authors show that the minimum sample size necessary for estimating the median using the exact method is substantially smaller than that using the normal approximation method. Therefore, researchers can use the exact method to enjoy a sample size savings.

In this paper, the a priori procedure is extended for estimating the population median under the skew normal settings. The mathematical derivation and with computer simulations of the exact method by using sample median to estimate the population median is new and a link to a free and user-friendly computer program is provided so researchers can make their own calculations.

The purpose of this paper is to construct a statistical hypotheses test for process capability indices and compare the pairs of them with a fixed sample size.

Since the sampling distribution of the estimators of pairs of two process capability indices (PCIs) is very complex, an exact statistical hypothesis test for them cannot be constructed. Therefore, the authors have proposed a bootstrap method to construct the hypothesis test for them on the basis of p-value.

The authors have shown that by increasing n, the bootstrap method has better output relative to other methods and it can be easily implemented. The authors have also demonstrated that sometimes an exact hypotheses test cannot be constructed and need some assumptions.

In the present paper, several methods to test of hypotheses about the difference between two process capability indices have been compared.

Purpose — Analysis of nonprismatic members has received a great deal attention from designers and engineers due to their ability in satisfaction of architectural and aesthetic necessities. Using these structural members in complex structures such as aircrafts, turbine blades and space vehicles, exact static and dynamic analyses of these members become more significant. Based on structural/mechanical principles, the purpose of this paper is to present a new method to evaluate exact structural matrices for nonprismatic Euler‐Bernoulli beam elements. Design/methodology/approach — Through introducing the concept of basic displacement functions (BDFs), it is shown that exact shape functions are derived in terms of BDFs. BDFs and their derivatives have structural interpretations; therefore, they are obtained via application of flexibility method. Unlike the conventional methods, which are almost categorized as displacement‐based methods, the flexibility basis of the method ensures the true satisfaction of equilibrium equations at any interior point of the element. Findings — The exact shape functions and consequently structural matrices are derived for general nonprismatic beam elements. Numerical examples are carried out to determine static deflection and natural frequencies, and the results are highly competent with the other methods in literature. Research limitations/implications — The method can be extended to structural analysis of curved beams, plates and shells as well. Moreover, it is possible to derive exact dynamic shape functions via BDFs by solving the governing equation for transverse vibration of beams. Theoretically, the method faces limitation in analysis of nonprismatic beams that converge to a point where cross‐sectional area and moment of inertia are equal to zero. Practical implications — The development of this idea, i.e. BDFs seems to lead to promotive novel approaches for structural analysis and could be a breaking point for developing new elements for plates and shells as it was shown for beam elements. Originality/value — The paper's introduction of special functions, namely BDFs and their application, in both static and dynamic analyses of structures, could be a breaking point in analysis procedures.

The purpose of this paper is to develop a novel model of a call center that must treat calls with distinctly different service depending on whether they orginate from VIP or regular customers. VIP calls must be responded to immediately but regular calls can be routed to a retrial queue if the operators are busy.

This study’s proposed model can easily reveal the optimal arrangement of operators while minimizing computational time and without losing any precision of the performance measure when dealing with a call center with more operators.

Based on the results of the comparison between the exact method and the proposed approximation method, the approach shows that the larger the number of operators or inbound calls, the smaller the error between the two methods.

This investigation presents a computational method and management cost function intended to identify the optimal number of operators for a call center. Because of computational limitations, many operators could not be easily analyzed using the exact method. For the manager of a call center, the sooner the optimal solution is found, the faster business strategies are deployed. This study develops an approximation method and compares it with the exact method.

An eigenvalue method is presented for solving the transient heat conduction problem with time‐dependent or time‐independent boundary conditions. The spatial domain is divided into finite elements and at each finite element node, a closed‐form expression for the temperature as a function of time can be obtained. Three test problems which have exact solutions were solved in order to examine the merits of the eigenvalue method. It was found that this method yields accurate results even with a coarse mesh. It provides exact solution in the time domain and therefore has none of the time‐step restrictions of the conventional numerical techniques. The temperature field at any given time can be obtained directly from the initial condition and no time‐marching is necessary. For problems where the steady‐state solution is known, only a few dominant eigenvalues and their corresponding eigenvectors need to be computed. These features lead to great savings in computation time, especially for problems with long time duration. Furthermore, the availability of the closed form expressions for the temperature field makes the present method very attractive for coupled problems such as solid—fluid and thermal—structure interactions.

Fuzzy numbers are often used to represent non-probabilistic uncertainty in engineering, decision-making and control system applications. In these applications, fuzzy arithmetic operations are frequently used for solving mathematical equations that contain fuzzy numbers. There are two approaches proposed in the literature for implementing fuzzy arithmetic operations: the α-cut approach and the extension principle approach using different t-norms. Computational methods for the implementation of fuzzy arithmetic operations in different applications are also proposed in the literature; these methods are usually developed for specific types of fuzzy numbers. This chapter discusses existing methods for implementing fuzzy arithmetic on triangular fuzzy numbers using both the α-cut approach and the extension principle approach using the min and drastic product t-norms. This chapter also presents novel computational methods for the implementation of fuzzy arithmetic on triangular fuzzy numbers using algebraic product and bounded difference t-norms. The applicability of the α-cut approach is limited because it tends to overestimate uncertainty, and the extension principle approach using the drastic product t-norm produces fuzzy numbers that are highly sensitive to changes in the input fuzzy numbers. The novel computational methods proposed in this chapter for implementing fuzzy arithmetic using algebraic product and bounded difference t-norms contribute to a more effective use of fuzzy arithmetic in construction applications. This chapter also presents an example of the application of fuzzy arithmetic operations to a construction problem. In addition, it discusses the effects of using different approaches for implementing fuzzy arithmetic operations in solving practical construction problems.

Double-beam/column systems have drawn much attention in many engineering fields. This work aims to present the free and forced vibrations of a novel and complex double-column system with concentrated masses, axial loads and discrete viscoelastic supports subjected to the excitation of ground acceleration are solved by the extended Laplace transform method (ELTM).

In this work, the authors proposed an extended Laplace transform method (ELTM), which is an exact and explicit analytical method. Firstly, the mathematical model simulating the vibrations of the double-column system is reformulated with Dirac's delta function. Secondly, the exact and explicit mode shape solutions are obtained, based on which the natural frequencies and dynamic responses are obtained. An illustrating example is presented to show the validity of the proposed method. A parametric study is carried out to investigate the influences of the non-dimensional column stiffness ratio and the support stiffness ratio on the peak dynamic displacement and velocity.

It is shown that the proposed method can give exact and explicit solutions of the mode shapes and natural frequencies. It is found that the asynchronous vibrations of the proposed double-column systems can be implemented to efficiently dissipate seismic energy, as shown in the time-histories of displacement and velocity.

This research systematically studied the free and forced vibrations of the complex double-column system. The proposed extended ELTM is a general method. Its application to studying the energy dissipation capability implicates that the double-column system can be utilized to reduce responses in structures under earthquake attacks.

The proposed extended ELTM is original and powerful. Its application to study the complex double-columns system with discrete supports, concentrated masses and axial loads is novel.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

This study aims to develop a mathematical programming model for preemptive multi-mode resource-constrained project scheduling problems in construction with the objective of levelling resources considering renewable and non-renewable resources.

The proposed model was solved by the exact method and the genetic algorithm integrated with the solution modification procedure coded with MATLAB software. The Taguchi method was applied for setting the parameters of the genetic algorithm. Different numerical examples were used to show the validation of the proposed model and the capability of the genetic algorithm in solving large-sized problems. In addition, the sensitivity analysis of two parameters, including resource factor and order strength, was conducted to investigate their impact on computational time.

The results showed that preemptive activities obtained better results than non-preemptive activities. In addition, the validity of the genetic algorithm was evaluated by comparing its solutions to the ones of the exact methods. Although the exact method could not find the optimal solution for large-scale problems, the genetic algorithm obtained close to optimal solutions within a short computational time. Moreover, the findings demonstrated that the genetic algorithm was capable of achieving optimal solutions for small-sized problems. The proposed model assists construction project practitioners with developing a realistic project schedule to better estimate the project completion time and minimize fluctuations in resource usage during the entire project horizon.

There has been no study considering the interruption of multi-mode activities with fluctuations in resource usage over an entire project horizon. In this regard, fluctuations in resource consumption are an important issue that needs the attention of project planners.

This paper attempts to evaluate the transverse stresses that are generated within the interface between two layers of laminated composite and sandwich laminates by using Cℴ finite element formulation of higher‐order theories. These theories do not require the use of a fictitious shear correction coefficient which is usually associated with the first‐order Reissner‐Mindlin theory. The in‐plane stresses are evaluated by using constitutive relations. The transverse stresses are evaluated through the use of equilibrium equations. The integration of the equilibrium equations is attempted through forward and central direct finite difference techniques and a new approach, named as, an exact surface fitting method. Sixteen and nine‐noded quadrilateral Lagrangian elements are used. The numerical results obtained by the present approaches in general and the exact surface fitting method in particular, show excellent agreement with available elasticity solutions. New results for symmetric sandwich laminates are also presented for future comparisons.