Calculating ARL and Other Control Chart Performance Measures – Numerics and Software
Sven Knoth
Institute of Mathematics and Statistics, School of Economics and Social Sciences, Helmut Schmidt University, Hamburg, Germany

There is a long tradition in SPC (or change point, surveillance etc.) literature in calculating performance measures such as the legendary Average Run Length (ARL). Statistics software, however, only seldom contains related algorithms. Especially SPC software offers almost always just simple ones or even no algorithms at all. In this talk, a comprehensive overview on numerical algorithms (different variants of the Nyström method and collocation for solving the ARL integral equation, survival function series, …) will be given. Additionally, the R package spc will be presented. That package provides a set of functions to calculate the ARL, the steady-state ARL, and other measures for different SPC schemes (control charts).

Keywords: SPC; ARL; Nyström method; R library

Biography: Sven Knoth studied Mathematics and got a MSc and PhD in Statistics. After about 10 years in biostatistics and statistics in economics at the universities of Düsseldorf and Frankfurt/Oder he worked for 5 years as SPC engineer in the semiconductor industry. He returned in 2009 to academia and works now as Professor at the Helmut Schmidt University in Hamburg.