A Decision Support System for Solving Multi‐Objective Redundancy Allocation Problems

The Redundancy Allocation Problem (RAP) is a reliability optimization problem in designing series‐parallel systems. The reliability optimization process is intended to select multiple components with appropriate levels of redundancy by maximizing the system reliability under some predefined constraints. Several methods have been proposed to solve the RAPs. However, most of these methods often treat RAP as a single objective problem of maximizing the system reliability (or minimizing the system design cost). We propose a Decision Support System for solving Multi‐Objective RAPs. Initially, we use the Technique for Order Performance by Similarity to Ideal Solution method to reduce the multiple objective dimensions of the problem. We then propose an efficient ε‐constraint method to generate non‐dominated solutions on the Pareto front. Finally, we use a Data Envelopment Analysis model to prune the non‐dominated solutions. A benchmark case is presented to assess the performance of the proposed system, demonstrate the applicability of the proposed framework, and exhibit the efficacy of the procedures and algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

Economic Design Approach for an SPC Inspection Procedure Implementing The Adaptive C Chart

The present paper proposes a design approach for a statistical process control (SPC) procedure implementing a c control chart for non‐conformities, with the aim to minimize the hourly total quality‐related costs. The latter take into account the costs arising from the non‐conforming products while the process is in‐control and out‐of‐control, for false alarms, for assignable cause locations and system repairs, for sampling and inspection activities and for the system downtime. The proposed economic optimization approach is constrained by the expected hourly false alarms frequency, as well as the available labor resource level. A mixed integer non‐linear constrained mathematical model is developed to solve the treated optimization problem, whereas the Generalized Reduced Gradient Algorithm implemented on the solver of Microsoft Excel is adopted to resolve it. In order to illustrate the application of the developed procedure, a numerical analysis based on a fractional factorial design scheme, to investigate on the influence of several operating and costs parameters, is carried out, and the related considerations are given. Finally, the obtained results show that only few parameters have a meaningful effect on the selection of the optimal SPC procedure. Copyright © 2013 John Wiley & Sons, Ltd.     

Comparing the Economic Effectiveness of Various Adaptive Schemes for the c Chart

In an attempt to improve the effectiveness of statistical process control (SPC) procedures, a variety of adaptive schemes has been developed in the last decades. However, considering control charts for attributes, relatively few works about adaptive schemes have been proposed, and most of them were proposed only recently. The common characteristic of those schemes is that one or more chart parameters are allowed to adaptively vary during the SPC operations according to the sampling information history, typically the current point plotted on the chart. In this way, the adaptive schemes are smarter than the related static ones, but they are also more complicated in terms of implementation. The purpose of the present work is to evaluate and compare the economic performance of the main adaptive schemes of a control chart for attributes, in order to derive conclusions on their relative effectiveness. In particular, the analysis is focused on the c chart that is used to monitor the total nonconformities number in an inspection unit. A numerical comparative study, based on a fractional factorial design scheme, to investigate on the influence of several operating and costs parameters, is carried out, and the related considerations are given. The obtained results show that the chart parameter having the most impact on the economic performance is the sampling interval. Therefore, in most cases, the use of a c chart with adaptive sampling intervals is the better choice than other adaptive schemes, which are also more complicated in terms of implementation. Copyright © 2013 John Wiley & Sons, Ltd.     

A Prediction Region‐based Approach to Model Uncertainty for Multi‐response Optimization

Multi‐response optimization methods rely on empirical process models based on the estimates of model parameters that relate response variables to a set of design variables. However, in determining the optimal conditions for the design variables, model uncertainty is typically neglected, resulting in an unstable optimal solution. This paper proposes a new optimization strategy that takes model uncertainty into account via the prediction region for multiple responses. To avoid obtaining an overly conservative design, the location and dispersion performances are constructed based on the best‐case strategy and the worst‐case strategy of expected loss. We reveal that the traditional loss function and the minimax/maximin strategy are both special cases of the proposed approach. An example is illustrated to present the procedure and the effectiveness of the proposed loss function. The results show that the proposed approach can give reasonable results when both the location and dispersion performances are important issues. Copyright © 2015 John Wiley & Sons, Ltd.     

A constrained non‐linear system approach for the solution of an extended limit analysis problem

A number of recent papers (see, e.g. (Int. J. Mech. Sci. 2007; 49 :454–465; Eur. J. Mech. A/Solids 2008; 27 :859–881; Eng. Struct. 2008; 30 :664–674; Int. J. Mech. Sci. 2009; 51 :179–191)) have shown that classical limit analysis can be extended to incorporate such important features as geometric non‐linearity, softening and various so‐called ductility constraints. The generic formulation takes the form of a challenging (nonconvex and nonsmooth) optimization problem referred to in the mathematical programming literature as a mathematical program with equilibrium constraints (MPEC). Similar to a classical limit analysis, the aim is to compute in a single step a bound (upper bound, in the case of the extended problem) to the maximum load. The solution algorithm so far proposed to solve the MPEC is to convert it into an iterative non‐linear programming problem and attempts to process this using a standard non‐linear optimizer. Motivated by the fact that no method is guaranteed to solve such MPECs and by the need to avoid the use of an optimization approach, which is unfamiliar to most practising engineers, we propose, in the present paper, a novel numerical scheme to solve the MPEC as a constrained non‐linear system of equations. We illustrate the application of this approach using the simple class of elastoplastic softening skeletal structures for which certain ductility conditions are prescribed. Copyright © 2009 John Wiley & Sons, Ltd.