ENBIS-17 in Naples

9 – 14 September 2017; Naples (Italy) Abstract submission: 21 November 2016 – 10 May 2017

Control Charts on Dependent Streams

12 September 2017, 19:00 – 19:20

Abstract

Submitted by
moshe pollak
Authors
Moshe Pollak (The Hebrew University of Jerusalem and Israel Central Bureau of Statistics)
Abstract
Consider a process that produces a series of independent vectors. A change in an underlying state may become manifest in a modification of one or more of the marginal distributions. Often, the dependence structure between coordinates is unknown, impeding surveillance based on the joint distribution. A popular approach is to construct control charts for each coordinate separately and raise an alarm the first time any (or some) of the control charts signals. The difficulty is obtaining an expression for the overall average run length to false alarm (ARL2FA).

We argue that despite the dependence structure, when the process is in control, for large ARL's to false alarm, run lengths of parallel Cusum-type control charts are asymptotically independent. Furthermore, often, in-control run lengths are asymptotically exponentially distributed, enabling uncomplicated asymptotic expressions for the ARL2FA. We prove this assertion for certain Cusum- and Shiryaev-Roberts-type control charts and illustrate it by simulations.
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