%0 Journal Article
%T An efficiency comparison of control chart for monitoring process variance: Non-normality case
%A Sangkawanit
%A R.
%A Budsaba
%A K.
%J Songklanakarin Journal of Science and Technology
%D 2005
%I Songkla University
%X The purposes of this research are to investigate the relation between upper control limit and parameters of weighted moving variance linear weight control chart (WMVL), weighted moving variance: exponential weight control chart (WMVE ), successive difference cumulative sum control chart (Cusum-SD) and current sample mean cumulative sum control chart (Cusum-UM) and to compare efficiencies of these control charts for monitoring increases in process variance, exponentially distributed data with unit variance and Student's t distributed data with variance 1.071429 (30 degrees of freedom) as the in control process. Incontrol average run lengths (ARL0) of 200, 400 and 800 are considered. Out-of-control average run lengths (ARL1) obtained via simulation 10,000 times are used as a criteria.The main results are as follows: the upper control limit of WMVL has a negative relation with moving span while the upper control limit of WMVE has a negative relation with moving span and a positive relation with exponential weight. Both the upper control limits of Cusum-SD and Cusum-UM have a negative relation with reference value in which such relation looks like an exponential curve.The results of efficiency comparisons in case of exponentially distributed data for ARL0 of 200, 400 and 800 turned out to be quite similar. When standard deviation changes less than 50%, Cusum-SD control chart and Cusum-UM control chart have ARL1 less than those of WMVL control chart and WMVE control chart. However, when standard deviation changes more than 50%, WMVL control chart and WMVE control chart have ARL1 less than those of Cusum-SD control chart and Cusum-UM control chart. The results are different from the normally distributed data case, studied by Sparks in 2003. In case of Student's t distributed data for ARL0 of 200 and 400 when process variance shifts by a small amount (less than 50%), Cusum- UM control chart has the lowest ARL1 but when process variance shifts by a large amount (more than 50%), WMVE control chart has the lowest ARL1. On the contrary, for ARL0 800, WMVE control chart has the lowest ARL1 when process variance shifts by a small amount (less than about 100%) and Cusum-UM control chart has the lowest ARL1 when process variance shifts by a large amount (more than 100%). The results are different from the normally distributed data case, studied by Sparks in 2003, though Student's t distribution is symmetried as is the normal distribution.
%K weighted moving variance
%K CUSUM
%K moving span
%K upper control limit
%K average run length
%U http://www.sjst.psu.ac.th/journal/27-6-pdf/18-variance.pdf