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

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.

Keywords:

• quantile approximation
• kernel methods
• recursive methods
• quality control

MSC 2000 Subject Classifications :

• 62G05
• 62P30
• 62E17