Article

Chart for Monitoring Capability Using Sensitivity Data

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Abstract

A control chart is proposed for monitoring the capability of a process when sensitivity data is all that is available on a particular measure of interest, such as the threshold height at which a dropped bottle will break. Sensitivity data is data that is collected as either pass or fail of a sample at a certain level exposure to a control variable, such as drop height. Methodology is presented for selecting a certain quantile of the distribution of the measure of interest and monitoring that quantile with a standard p chart. The tradeoffs between increasing the power of the control chart and decreasing the number of measurements are explored. Introduction A special type of data, called sensitivity data, presents a unique set of problems for those wishing to monitor the performance of a process. Sensitivity data refers to data that is collected as a pass or fail of a sample at a certain level or intensity of exposure to a control variable. Dixon and Mood [1] originally presented this ...

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... Many researchers, both from academia and industry, have studied the use and misuse of various ratios in their respective disciplines. For example, Ankenman and McDaniel (2000) propose the use of the 'p' chart (i.e. the ratio of number of defectives to sample size) for monitoring the capability of a process when sensitivity data are all that are available on a particular measure of interest. Spisak (1990) talks about building a control chart for the ratio of two variables and estimating the bias in a ratio estimator. ...
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A class of sequential designs for estimating the percentiles of a quantal response curve is proposed. Its updating rule is based on an efficient summary of all of the data available via a parametric model. The logit-MLE version of the proposed designs can be viewed as a natural analog of the Robbins—Monro procedure in the case of binary data. It is shown to be asymptotically consistent, optimal, and nonparametric via its connection with the latter procedure. For certain choices of initial designs, the proposed method performs very well in a simulation study for sample sizes up to 35. A nonparametric sequential design, via the Spearman—Kärber estimator, for estimating the median is also proposed.
  • W J Dixon
  • A M Mood
Dixon, W. J., and Mood, A. M. (1948), "A Method for Obtaining and Analyzing Journal of the American Statistical Association, 60, 967-978.
Standard Test Method for Drop Impact Resis-About the Authors: William R. McDaniel is a doctoral can-tance of Blow-Molded Thermoplastic Containers, American didate in industrial engineering at Northwestern University His research interests include experimental design for the
  • Astm D
ASTM D2463, Standard Test Method for Drop Impact Resis-About the Authors: William R. McDaniel is a doctoral can-tance of Blow-Molded Thermoplastic Containers, American didate in industrial engineering at Northwestern University. Society for Standards and Testing, Philadelphia, 1974. His research interests include experimental design for the
Optimal Design for Percentile Estimation of a Quantal Optimal Design and Analysis of Experiments
  • C F J Wu
Wu, C. F. J. (1988), "Optimal Design for Percentile Estimation of a Quantal Optimal Design and Analysis of Experiments, Dodge, Y.,