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Engineers and scientists often identify robust parameter design as one of the most important process and quality improvement methods. Focused on statistical modeling and numerical optimization strategies, most researchers typically assume a process with reasonably small variability. Realistically, however, industrial processes often exhibit larger variability, particularly in mass production lines. In such cases, many of the modeling assumptions behind the robust parameter design models available in the literature do not hold. Accordingly, the results and recommendations provided to decision makers could generate suboptimal modifications to processes and products. As manufacturers seek improved methods for ensuring quality in resource-constrained environments, experimenters should examine trade-offs to achieve the levels of precision that best support their decision making. In contrast to previous research, this paper proposes a trade-off analysis between the cost of replication and the desired precision of generated solutions. We consider several techniques in the early stages of experimental design, using Monte Carlo simulation as a tool, for revealing potential options to the decision maker. This is perhaps the first study to show the avenue which may lead to more effective robust parameter design models with the optimal combination of cost constraints and desired precision of solutions.

For complex manufacturing systems, process or product optimization can be instrumental in achieving a significant economic advantage. To reduce costs associated with product non-conformance or excessive waste, engineers often identify the most critical quality characteristics and then use methods to obtain their ideal parameter settings. The optimal process mean problem is one such statistical method; it begins with the assumption of the characteristic parameters, whereby the ideal settings are determined based upon the tradeoff among various processing costs. Unfortunately, however, the ideal parameter settings for a characteristic mean can be unpredictable, as it is directly influenced by changes in the process variability, tolerance, and cost structure. In this paper, a method is proposed that relates the optimal process mean to the ideal settings through experimental design. With the method, one may gain greater predictability of the new optimal process mean when the process conditions are altered. The methodology is illustrated for a process with multiple mixed quality characteristics; such an optimal process mean problem is seldom treated in the literature.

One technique used frequently among quality practitioners seeking solutions to multi-response optimization problems is the desirability function approach. The technique involves modeling each characteristic using response surface designs and then transforming the characteristics into a single performance measure. The traditional procedure, however, calls for estimating only the mean response; the variability among the characteristics is not considered. Furthermore, the approach typically relies on the accuracy of second-order polynomials in its estimation, which are not always suitable. This paper, in contrast, proposes a methodology that utilizes higher-order estimation techniques and incorporates the concepts of robust design to account for process variability. Several examples are provided to illustrate the effectiveness of the proposed methodology.

For the manufacturing community, determining the optimal process mean can often lead to a significant reduction in waste and increased opportunity for monetary gain. Given the process specification limits and associated rework or rejection costs, the traditional method for identifying the optimal process mean involves assuming values for each of the process distribution parameters prior to implementing an optimization scheme. In contrast, this article proposes integrating response surface methods into the framework of the problem, thus removing the need to make assumptions on the parameters. Furthermore, whereas researchers have studied models to investigate this research problem for a single quality characteristic and multiple nominal-the-best type characteristics, this article specifically examines the mixed multiple quality characteristic problem. A non-linear programming routine with economic considerations is established to facilitate the identification of the optimal process mean vector. An analysis...

For the manufacturer that intends to reduce the processing costs without sacrificing product quality, the identification of the optimal process mean is a problem frequently revisited. The traditional method to solving this problem involves making assumptions on the process parameter values and then determining the ideal location of the mean based upon various constraints such as cost or the degree of quality loss when a product characteristic deviates from its desired target value. The optimal process mean, however, is affected not only by these settings but also by any shift in the variability of a process, thus making it extremely difficult to predict with any accuracy. In contrast, this paper proposes the use of a reverse programming scheme to determine the relationship between the optimal process mean and the settings within an experimental factor space. By doing so, one may gain increased awareness of the sensitivity and robustness of a process, as well as greater predictive capability in the setting of the optimal process mean. Non-linear optimization programming routines are used from both a univariate and multivariate perspective in order to illustrate the proposed methodology.

PurposeThe selection of the optimal process target for a manufacturing process is critically important as it directly affects the defect rate, rejection and rework costs, and the loss to customers. A recent review of process target literature suggests that future work should incorporate models using multiple quality characteristics. Thus, the purpose of this paper is to create a more flexible and realistic approach to solving the multi‐response process target problem.Design/methodology/approachA design of experiments methodology is proposed to provide estimates of process parameters and a nonlinear constrained optimization scheme is employed to identify optimal settings.FindingsThe approximation of cost savings undoubtedly has a higher degree of accuracy than in the case where the engineer assumes values for the process parameters. Furthermore, greater flexibility is obtained in finding solutions that support both the manufacturer and the customer.Research limitations/implicationsThis methodology relies on controlled experimentation and the replication of observations made on multiple nominal‐the‐best quality characteristics. Future research may include examining the effects of using smaller‐the‐better or larger‐the‐better type characteristics.Originality/valueUnlike traditional attempts at solving the process target problem where the process mean, variance, and covariance between characteristics are assumed known in advance, this paper uses an approach that removes these assumptions, thereby providing a more practical depiction of the overall system. Furthermore, this methodology broadens the scope of process target problem research by seeking the simultaneous optimization of process parameters and considering a loss in quality attributed to deviation from a target value.

Within an industrial manufacturing environment, Process Capability Indices (PCIs) enable engineers to assess the process performance and ultimately improve the product quality. Despite the fact that most industrial products manufactured today possess multiple quality characteristics, the vast majority of the literature within this area primarily focuses on univariate measures to assess process capability. One particular univariate index, Cpm, is widely used to account for deviations between the location of the process mean and the target value of a process. While some researchers have sought to develop multivariate analogues of Cpm, modeling the loss in quality associated with multiple quality characteristics continues to remain a challenge. This paper proposes a multivariate PCI that more appropriately estimates quality loss, while offering greater flexibility in conforming to various industrial applications, and maintaining a more realistic approach to assessing process capability. Copyright © 2010 John Wiley & Sons, Ltd.

Innovative engineering techniques are often sought within the manufacturing environment to improve product quality and promote more cost-effective strategies. Robust design methods are frequently used to serve this purpose, with the objective of minimizing the variability inherent within a particular process or system. A review of the literature suggests that most robust design research involves the study of static quality characteristics, given a pre-defined specification interval or region and target value. In addition to proposing a methodology for working with dynamic quality characteristics where the specifications and target value may change over time, this paper offers two other distinct contributions. First, those researchers who have examined dynamic systems traditionally consider the effects of a signal factor on a response variable on the identification of optimal factor settings. In contrast, this paper will consider the effects of a quality characteristic changing over time, thus removing the need to confine the problem to signal–response systems. Furthermore, most researchers consider the optimization of the process mean according to the costs of non-conforming to an established specification interval or region. This paper, however, utilizes a methodology involving the simultaneous optimization of the process mean and variance while expanding the problem to consider a loss in quality attributed to deviation from a target value over time. Copyright © 2010 John Wiley & Sons, Ltd.

One of the most popular quality engineering tools is the process capability index (PCI), which relates the allowable spread of a process defined by engineering specifications to the natural spread of a process. The traditional PCI does not account for the loss in quality when product characteristics fail to achieve their process target value. This research, in contrast, proposes indices, namely posterior PCIs, that consider the underlying result of observations after inspection. Utilising a truncated distribution as the basis for measurement along with a target-based quality loss function for capability analyses, several posterior indices are developed in this paper. A simulation technique is implemented to compare the proposed posterior PCIs with traditional measures. Finally, the confidence interval approximations for the posterior PCIs are derived. Our results suggest using the proposed posterior indices for capability analyses when industrial processes require that non-conforming products be scrapped prior to shipping to the customer.

When the manufacturing objective is process or product improvement, quality practitioners will frequently resort to one or more approaches within the broader class of response surface methodology. Several techniques, such as the dual response, robust parameter design, and desirability function approach, may be effective tools to solve the multi-response optimisation problem. All of these techniques are designed to identify the factor settings that lead to an optimal solution in terms of the mean or variance among characteristics. The skewness in the distribution of observations for one or more characteristics, however, is not considered. The techniques also traditionally rely on the fit of second-order response surface designs in estimating each response, which may be unreliable in some cases. In contrast, this paper offers an approach to solving complex multi-response optimisation problems that considers both the error associated with process skewness and the accuracy of a response surface.

Within the last 20 years, the opportunities for manufacturing at the nano-level have risen substantially. Despite this growth, the industry continues to face the challenge of obtaining a significant experimental yield that is worthy of the cost to produce at the atomic level. Today, most researchers utilise response surface methodology to evaluate and improve existing techniques in nanoparticle production. While these methods are appropriate for identifying optimal factor settings in the traditional manufacturing process, they require some refinement under significantly elevated degrees of quality. This paper investigates the use of higher-order response surface designs in the improvement of nanomanufacturing processes.

In a manufacturing environment where concerns for product quality or excessive cost are often present, process optimisation is typically an engineering objective. One method that supports the reduction of nonconformance costs and loss in product quality is the identification of the optimal process mean. Given the specification limits and associated costs for a process, the traditional method uses assumed values for the process parameters to estimate the ideal location of the mean. In contrast, this paper proposes using a methodology that removes the need to make assumptions on the process parameters. Furthermore, while most research examines the role of the nominal-the-best characteristic in the design of the optimal process mean, this paper specifically looks at smaller-the-better and larger-the-better quality characteristics. The skew normal distribution, which is relatively new to engineering applications, is considered in modelling these characteristics. A non-linear programming routine with economic considerations is used to facilitate this study.

For any given manufacturing system, the initial setting of the process target is critical in preventing excessive product rejection and rework costs. Often referred to as the ‘process target problem’, the traditional approach relies first on the assumption of certain values for the process mean and variance, prior to identifying the optimal setting. This paper, in contrast, proposes integrating estimated response surface functions developed for the mean and variance based upon observations made on a given process, thus removing any assumption on the parameters. In addition, this paper considers non-standard experimental regions, where constraints may exist on the factor space or restrictions are implemented on the number of experimental runs conducted. In doing so, greater flexibility is obtained in finding solutions to process target problems and the scope of the research field is broadened. Non-linear programming methods are used to facilitate this approach, and numerical examples are provided to illust...