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There is extensive research in the monitoring of a process whose characteristics are represented as profiles. However, most current techniques require all observations from each profile to determin...

The operation of many batch processes involves critical characteristics that follow specific patterns over time. Sometimes the batch time is long enough that the operator can take corrective action...

This paper studies the impact when the experimenter does not randomize the design for split-plot experiments when there is a linear trend. The paper uses both simulation and basic theory to...

As systems grow more complex, so does our propensity to use computers to emulate complex real-world systems. Often these real-world systems possess dynamic response behavior over the operational domain of input parameter configurations. This domain is referred to as the design space or experimental region. It is critical we ensure that computer models which emulate such dynamic behavior be validated over the full design space. This paper presents a dual-interval validation methodology. Confidence intervals and tolerance intervals are developed based on a system response surface function. Model samples are compared to each interval to develop a complete model validation conclusion. The methodology is described, its robustness to noise and model lack-of-fit examined, and then it is applied to a well-established engineering validation challenge problem.

This article examines Soren’s impact on the design and analysis of experiment through three of his published articles in ASQ journals. These articles demonstrate Soren’s unique blend of engineer an...

In practice, engineers seek to find reasonable solutions for complex and unstructured problems, which are common in many areas. The workable solutions for these problems are never a one-shot experi...

High-resolution computer models can simulate complex systems and processes in order to evaluate a solution quickly and inexpensively. Many simulation models produce dynamic functional output, such as a set of time-series data generated during a process. These computer models require verification and validation (V&V) to assess the correctness of these simulations. In particular, the model validation effort evaluates if the model is an appropriate representation of the real-world system that it is meant to simulate. However, when assessing a model capable of generating functional output, it is useful to learn more than simply whether the model is valid or invalid. Specifically, if the model is deemed invalid, then what aspects of the model are incorrect? Is it possible to identify over what range the model data are a poor representation of the system data? Current V&V methods cannot identify these ranges. This paper proposes a wavelet analysis of variance (WANOVA) bisection method that first assesses model validity and can also identify the interval(s) over which the model is biased. The technique is illustrated using several simulation studies. Ultimately, this new method supports and expands the efficacy of model validation efforts.

Manufacturing process parameters often affect product reliability significantly. Practitioners need to improve product lifetime and reduce its variance simultaneously by optimizing process parameters. However, an important feature of lifetime distributions is that the variance increases as the mean increases. Practitioners should make a trade-off between them. In this article, we present a dual-response optimization approach to get optimal trade-off of percentile lifetime and lifetime variance. A new criterion is introduced to maximize the product reliability in the warranty period. We illustrate the proposed method via a real example and a simulated example. The optimization results show that the optimal solution is not a constant for different warranty periods. Practitioners should select different important factor levels for different scenarios. Furthermore, we compare the proposed method with other methods. The proposed method performs better than other methods significantly. Additionally, we present some discussions about the determination of significant factor levels.

I very much thank Dr. Saraiva for his paper and his talk. It is far too easy for academic researchers, even researchers in applied statistics and quality engineering, to lose proper perspective abo...

Model validation is that critical component in the simulation development process that ensures a model is truly representative of the system that it is meant to model. Although there are numerous validation techniques described in the literature, many of these techniques still require some amount of subjective analysis in order to assess validity. This is particularly true with dynamic simulation output. To reduce or eliminate this subjectivity, this paper proposes a validation process that uses wavelet analysis of variance (WANOVA) as an effective method to statistically accept or reject a model as valid. This WANOVA validation approach performs statistical inference in the time-frequency domain to take advantage of wavelet sparsity and decorrelation. This process uses a test statistic based on thresholded wavelet coefficients to test the null hypothesis that the set of system data and model data are statistically equivalent. The validation technique is illustrated using a simulation study and empirical data from an automobile crash study.

Many practical situations have both a quality characteristic and a reliability characteristic with the goal to find an appropriate compromise for the optimum conditions. Standard analyses of quality and reliability characteristics in designed experiments usually assume a completely randomized design. However, many experiments involve restrictions on randomization, e.g., subsampling, blocking, split-plot.This article considers an experiment involving both a quality characteristic and a reliability characteristic (lifetime) within a subsampling protocol. The particular experiment uses Type I censoring for the lifetime. Previous work on analyzing reliability data within a subsampling protocol assumed Type II censoring. This article extends such an analysis for Type I censoring. The method then uses a desirability function approach combined with the Pareto front to obtain a trade-off between the quality and reliability characteristics. A case study illustrates the methodology.

Definitive screening designs (DSDs) are a very interesting, academic advance in the design of experiments to support second-order response surface models. Their construction is extremely clever and...

Model verification and validation (V&V) remain a critical step in the simulation model development process. A model requires verification to ensure that it has been correctly transitioned from a conceptual form to a computerized form. A model also requires validation to substantiate the accurate representation of the system it is meant to simulate. Validation assessments are complex when the system and model both generate high-dimensional functional output. To handle this complexity, this paper reviews several wavelet-based approaches for assessing models of this type and introduces a new concept for highlighting the areas of contrast and congruity between system and model data. This concept identifies individual wavelet coefficients that correspond to the areas of discrepancy between the system and model.

Bayesian approaches are increasingly popular within the statistics community. However, they currently do not seem to find wide application within the industrial statistics/quality improvement community. This chapter examines some of the basic reasons why. It begins by reviewing Box’s perspective on the scientific method and discovery. It then examines Deming’s concepts of analytic versus enumerative studies. Together, these concepts provide a framework for evaluating when Bayesian approaches make good sense, where they make little sense, and where they fall somewhere in between. This chapter touches on statistical sampling plans, statistical process monitoring, and the design and analysis of experiments.

The authors propose a nonlinear mixed-model analysis for reliability experiments with random blocks and subsampling. A simulation study compares this nonlinear mixed model analysis with a two-stage analysis and traditional reliability analyses.

As we continue to model more complex systems, the validation of dynamical responses has come to the forefront of modeling and simulation. One form of dynamic response is when the output is a function of time. The proper evaluation of functional data over an array of desired input parameters is critical to achieving a robust validation assessment of a simulation model. We extend the correlation analysis (CORA) objective rating system to validate functional data across experimental regions. Functional regression analysis is used to generate surrogate estimations of the system response functions at points within the region where experimental observations are absent. These CORA scores provide a measure of disagreement at each desired parameter configuration. An overall score for model validity is achieved using a weighted linear combination of the individual CORA scores. Finally, an improved CORA size scoring metric is introduced.

Model validation is a vital step in the simulation development process to ensure that a model is truly representative of the system that it is meant to model. One aspect of model validation that deserves special attention is when validation is required for the transient phase of a process. The transient phase may be characterized as the dynamic portion of a signal that exhibits nonstationary behavior. A specific concern associated with validating a model's transient phase is that the experimental system data are often contaminated with noise, due to the short duration and sharp variations in the data, thus hiding the underlying signal which models seek to replicate. This paper proposes a validation process that uses wavelet thresholding as an effective method for denoising the system and model data signals to properly validate the transient phase of a model. This paper utilizes wavelet thresholded signals to calculate a validation metric that incorporates shape, phase, and magnitude error. The paper compares this validation approach to an approach that uses wavelet decompositions to denoise the data signals. Finally, a simulation study and empirical data from an automobile crash study illustrates the advantages of our wavelet thresholding validation approach.

The authors illustrate the development and implementation of a proposed CUSUM chart and evaluate its properties through a simulation study.

Reliability experiments provide important information regarding the life of a product, including how various factors affect product life. Current analyses of reliability data usually assume a completely randomized design. However, reliability experiments frequently contain subsampling, which represents a restriction on randomization. A typical experiment involves applying treatments to test stands, with several items placed on each test stand. In addition, raw materials used in experiments are often produced in batches, leading to a design involving blocks. This article proposes a method using Weibull regression for analyzing reliability experiments with random blocks and subsampling. An illustration of the method is provided.

This tutorial outlines the basic procedures for planning experiments within the context of the scientific method.

This article provides a technical answer to the following question: "I just finished my organization’s Six Sigma training. We covered quite a bit of material on designing experiments. The instructor said that randomizing the design and blocking wer..

Our Six Sigma program puts a very heavy emphasis on the importance of data for the success of our projects. However, our training really does not tell us how we should collect data other than an occasional designed experiment. Can you enlighten me?

The ability to model lifetime data from life test experiments is of paramount importance to all manufacturers, engineers and consumers. The Weibull distribution is commonly used to model the data from life tests. Standard Weibull analysis assume completely randomized designs. However, not all life test experiments come from completely randomized designs. Experiments involving sub-sampling require a method for properly modeling the data. We provide a Weibull nonlinear mixed models (NLLMs) methodology for incorporating random effects in the analysis. We apply this methodology to a reliability life test on glass capacitors. We compare the NLLMs methodology to other available methods for incorporating random effects in reliability analysis. A simulation study reveals the method proposed in this paper is robust to both model misspecification and increasing levels of variance on the random effect. Copyright © 2012 John Wiley & Sons, Ltd.

Technical advice on design of experiments, response surface methodology, and sequential experimentation.

Question: I have been told that we should look at residual plots whenever we perform a designed experiment or a regression analysis, but I do not understand why. I also am confused by Minitab becau...

The classical approach to the calibration of measurement systems is examined. This method treats the standards as the regressor and the observed values as the response when calibrating the instrument. However, the resulting regression model must then be..

Six Sigma Black Belt consultants often insist on an Anderson-Darling test to confirm that data are normally distributed before performing any analysis. Unfortunately, the Anderson-Darling test is insensitive to deviations from normality in small sample ..

Analysis techniques currently in use for product reliability assume a completely randomized design. Analysis methods for more complex experimental designs that are not completely randomized have received less attention from the reliability field. A simple analysis technique is described for reliability data from designed experiments containing subsampling. A popular reliability data set illustrates the method, and a comparison is made with previous analysis methods.

Elevated concentrations of ground-level ozone (O3) are frequently measured over farmland regions in many parts of the world. While numerous experimental studies show that O3 can significantly decrease crop productivity, independent verifications of yield losses at current ambient O3 concentrations in rural locations are sparse. In this study, soybean crop yield data during a 5-year period over the Midwest of the United States were combined with ground and satellite O3 measurements to provide evidence that yield losses on the order of 10% could be estimated through the use of a multiple linear regression model. Yield loss trends based on both conventional ground-based instrumentation and satellite-derived tropospheric O3 measurements were statistically significant and were consistent with results obtained from open-top chamber experiments and an open-air experimental facility (SoyFACE, Soybean Free Air Concentration Enrichment) in central Illinois. Our analysis suggests that such losses are a relatively new phenomenon due to the increase in background tropospheric O3 levels over recent decades. Extrapolation of these findings supports previous studies that estimate the global economic loss to the farming community of more than $10 billion annually.

Split-plot experiments are very common, although the textbooks and the statistical software do not discuss them very much. However, times are changing quickly. A split-plot experimental situation a...

When all experimental runs cannot be performed under homogeneous conditions, blocking can be used to increase the power for testing the treatment effects. Orthogonal blocking provides the same estimator of the polynomial effects as the one that would be obtained by ignoring the blocks. In many real-life design scenarios, there is at least one factor that is hard to change, leading to a split-plot structure. This paper shows that for a balanced ordinary least square–generalized least square equivalent split-plot design, orthogonal blocking can be achieved. Orthogonally blocked split-plot central composite designs are constructed and a catalog is provided.

Although split-plot experiments are encountered in many industrial settings, the literature for second-order response surface designs usually assumes a completely randomized design. By choosing the correct design for response surface experiments, the o..

Restricting the randomization of hard-to-change factors in industrial experiments is often performed by employing a split-plot design structure. From an economic perspective, these designs minimize the experimental cost by reducing the number of resets of the hard-to- change factors. In this paper, unbalanced designs are considered for cases where the subplots are relatively expensive and the experimental apparatus accommodates an unequal number of runs per whole-plot. We provide construction methods for unbalanced second-order split- plot designs that possess the equivalence estimation optimality property, providing best linear unbiased estimates of the parameters; independent of the variance components. Unbalanced versions of the central composite and Box-Behnken designs are developed. For cases where the subplot cost approaches the whole-plot cost, minimal point designs are proposed and illustrated with a split-plot Notz design.

Practical restrictions on randomization are commonplace in industrial experiments due to the presence of hard-to-change or costly-to-change factors. Using a split-plot design (SPD) structure reduces the number of times that these hard-to-change factors are reset during the experiment. A class of second-order response surface SPDs has been proposed in which the ordinary least squares estimates of the model are equivalent to the generalized least squares estimates. Equivalent estimation designs provide best linear unbiased estimates that are independent of the variance components and can be obtained with standard statistical software. Moreover, design selection is robust to model misspecification and does not require previous knowledge of the variance components. This article expands the conditions to obtain equivalent estimation designs and outlines two systematic design construction techniques for building balanced versions of the central composite design. In addition, it presents an approach to generatin...

The reliability of products and processes will become increasing important in the near future. One definition of reliability is “quality over time.” Customers increasing will make their purchasing decisions on how long they can expect their products and processes to deliver high quality results. As a result, there will be increasing demands for manufacturers to design appropriate experiments to improve reliability. This paper begins with a review of the current practice for planning reliability experiments. It then reviews some recent work that takes into proper account the experimental protocol. A basic issue is that most reliability engineers have little training in planning experiments while most experimental design experts have little background in reliability data.

The origins of quality engineering are in manufacturing, where quality engineers apply basic statistical methodologies to improve the quality and productivity of products and processes. In the past decade, people have discovered that these methodologies are effective for improving almost any type of system or process, such as financial, health care, and supply chains. This paper begins with a review of key advances and trends within quality engineering over the past decade. The second part uses the first part as a foundation to outline new application areas for the field. It also discusses how quality engineering needs to evolve in order to make significant contributions to these new areas. © 2015 The Authors Quality and Reliability Engineering International Published by John Wiley & Sons Ltd.