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02/05/2012, 14:30 — 15:30 — Room P3.10, Mathematics Building

Manuel Cabral Morais, *Departamento de Matemática - CEMAT - IST*

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On the Aging Properties of the Run Length of Markov-Type Control
Charts

A change in a production process must be detected quickly so
that a corrective action can be taken. Thus, it comes as no
surprise that the run length (RL) is usually used to describe the
performance of a quality control chart.

This popular performance measure has a phase-type distribution
when dealing with Markov-type charts, namely, cumulative sum
(CUSUM) and exponentially weighted moving average (EWMA) charts, as
opposed to a geometric distribution, when standard Shewhart charts
are in use.

In this talk, we briefly discuss sufficient conditions on the
associated probability transition matrix to deal with run lengths
with aging properties such as new better than used in expectation,
new better than used, and increasing hazard rate.

We also explore the implications of these aging properties of
the run lengths, namely when we decide to confront the in control
and out-of-control variances of the run lengths of matched in
control Shewhart and Markov-type control charts.

#### Keywords

Phase-type distributions; Run length; Statistical process
control; Stochastic ordering.

#### Bibiography

Morais, M.C. and Pacheco, A. (2012). A note on the aging
properties of the run length of Markov-type control charts.
Sequential Analysis 31, 88-98.