SENSITIVITY ANALYSIS ON THE CUSUM METHOD

The cumulative sum (CUSUM) control chart is considered to be an altern ative or complementary to Shewhart control charts in statistical proce ss control (SPC) applications, owing to its higher sensitivity to smal l shifts in the process mean. It utilizes all the available data rathe r than the last few ones used in Shewhart control charts for quick dec ision making. The CUSUM method assumes that the process is stable and under control. In addition, the variability of the process should be w ell below when compared to the specification limits, i.e. the process must have a high capability ratio to permit variations in the mean of the process without affecting the quality of the product or operations . In this manner, the practical purpose of the CUSUM method is not rea lly to verify whether the process is out of control or meets the speci fication limits, but for analyzing the shift in the process mean, stre ssing the aspects such as performance, productivity, cost, etc. The se nsitivity analysis conducted on the CUSUM method establishes that it i s not effective in a certain range of shifts in the mean of the proces s. The analysis on effects of shift in the mean and type-I error on th e effectiveness of the method shows that the CUSUM does not predict th e existence of shift in the process mean when the real shift is much h igher than the shift that is being searched for its existence. A compu tational program has been developed for calculating the minimum value of alpha (type-I error) given certain values of the shift in the mean. With these results it is possible to observe that, for a given value of alpha, the CUSUM method may not detect a shift in the mean greater than the value of the expected shift.