Joseph J. Pignatiello

STRATEGIES FOR ROBUST MULTIRESPONSE QUALITY ENGINEERING

Virtually every manufactured product has more than one characteristic by which its overall quality is determined. Since those quality characteristics may be correlated, some changes in the levels of the controllable product design and process design variables may improve one of the quality characteristics while adversely affecting one or more of the other quality characteristics. In this paper we define a quadratic loss function for use with multiple quality characteristics. We discuss several strategies that could be employed for robust quality engineering of products and processes when there is more than one quality characteristic of interest.

Comparisons of Multivariate CUSUM Charts

We consider several distinct approaches for controlling the mean of a multivariate normal process including two new and distinct multivariate CUSUM charts, several multiple univariate CUSUM charts, and a Shewhart x2 control chart. The performances of th..

Adaptive Sampling for Process Control

Statistical process control procedures typically entail monitoring the process by selecting rational subgroups of equal size at equal time intervals. A generalization of this standard paradigm removes the restriction of equal waiting times between subgr..

IDENTIFYING THE TIME OF A STEP-CHANGE WITH X 2 CONTROL CHARTS

A maximum likelihood estimator is proposed for the time of a step-change in a multivariate process mean when the observations follow a multivariate Normal distribution. The estimator can be used to identify the change point when a multivariate x(2) cont..

ESTIMATION OF THE CHANGE POINT OF A NORMAL PROCESS MEAN IN SPC APPLICATIONS

Knowing when a process has changed would simplify the search for and the identification of the special cause. In this paper, we compare the maximum likelihood estimator of the process change point (that is, when the process changed) to built-in change point estimators from CUSUM and EWMA control charts. We conclude that it is better to use the maximum likelihood change point estimator when a CUSUM or EWMA control chart signals a change in the process mean. We also present an approach based on the likelihood function for estimating a confidence region for the process change point. We study the performance of this estimator when it is used with the Shewhart X̄ control chart, the CUSUM control chart, and the EWMA control chart. The results show that the estimator provides process engineers with an accurate and useful estimate of the time of the process change.

An Overview of the Strategy and Tactics of Taguchi

Abstract The methods of Taguchi have received considerable attention in recent years. Part of the attention is due to the success of Genichi Taguchi and his colleagues and part of the attention is due to the mystique and controversy surrounding these methods. In this paper we discuss two separate aspects of the Taguchi method: the strategy of Taguchi and the tactics of Taguchi. The Taguchi tactics involve the specific methods and techniques recommended by Taguchi such as the use of signal-to-noise ratios and the so-called Taguchi designs. We discuss the parameter design strategy of Taguchi for designing and improving products and processes from a statistical point of view. We point out that although there are some apparent flaws in Taguchis tactics, the basic strategy is a sound one.

A Genetic Algorithm Approach to Multiple-Response Optimization

Many designed experiments require the simultaneous optimization of multiple responses. A common approach is to use a desirability function combined with an optimization algorithm to find the most desirable settings of the controllable factors. However, as the problem grows even moderately in either the number of factors or the number of responses, conventional optimization algorithms can fail to find the global optimum. An alternative approach is to use a heuristic search procedure such as a genetic algorithm (GA). This paper proposes and develops a multiple-response solution technique using a GA in conjunction with an unconstrained desirability function. The GA requires that several parameters be determined in order for the algorithm to operate effectively. We perform a robust designed experiment in order to tune the genetic algorithm to perform well regardless of the complexity of the multiple-response optimization problem. The performance of the proposed GA method is evaluated and compared with the performance of the method that combines the desirability with the generalized reduced gradient (GRG) optimization. The evaluation shows that only the proposed GA approach consistently and effectively solves multiple-response problems of varying complexity.

A comparison of control charting procedures for monitoring process dispersion

We consider several control charts for monitoring normal processes for changes in dispersion. We present comparisons of the average run length performances of these charts. We demonstrate that a CUSUM chart based on the likelihood ratio test for the change point problem for normal variances has an ARL performance that is superior to other procedures. Graphs are given to aid in designing this control chart.

IDENTIFYING THE TIME OF A STEP CHANGE IN A NORMAL PROCESS VARIANCE

Information concerning the time of a process change is valuable to process engineers since it can simplify their search for the special cause. In this article we propose an estimator of the time of a step change in the variance of the normal process. Th..

Statistical Process Monitoring of Nonlinear Profiles Using Wavelets

Many modern industrial processes are capable of generating rich and complex data records that do not readily permit the use of traditional statistical process-control techniques. For example, a “single observation” from a process might consist of n pairs of (x, y) data that can be described as y = f (x) when the process is in control. Such data structures or relationships between y and x are called profiles. Examples of profiles include calibration curves in chemical processing, oxide thickness across wafer surfaces in semiconductor manufacturing, and radar signals of military targets. In this paper, a semiparametric wavelet method is proposed for monitoring for changes in sequences of nonlinear profiles. Based on a likelihood ratio test involving a changepoint model, the method uses the spatial-adaptivity properties of wavelets to accurately detect profile changes taking nearly limitless functional forms. The method is used to differentiate between different radar profiles and its performance is assessed with Monte Carlo simulation. The results presented indicate the method can quickly detect a wide variety of changes from a given, in-control profile.