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02/10/2013, 11:00 — 12:00 — Room P3.10, Mathematics Building

Manuel Cabral Morais, *CEMAT & Department of Mathematics, IST*

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Strategies to reduce the probability of a misleading signal

Standard practice in statistical process control is to run two
individual charts, one for the process mean and another one for the
process variance. The resulting scheme is known as a simultaneous
scheme and it provides a way to satisfy Shewhart's dictum that
proper process control implies monitoring both location and
dispersion.

When we use a simultaneous scheme, the quality characteristic is
deemed to be out-of-control whenever a signal is triggered by
either individual chart. As a consequence, the misidentification of
the parameter that has changed can occur, meaning that a shift in
the process mean can be misinterpreted as a shift in the process
variance and vice-versa. These two events are known as misleading
signals (MS) and can occur quite frequently.

We discuss (necessary and) sufficient conditions to achieve
values of PMS smaller than or equal to \(0.5\), explore, for
instance, alternative simultaneous Shewhart-type schemes and check
if they lead to PMS which are smaller than the ones of the popular
\((\bar{X}, S^2)\) simultaneous scheme.