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The variable-dimension approach in multivariate SPC

Abstract:

With multivariate processes, it may happen that some quality variables are more expensive and/or difficult to measure than the other ones, or they may demand much more time to measure. Their measurement may even be destructive. For monitoring such processes, the variable dimension approach was recently proposed. The idea is to measure always (at each sampling time) the "non-expensive" variables and to measure the expensive ones only when the values of the non-expensive variables give some level of evidence that the the process may be out of control. The procedure bears much similarity with the one of variable parameters (or adaptive) control charts, but differs in that it is not the sample size or sampling interval or control limits that are made dynamically variable, but rather the very variables being measured (thus the denomination "variable dimension").We review and compare the several variants of the approach, the last one being an EWMA version. The approach may lead to significant savings in sampling costs (the savings depending, of course, on the ratio between the costs of measuring the "expensive" and the "inexpensive" variables). In many cases, the variable approach, contradicting the intuition, may also result in faster detection of special causes.