Type I(α) error performance of Shewhart control chart with interpretation rules

The Shewhart (X) over bar chart usually supplemented with interpretation rides in order to detect the small shifts in the process mean is very popular tool in practice. The interpretation rules also increase the probability of type I (alpha) error, even though theme rides are considered to be valuable in detecting the trite problems. In this paper an EXCEL spread sheet model for the normal and gamma distributions were developed for the calculations of the type I (alpha) error performance of individual and combination of the Shewhart (X) over bar control chart with most used seven interpretation rides. The EXCEL spread sheet model was than compared with SIMULATION model. The results show that the type I (alpha) error performance can be fairly high for particular rules 1, 4 and 6 when the underlying data from a gamma distribution rather than normal distribution. It was also observed that the type I (alpha) error performance of gamma distribution is fairly high when the combinations of rides were used.