ISTAB takes advantage of the statistical nature of processes by comparing the observed average run length (OARL) to the expected run length (ARL), resulting in a gap value called the ISTAB index. The ISTAB index has three characteristic behaviors that are indicative of defects in an SPC instance.
Case 1: The observed average run length is excessively long relative to expectation. ISTAB > 0 is indicating the possibility that the limits are too wide.
Case 2: The observed average run length is consistent with expectation. ISTAB near zero is indicating that the process is stable.
Case 3: The observed average run length is inordinately short relative to expectation. ISTAB < 0 is indicating that the limits are too tight, the process is unstable or both.
The probability distribution of run length is the basis for establishing an ARL. We demonstrate that the geometric distribution is a good approximation to run length across a wide variety of rule sets. Excessively long run lengths are associated with one kind of defect in an SPC instance; inordinately short run lengths are associated with another. A sampling distribution is introduced as a way to quantify excessively long and inordinately short observed run lengths. This paper provides detailed guidance for action limits on these run lengths. ISTAB as a statistical method of review facilitates automated instability detection.
This paper proposes a management system based on ISTAB as an enhancement to more traditional SPC approaches.