Quality by process control

"semiparametrics and statistical process control"

In Statistical Process Control (SPC) the most important problem is the current c ontrol situation. In statistical terms this problem reads as follows. Realisatio ns of independent random variables are observed. At the current timepoint k, whe n k (groups of) observations are available, the question is if there has occurre d a change in the distribution of corresponding random variables. If not, the pr ocess generating the random variables is called in control; if a change has occu rred it is called out of control (at timepoint k). Any procedure answering the a bove question can be formulated as a stopping rule for the process.
The classical solution for this current control problem is the Shewhart control chart, in which averages are registered and in which the process is stopped if a verages go outside limits. This solution relies heavily on the assumption of nor mality, cf. Does and Schriever (1992). The basic model of independent, normally distributed observations is prominent in most textbooks on control charts. In ap plications, control charts have to be tailored to the nature of the process. Cha rting individual measurements instead of averages occurs very frequently in prac tice. In Roes, Does and Schurink (1993) charts for individual measurements are d iscussed. Also the presence of multiple components of variation as process inher ent variation is usually standard in many applications. Methods have been propos ed for this situation by Roes and Does (1995).
Today's manufacturing hardly resembles the high volume production environment at the time of introduction of control charting methods. Low volume manufacturing requires adapted control charting methods. Some results have been derived by Roe s, Does and Stam (1995).
All the situations mentioned rely on the assumption of normality. However, in pr actice distributions are definitely not normal. Therefore, it makes sense to dro p the assumption of normality and to develop semiparametric theory for these SPC -problems. In semiparametrics many important models have been studied and quite some asymptotic theory (sample sizes growing beyond limits) has been developed, cf. Bickel, Klaassen, Ritov and Wellner (1993). This theory is very well apllica ble in situations with large sample sizes, e.g. time series models for exchange rates, and simulations suggest good performance for moderate sample sizes in e.g . the symmetric location model.
The key topic of the proposed research is the question: - Can semiparametrics yield improved procedures for the current control problem in SPC? More specific questions would be: - Which statistics should be used in semiparametric Shewhart control charts? - How should control limits be chosen? Research in this area, leading to answers to the above questions, is quite ambit ious and a little bit risky. Typically sample sizes are small in SPC and big in semiparametrics and even under the assumption of normality the present mathemati cal statistical theory is quite hard.
References
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For more information, please contact Prof. dr Ronald J.M.M. Does or Dr Kit C.B. Roes at
rjmmdoes@wins.uva.nl or kitroes@wins.uva.nl .