A control chart for variance based on squared ranks |
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Authors: | Elena Cristina Villanueva-Guerra Vìctor Gustavo Tercero-Gómez William Jay Conover |
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Institution: | 1. School of Engineering and Sciences, Tecnologico de Monterrey, Monterrey, México;2. Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, USA |
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Abstract: | A nonparametric control chart for variance is proposed. The chart is constructed following the change-point approach through the recursive use of the squared ranks test for variance. It is capable of detecting changes in the behaviour of individual observations with performance similar to a self-starting CUSUM chart for scale when normality is assumed, and a relatively better power when assessing nonnormal observations. A comparison is also made with two equivalent nonparametric charts based on Mood and Ansari-Bradley statistics. When dealing with symmetrical distributions, the proposed chart shows smaller (better) out-of-control average run length (ARL), and a competing performance otherwise. In addition, sensitivity to changes in mean and variance at the same time was tested. Extensive Monte Carlo simulation was used to measure performance, and a practical example is provided to illustrate how the proposed control chart can be implemented in practice. |
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Keywords: | Squared ranks test nonnormal SPC change-point self-starting |
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