Interpretation & Calculations
A V-mask is used to determine whether the process mean has drifted from the target. Subgroups with missing data are not included in the analysis (i.e. the subgroup sample size, n, must be constant for all subgroups). The performance of the control chart is influenced by the design of the V-mask, which are used to define the CuSum control limits . The design parameters of the V-mask are the angle (q), which sets the size of the V, and the distance (d), which sets the location of the vertex of the V from the current subgroup. The user influences the value of these parameters by specifying:
1. alpha (a): the probability of incorrectly concluding that a shift in the process mean has occurred (i.e. a false alarm),
2. beta (b): the probability of failing to detect a shift in the process mean, and
3. Amount of Concern: the shift in the process mean that the user desires to detect. Delta must be expressed in the same units as the measurements.
An interesting property of the Cu Sum V-mask is its ability to detect when a shift occurred. With any control chart, if you are collecting and analyzing data and a process shift occurs, it may be several groups before the shift is detected as a group out of control. The Cu Sum chart V-mask will tend to indicate when the out of control condition originated. For example, if the shift really begins at group 40, the first out of control condition may occur when group 45 is collected, but the Cu Sum chart may indicate at that time that group 40 is out of control.
Run test rules are never applied to a Cu Sum chart, since the plotted points are inherently dependent, containing common points. Never consider the points on the Cu Sum chart relative to specifications, since the observations from the process vary much more than the cumulative sum.
If the process shows control relative to the statistical limits for a sufficient period of time, then we can analyze the process capability relative to requirements. Process capability is only meaningful when the process moving averages are stable, since we cannot predict the outcome of an unstable process.
Learn more about the SPC principles and tools for process improvement in Statistical Process Control Demystified (2011, McGraw-Hill) by Paul Keller, in his online SPC Concepts short course (only $39), or his online SPC certification course ($350) or online Green Belt certification course ($499).