Contributed Session: Control Charts in Advanced SPC
ARL-Unbiased Control Charts for Monitoring the Fraction of Nonconforming Units
Cesar A. Acosta-Mejia
The fraction of nonconforming units p of a process is commonly monitored by a Shewhart chart. It is assumed that the number of nonconforming units in a subgroup is approximately normal. In practice p can be expected to be so small that this approximation might fail even for large subgroup sizes. When the approximation is not accurate the performance of the chart is poor.
To correct this problem researchers have suggested the use of probability limits such that it would be equally likely for a false alarm to happen on either side of the control chart. This practice is not optimal. By establishing specific probabilities of false alarm for increases and for decreases a better performance can be achieved.
This paper introduces the class of ARL-unbiased control charts for monitoring the fraction of nonconforming units. The ARL is defined as the expected number of subgroups until the chart signals a shift in the monitored parameter. To evaluate the performance of these charts, several control charts are compared. This comparison includes the p chart with probability limits, the geometric chart proposed by Calvin (1983), the CUSUM chart for p, and the CUSUM chart based on an arcsin transformation as suggested by Ryan (1989).
[Cesar A. Acosta-Mejia, Instituto Tecnologico Autonomo de Mexico, Departamento de Administracion, Rio Hondo 1, Mexico D.F. 01000, MEXICO; firstname.lastname@example.org ]
The Effect of Autocorrelation in the Multivariate T-Squared Control Chart
T squared control chart is often employed to control simultaneously several related quality characterisitics of a process due to its simplicity. Moreover the overall Type I error can be exactly fixed and this chart yields a more powerful scheme to detect a shift in the process in comparison with the simultaneous use of univariate charts, e.g. Shewhart charts.
The effect of autocorrelation in the T squared chart is studied in this work showing the changes in the ARL when the process is in control and out of control. Also a comparison of the effect of autocorrelation in the T squared chart with the equivalent scheme constituted by simultaneous Shewhart charts is given. Some examples of application are shown.
[Francisco Aparisi, Departamento de Estadistica, ETS Ingenieros Agronomos, Universidad Politecnica de Valencia, 46020 Valencia, SPAIN; email@example.com ]
A Nonparametric Control Chart for Multivariate Data
This paper presents a nonparametric method of control charting that applies to both univariate and multivariate data. This method transforms a sample of d-dimensional data into one-dimensional statistics by using techniques such as kernel density estimation. Changes in the distribution of the data are then detected using nonparametric rank tests. A simulation study in one and two dimensions suggests that this method is able to detect rather general changes, including some scenarios that are difficult for standard procedures. An encouraging aspect of this study is that the new procedure also performs well in simpler problems that might be expected to favor the more standard charts, such as shifts in location and changes within a Gaussian family. The method is easily implemented, and its performance seems quite insensitive to various choices that must be made by the user.
[R.D. Fricker, Jr., Dept. of Statistics, Yale Univ., P.O. Box 208290, New Haven, CT 06520 USA; firstname.lastname@example.org ]
Multivariate Control Charts Based on Data Depth
Regina Y. Liu
Based on the concept of data depth, we have introduced several new control charts for monitoring processes of multivariate quality measurements. For any dimension of the measurements, these charts are in the form of two-dimensional graphs which can be visualized and interpreted just as easily as the well-known univariate X-, bar X-, and CUSUM-charts. Moreover they have the following significant advantages. First, they can detect simultaneously the location shift and scale increase of the process, unlike the existing methods which can only detect the location shift. Second, their construction is completely nonparametric. In particular, it does not require the assumption of normality for the quality distribution which was needed in standard approaches such as the chi^2- or Hotelling's T^2- charts. Thus these new charts generalize the principle of control charts to multivariate settings and apply to a much broader class of quality distributions.
[Regina Y. Liu, Dept. of Statistics, Rutgers Univ., Hill Center, Piscataway, NJ 08855, USA; email@example.com ]
Date created: 6/5/2001