Ratchada Sangkawanit and Kamon Budsaba

pp. 1299 - 1310

Abstract

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%), CusumUM 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.

Keywords

• weighted moving variance
• CUSUM
• moving span
• upper control limit
• average run length