Type i (α) error and arl performance of shewhart control chart with interpretation rules

The Shewhart Ẋ chart is very popular tool in practice usually supplemented with interpretation rules in order to detect the small shifts in the process mean. In this paper an EXCEL spread sheet model for the normal and gamma distributions were developed for the calculations of the type I (α) error and ARL performance of individual and combination of the Shewhart Ẋ control chart with most used seven interpretation rules. The EXCEL spread sheet model was than compared with SIMULA TION model developed in MA TLAB. The results show that the type I (α) error performance can be fairly high for particular rules 1, 4 and 6 when the underlying data is from a gamma distribution rather than normal distribution. It was also observed that the high type I (α) error and low ARL performance of gamma distribution is present when the combinations of rules were used.