Onur Köksoy

Joint Optimization of Mean and Standard Deviation Using Response Surface Methods

Taguchis robust parameter design calls for simultaneous optimization of the mean and standard deviation responses. The dual response optimization procedures have been adapted to achieve this goal by taking into account both the mean and standard deviation response functions. The popular formulations of the dual response problem typically impose a restriction on the value of the secondary response (i.e., keeping the standard deviation below a specified value) and optimize the primary response function (i.e., maximize or minimize the mean). Restrictions on the secondary response, however, may rule out better conditions, since an acceptable value for the secondary response is usually unknown. In fact, process conditons that result in a smaller standard deviation are often preferable. A more flexible formulation of the problem can be achieved by considering the secondary response as another primary response. The proposed method will generate more alternative solutions, called Pareto optimal solutions. This gives more flexibility to the decision-maker in exploring alternative solutions. It is also insightful to examine graphically how the controllable variables simultaneously impact the mean and standard deviation. The procedure is illustrated with three examples, using both the NIMBUS software for nonlinear multiobjective programming and the Solver in the Excel spreadsheet.

A nonlinear programming solution to robust multi-response quality problem

Quite often, engineers obtain measurements associated with several response variables. Both the design and analysis of multi-response experiments with a focus on quality control and improvement have received little attention although they are sorely needed. In a multi-response case the optimization problem is more complex than in the single-response situation. In this paper we present a method to optimize multiple quality characteristics based on the mean square error (MSE) criterion when the data are collected from a combined array. The proposed method will generate more alternative solutions. The string of solutions and the trade-offs aid in determining the underlying mechanism of a system or process. The procedure is illustrated with an example, using the generalized reduced gradient (GRG) algorithm for nonlinear programming.

MULTIRESPONSE ROBUST DESIGN: MEAN SQUARE ERROR (MSE) CRITERION

Abstract Most of the published literature on robust design methodology is basically concerned with optimization of a single response or quality characteristic which is often most critical to consumers. However, manufactured products are typically characterized by numerous quality characteristics. In this paper we present a general framework for the multivariate problem when data are collected from a combined array. Within the framework, a mean square error (MSE) criterion is utilized and a non-linear multiobjective programming problem based on the individual MSE functions of each response is proposed for quality improvement. We adapted a suitable non-linear optimization algorithm to solve the proposed formulation. The optimization method used in this paper generates a string of solutions, called Pareto optimal solutions, rather than a “one shot” optimum solution to make selections and evaluate the trade-offs. The paper also presents an example and comparative results in order to demonstrate the potentials of the proposed approach.

Robust Design using Pareto type optimization: A genetic algorithm with arithmetic crossover

In dual response systems (DRSs) optimization restrictions on the secondary response may rule out better conditions, since an acceptable value for the secondary response is usually unknown. In fact, process conditions that result in a smaller standard deviation are often preferable. Recently, several authors stated that the standard deviation of any performance property could be treated as a new property in its own right as far as Pareto optimizer was concerned. By doing this, there will be many alternative solutions (i.e., the trade-offs between the mean and standard deviation responses) of the DRS problem and Pareto optimization can explore them all. Such analysis is useful, and that is required in order to achieve an improved understanding of the problem before searching for a final optimal solution. In this paper, we again follow this new philosophy and solve the DRS problem by using a genetic algorithm with arithmetic crossover. The genetic algorithm is applied to the printing process problem for improving the quality of a printing process. Genetic algorithms, in contrast to the one-solution-at-a-time approach of most optimization algorithms, maintain a population of hundreds, or thousands, of solutions in speedy manner.

Mean square error criteria to multiresponse process optimization by a new genetic algorithm

The recent push for quality in industry has brought response surface methodology to the attention of many users. Most of the published literature on robust design methodology is basically concerned with optimization of a single response or quality characteristic which is often most critical to consumers. For most products, however, quality is multidimensional, so it is common to observe multiple responses in an experimental situation. In this paper, we present a methodology for analyzing several quality characteristics simultaneously using the mean square error (MSE) criterion when data are collected from a combined array. Problems with highly nonlinear, or multimodal, objective functions are extremely difficult to solve and are further complicated by the presence of multiple objectives. An alternative approach is to use a heuristic search procedure such as a genetic algorithm (GA). The GA generates a string of solutions using genetics-like operators such as selection, crossover and mutation. In this paper, a genetic algorithm based on arithmetic crossover for the multiresponse problem is proposed. The string of solutions highlight the trade-offs that one needs to consider in order to obtain a compromise solution. A numerical example has been presented to illustrate the performance and the applicability of the proposed method.

Is Low Self-Control Associated With Violence Among Youths in Turkey?:

Self-control theory is tested in relation to violence on a sample of university students in Turkey. The primary findings indicate support for the theory net of the impacts of strain, deterrence, differential association, social bonding, and routine activity theories: The greater the low self-control, the greater the violence. No subdimensions of self-control have consistent significant impacts on violence. Most high-opportunity measures have positive impacts on violence. Interaction effects occur only among subdimensions of self-control and opportunity variables. Social class and age are significant even when low self-control measures were controlled.

An upside-down normal loss function-based method for quality improvement

Traditional measures of process quality do not offer much information on how much better or worse a process is when finding optimal settings of a given problem. The upside-down normal loss function (UDNLF) is a weighted loss function that provides a more reasonable risk assessment to the losses of being off-target in product engineering research. The UDNLF can be used in process design and optimization to accurately reflect and quantify the losses associated with the process in a way which minimizes the expected loss of the upside-down normal (UDN). The function has a scale parameter which can be adjusted by the practitioners to account for the actual percentage of materials failing to work at specification limits. In this article, the ‘target is best’ case is addressed to estimate the expected loss of UDN due to variation from target in the robust process design and response surface modelling context. An approach is proposed to find the control factor settings of a system by directly minimizing the expected loss. The procedure and its merits are illustrated through an example.

A tabu search meta-heuristic approach to the dual response systems problem

This paper presents an alternative approach to the dual response systems problem by utilizing a tabu search algorithm that yields a string of solutions and examine the trade-offs graphically and systematically how the controllable variables simultaneously impact the mean and the standard deviation of a characteristic of interest relevant to an industrial process. Heuristic-based search techniques may be very useful for cases where interactive multi-objective optimization techniques are not available due to lack of willingness of decision-makers. A further advantage of tabu search is its simplicity and we show that the entire process only occupies a few lines of codes and generates string of solutions in speedy manner especially for the larger-the-better/smaller-the-better cases of Taguchis robust parameter design. The procedure is illustrated with an example.

Cumulative correspondence analysis of ordered categorical data from industrial experiments

Most studies of quality improvement deal with ordered categorical data from industrial experiments. Accounting for the ordering of such data plays an important role in effectively determining the optimal factor level of combination. This paper utilizes the correspondence analysis to develop a procedure to improve the ordered categorical response in a multifactor state system based on Taguchis statistic. Users may find the proposed procedure in this paper to be attractive because we suggest a simple and also popular statistical tool for graphically identifying the really important factors and determining the levels to improve process quality. A case study for optimizing the polysilicon deposition process in a very large-scale integrated circuit is provided to demonstrate the effectiveness of the proposed procedure.