An approximation procedure of quantiles using an estimation of kernel method for quality control

Author: Hasu Vesa   Halmevaara Kalle   Koivo Heikki  

Publisher: Taylor & Francis Ltd

ISSN: 1048-5252

Source: Journal of Nonparametric Statistics, Vol.23, Iss.2, 2011-06, pp. : 399-413

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Abstract

Testing measurements against quantiles of their distributions is a basic quality control technique. Unfortunately, the methods for the empirical quantile computation require usually ordered observations, which is not feasible for on-line use in large systems. This paper proposes a procedure for approximation of quantiles from a random sample of observations. The procedure is applicable on-line without exhaustive database searches, and it enables also approximation of high quantiles and nonstationary distributions. Our approach is based on using a linear approximation of the kernel smoothed quantile estimation for the cumulative distribution function. We apply the procedure in the quality control of temperature measurement with a tail frequency estimation approach.