George C. Runger

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..

GAUGE CAPABILITY AND DESIGNED EXPERIMENTS. PART I: BASIC METHODS

Important aspects of the data collection for gauge capability studies are discussed and recommendations are provided for the planning of a study. The connection between these studies and designed experiments to estimate components of variance is emphasi..

Gauge Capability Analysis and Designed Experiments. Part II: Experimental Design Models and Variance Component Estimation

This article discusses experimental design models for the classical gauge repeatability and reproducibility study. Both factorial and nested models are considered, and the conditions under which each model is appropriate are described. Point estimates a..

ADAPTIVE SAMPLING ENHANCEMENTS FOR SHEWHART CONTROL CHARTS

Adaptive sampling is an enhancement to a classical statistical process control scheme in which the time between samples from the process is varied based on the available information. Unlike the classical Shewhart control schemes, the performance of an adaptive sampling scheme for detecting a process which is off-target before the First observation is selected can differ from the steady-state performance, which is the performance of the scheme for detecting a process shift after the control scheme has been operating for some time. Often steady-state performance is the more important criterion for evaluating statistical process control schemes. Previous work has considered initial performance and steady-state performance, but the charts examined were optimized for initial performance. The development of charts optimized for steady-state performance and a comparison to previously developed schemes are the topics of this paper. Tables providing performance information on adaptive schemes are included.

The threshold bootstrap: a new approach to simulation output analysis

The threshold bootstrap (TB) is a promising new method of inference for a single autocorrelated data series, such as the output of a discrete event simulation. The method works by resampling runs of data created when the series crosses a threshold level, such as the series mean. We performed a Monte Carlo evaluation of the TB using three types of data: white noise, first-order autoregressive, and delays in an M/M/1 queue. The results show that the TB produces accurate and tight estimates of the standard deviation of the sample mean and valid confidence intervals.

Statistical process control using level crossings

Conventional SPC methods do not adequately cope with autocorrelated processes. We develop a new method based on the random run lengths created when a process crosses a threshold level. We combineinformation on runs above and below the threshold into a statistic that can be treated as iid Normal and monitored with traditional SPC methods, such as Shewhart charts. The method is simpler than alternative approaches based on ARMA modeling, works without modification for both lid and autocorrelated processes, is robust to the marginal distribution of the data. and performs well compared to Shewhart charts based on ARMA residuals.

Statistical process control using run sums

We develop a novel and effective way to monitor quality using the large volumes of positively autocorrelated data produced by high-frequency sampling of a process. We regard the process as a sequence of runs above and below the mean. The sums of the observations in these runs behave as independent random variables suitable for charting. Using simulated data, we show that the average run length performance of charts based on run sums compares favorably to that of alternative charts based on ARMA residuals, while avoiding the need for ARMA modeling. Furthermore, we obtained the same relative performance results for iid data. Thus, run sum charts provide a powerful and comprehensive method for SPC in data-rich environments.

Most powerful invariant permutation tests

For testing that a distribution is invariant under the action of a finite group (e.g., the distribution is exchangeable) a most powerful test, against a specific alternative, among the class of tests invariant under a second, arbitrary group is obtained. After a class of permutation tests suitable for multivariate testing problems is described, application is made to a multivariate, nonparametric, two-sample problem.

ROBUSTNESS OF VARIANCE ESTIMATES FOR BATCH AND CONTINUOUS PROCESSES

The complexity of a hierarchical process structure containing nested and crossed factors is an important concern for estimating variability. This article considers the effects of such a structure on traditional estimates and recommends sampling strategi..