Oct 11

3:30 pm

## A Likelihood Approach to Control Charts

### Moshe Pollak (Joint with NRCSE)

Seminar

The Hebrew University of Jerusalem - Department of Statistics

Some of the basic problems underlying the application of classical control charts are:

1. The process being observed is multivariate, and applying separate surveillance schemes to each variable separately is impractical.

2. Baseline pre-change parameter values are not really known, and a large enough learning sample cannot be obtained readily. Consequently, true ARL's may deviate considerably from nominal ones.

3. Often one does not know in advance what the direction and magnitude of a change will be, ignorance of which may seriously affect the efficiency of a scheme. This is especially true in a multivariate setting.

4. A change may be gradual, whereas classical surveillance schemes are usually designed for detecting an abrupt change.

5. The nature of the data may be completely unknown, suggesting a need for nonparametric surveillance schemes.

6. Often, the observations in a process are dependent, whereas classical surveillance schemes are designed for sequences made up of independent variables.

The last decade has seen advances on these fronts. A central idea underlying some of these advances is the construction of appropriate likelihood ratios and the exploitation of their statistical characteristics. For example, Cusum and other schemes can be viewed as likelihood-ratio based. Extension of this view to settings more complicated than the classical simple changepoint problem yields reasonably efficient procedures for the more complicated cases.

In this talk, this basic idea will be illustrated, and its implementation to some of the problems listed above will be given. Time permitting, applications will be presented (such as an analysis of global warming data, and/or an application to mass calibration at the National Institute of Standards and Technology).