OPTIMIZING THE MEAN AND STANDARD DEVIATION
The principal objective of this article is to come up with an alternative way to optimize the standard deviation of the quality characteristic of a product or process enabling the practitioner to assign distinct weights to process mean and standard deviation and to find trade-off solutions between them, taking their relative magnitudes into account.

In this article various approaches have been proposed e.g. Response surface methodology and robust parameter design. RSM and RPD are used to get low variability, low cost, high quality, and high reliability in the process and product .The priority-based, mean squared–based, and
Goal programming–based approaches in the RSM framework are attached to many drawbacks necessitating alternative methods to be used. The dual response optimization approach may be difficult for practitioners who do not have sufficient mathematical knowledge and are mostly found in journals that are difficult to find. RSM framework approaches have been proposed by Vining and Myers(1990), Copeland and Nelson(1996) and Lind and Tu(1995).Other data-driven approaches that are applicable include the ones by Ding et al.(2004), Jeong et al.(2005) and Shaibu and Cho(2009).Although the weighted square sum-based method allow overtaking of drawbacks of the priority based methods, they do not capture solutions. The proposed method uses less complicated techniques and it is assumed that an optimal solution for a dual response may require trade-off between process mean and standard deviation. Therefore, it minimizes both the mean and standard deviation departure from their target values. It is assumed that those involved in process and product optimization have the necessary background knowledge in allocating the appropriate values to targets and bounds for each response.

This is necessary to come up with better ways way since the journals containing the approaches are not readily available. Though the ideal univariate response is simultaneously on-target and of minimal variance, reality usually forces the practitioner to make trade-offs between on-target performance and low variance. The proposed method takes into account the nature of quality characteristics, takes relative magnitude of responses into account, and makes it possible for practitioners to assign priorities discretely for each one of them. In addition, it has a direct physical interpretation, can be easily implemented by practitioners, and provides appropriate trade-off solutions between the two process parameters. These attributes, and in particular the low number of priorities (weights) the user has to input, justify using the proposed method for optimizing dual response problems and are a stimulus to apply it to multiple dual response problems, where trade-offs among several means and standard deviations are required. Future research will explore its potential with this type of problem.
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