Paul L. Goethals

The development of a robust design methodology for time‐oriented dynamic quality characteristics with a target profile

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

The development of a target‐focused process capability index with multiple characteristics

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

Solving the optimal process target problem using response surface designs in heteroscedastic conditions

The contemporary industrial environment continues to rely on the identification of the optimal process target as a means to minimise the product defect rate and ultimately reduce manufacturing costs. Within the context of the optimal process target problem, this paper will offer three distinct contributions. First, a review of literature associated with the process target problem indicates that most research work assumes a known process distribution mean and variance prior to the identification of optimal settings. In contrast, this paper will incorporate the use of response surface designs into solving the process target problem, thus removing the need to make assumptions regarding the process parameters. Second, most research regarding the development of response surface designs either assumes that the same number of observations are made on a quality characteristic of interest, or model error always exhibits a uniform pattern of constant variance. This paper, however, will incorporate alternative modelling techniques to investigate instances when these assumptions are not present, thus broadening the scope of the process target problem. Finally, most research in this area focuses on the determination of the optimal process mean; in this paper, however, we propose a model for simultaneously determining the optimal process mean and variance.

Extending the desirability function to account for variability measures in univariate and multivariate response experiments

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.

Experimental investigations of estimated response surface functions with different variability measures

The primary goal of robust design is to determine the optimum operating conditions which minimise the variability of system performance and the deviation of the performance from its ideal target value. Response surface methodology (RSM), which is a key statistical method in modelling robust design, explores the functional relationship between several explanatory factors and a response variable. Our literature study indicates that three different estimators for variability measure, such as standard deviation, variance and the logarithmic transformation of standard deviation, are typically used; however, depending on which estimator is selected, different sets of optimum operating conditions are obtained which can further complicate comparison studies and data analysis. This question has not been addressed adequately in the robust design research community. This paper investigates how the selection of the three different estimators of variability affects optimal operating conditions in the context of response surface designs. The nominal-the-best quality characteristic is used to facilitate this experiment and numerical examples are provided to illustrate the findings.

Designing the optimal process mean vector for mixed multiple quality characteristics

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 of the sensitivity corresponding to the cost structure, tolerance, and quality loss settings is also provided to illustrate their effect on the solutions.

Reverse programming the optimal process mean problem to identify a factor space profile

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.

The development of multi‐response experimental designs for process parameter optimization

Purpose – The 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/approach – A design of experiments methodology is proposed to provide estimates of process parameters and a nonlinear constrained optimization scheme is employed to identify optimal settings.Findings – The 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/implications – This methodol...

The optimal process mean problem: Integrating predictability and profitability into an experimental factor space

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.

Designing the optimal mean for an asymmetrically distributed process

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.