Inference for Weibull distribution under generalized order statistics

Based on generalized order statistics from Weibull distribution the approach of Bayesian and non-Bayesian estimation are discussed. We present a simple and efficient simulational algorithm for generating a generalized order statistics sample from any continuous distribution. Specializations to Bayesian and non-Bayesian estimators, some lifetime parameters and confidence intervals of progressive II censoring and record values are obtained and compared with the existing results. Two examples are given to illustrate the proposed estimators and the simulation algorithm.     

ADAPTIVE RANKS CLONE AND k‐NEAREST NEIGHBOR LIST–BASED IMMUNE MULTI‐OBJECTIVE OPTIMIZATION

Artificial immune systems (AIS) are computational systems inspired by the principles and processes of the vertebrate immune system. The AIS‐based algorithms typically exploit the immune system's characteristics of learning and adaptability to solve some complicated problems. Although, several AIS‐based algorithms have proposed to solve multi‐objective optimization problems (MOPs), little focus have been placed on the issues that adaptively use the online discovered solutions. Here, we proposed an adaptive selection scheme and an adaptive ranks clone scheme by the online discovered solutions in different ranks. Accordingly, the dynamic information of the online antibody population is efficiently exploited, which is beneficial to the search process. Furthermore, it has been widely approved that one‐off deletion could not obtain excellent diversity in the final population; therefore, a k‐nearest neighbor list (where k is the number of objectives) is established and maintained to eliminate the solutions in the archive population. The k‐nearest neighbors of each antibody are founded and stored in a list memory. Once an antibody with minimal product of k‐nearest neighbors is deleted, the neighborhood relations of the remaining antibodies in the list memory are updated. Finally, the proposed algorithm is tested on 10 well‐known and frequently used multi‐objective problems and two many‐objective problems with 4, 6, and 8 objectives. Compared with five other state‐of‐the‐art multi‐objective algorithms, namely NSGA‐II, SPEA2, IBEA, HYPE, and NNIA, our method achieves comparable results in terms of convergence, diversity metrics, and computational time.     

Integrating customer's preferences in the QFD planning process using a combined benchmarking and imprecise goal programming model

Quality function deployment (QFD) is a customer-oriented design tool for developing new or improved products to achieve higher customer satisfaction by integrating various functions of an organization. The engineering characteristics (ECs) affecting the product performances are designed to match the customer attributes (CAs). However, from the viewpoint of the QFD team, product design processes are performed in imprecise environments, and more than one factor must be taken into account in determining the target levels of ECs, especially the limited resources and increased market competition. This paper presents an imprecise goal programming (GP) approach to determine the optimum target levels of ECs in QFD for maximizing customer satisfaction under resource limitation and considerations of market competition. Based on benchmarking data of CAs, the concept of satisfaction functions is utilized to formulate explicitly the customer's preferences and to integrate the competitive analysis of target market into the modelling and solution process. In addition, the relationships linking CAs and ECs and the ECs to each other are integrated by functional relationships. The proposed approach will be illustrated through a car door design example.     

The structure of canalizing functions

The structure of a canalizing function is discussed. Using a new matrix product, namely semitensor product, the logical function is expressed in its matrix form. From its matrix expression, a criterion is obtained to test whether a logical function is a canalizing function. Then a formula is obtained to calculate the number of canalizing functions. Moreover, an algorithm is presented to generate canalizing functions. Finally, some results obtained are extended to seminested canalizing functions.     

Development of a sequential robust–tolerance design model for a destructive quality characteristic

Robust design (RD) and tolerance design (TD) have received much attention from researchers and practitioners for more than two decades, and a number of methodologies for modeling and optimizing the RD and TD processes have been studied. However, there is ample room for improvement. Because most existing research considers RD and TD as separate research fields, the primary objective of this paper is to develop a sequential robust–tolerance design method to jointly determine the best factor settings and the closed-form solutions for the optimal specification limits. We then apply the proposed method to a destructive quality characteristic. Finally, a case study and sensitivity analyses are performed for verification purposes, and further studies are discussed.     

Some algebraic methods for solving multiobjective polynomial integer programs

Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the past few years. However, the polynomial case has not been studied in detail due to its theoretical and computational difficulties. This paper presents an algebraic approach for solving these problems. We propose a methodology based on transforming the polynomial optimization problem to the problem of solving one or more systems of polynomial equations and we use certain Gröbner bases to solve these systems. Different transformations give different methodologies that are theoretically stated and compared by some computational tests via the algorithms that they induce.     

Numerical method using cubic B-spline for the heat and wave equation

In the present paper, the cubic B-splines method is considered for solving one-dimensional heat and wave equations. A typical finite difference approach had been used to discretize the time derivative while the cubic B-spline is applied as an interpolation function in the space dimension. The accuracy of the method for both equations is discussed. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.     

Fault tolerant machine learning for nanoscale cognitive radio

We introduce a machine learning-based classifier that identifies free radio channels for cognitive radio. The architecture is designed for nanoscale implementation, under nanoscale implementation constraints; we do not describe all physical details but believe future physical implementation to be feasible. The system uses analog computation and consists of cyclostationary feature extraction and a radial basis function network for classification. We describe a model for nanoscale faults in the system, and simulate experimental performance and fault tolerance in recognizing WLAN signals, under different levels of noise and computational errors. The system performs well under expected non-ideal manufacturing and operating conditions.     

A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems

This paper presents a systematic approach for decreasing conservativeness in stability analysis and control design for Takagi-Sugeno (TS) systems. This approach is based on the idea of multiple Lyapunov functions together with simple techniques for introducing slack matrices. Unlike some previous approaches based on multiple Lyapunov functions, both the stability and the stabilization conditions are written as linear matrix inequality (LMI) problems. The proposed approach reduces the number of inequalities and guarantees extra degrees of freedom to the LMI problems. Numeric examples illustrate the effectiveness of this method.