TY - BOOK
T1 - Empirical nonparametric control charts
T2 - estimation effects and corrections
AU - Albers, Willem
AU - Kallenberg, Wilbert C.M.
PY - 2002
Y1 - 2002
N2 - Due to the extreme quantiles involved, standard control charts are very sensitive to the effects of parameter estimation and nonnormality. More general parametric charts have been devised to deal with the latter complication and corrections have been derived to compensate for the estimation step, both under normal and parametric models. The resulting procedures offer a satisfactory solution over a broad range of underlying distributions. However, situations do occur where even such a larger model is inadequate and nothing remains but to consider nonparametric charts. In principle these form ideal solutions, but the problem is that huge sample sizes are required for the estimation step. Otherwise the resulting stochastic error is so large that the chart is very unstable, a disadvantage which seems to outweigh the advantage of avoiding the model error from the parametric case. Here we analyze under what conditions nonparametric charts actually become feasible alternatives for their parametric counterparts. In particular, corrected versions are suggested for which a possible change point is reached at sample sizes which are markedly less huge (but still larger than the customary range). These corrections serve to control the behavior during in-control (markedly wrong outcomes of the estimates only occur sufficiently rarely). The price for this protection clearly will be some loss of detection power during out-of-control. A change point comes in view as soon as this loss can be made sufficiently small.
AB - Due to the extreme quantiles involved, standard control charts are very sensitive to the effects of parameter estimation and nonnormality. More general parametric charts have been devised to deal with the latter complication and corrections have been derived to compensate for the estimation step, both under normal and parametric models. The resulting procedures offer a satisfactory solution over a broad range of underlying distributions. However, situations do occur where even such a larger model is inadequate and nothing remains but to consider nonparametric charts. In principle these form ideal solutions, but the problem is that huge sample sizes are required for the estimation step. Otherwise the resulting stochastic error is so large that the chart is very unstable, a disadvantage which seems to outweigh the advantage of avoiding the model error from the parametric case. Here we analyze under what conditions nonparametric charts actually become feasible alternatives for their parametric counterparts. In particular, corrected versions are suggested for which a possible change point is reached at sample sizes which are markedly less huge (but still larger than the customary range). These corrections serve to control the behavior during in-control (markedly wrong outcomes of the estimates only occur sufficiently rarely). The price for this protection clearly will be some loss of detection power during out-of-control. A change point comes in view as soon as this loss can be made sufficiently small.
KW - MSC-62G15
KW - MSC-62P30
KW - ME
M3 - Report
T3 - Memorandum
BT - Empirical nonparametric control charts
PB - University of Twente
CY - Enschede
ER -