Kvadratická kalibrace

Calibration is a set of tasks which gives relationship between the reference device and the calibrated device (if some special conditions are realized). This relationship is described by the calibration function and represented by the calibration curve. In the contribution we assume that the calibration curve is a parabola. So we focus on the quadratic calibration. We use the maximum likelihood method and method based on linearized errors-in-variables model and Kenward-Rogers type approximation for obtaining the calibration curve. Both method will be presented and compared. Calibration process can be divided into two parts: 1) creation of the calibration model (calibration of the device), 2) application (use) of the calibration model (measuring by calibrated device). In the contribution we estimate parameters of the calibration function and their confidence region by both above mentioned methods and we also show the use of the calibration curve in the measuring process. At the conclusion both methods will be compared in a small simulation study. Programs used for the simulation study are programmed in software Matlab. We assume that we measure m different objects by two different devices with different precision (we assume that device A is less precise than device B). Each measurement is n-times repeated. It is assumed that measured values on both devices are realizations of independent random variables with normal distribution and the calibration curve is a quadratic function.

Simulace

simulations

programs

Programy v Matlabu

odhad parametrů a,b,c pomocí metody nejmenších čtverců

generování náhodné matice m x n s normálním rozdělením

Metoda maximální věrohodnosti

logaritmická věrohodnostní funkce

výpočet odhadu vektoru parametrů

empirické pokrytí

konfidence5

graf pásu spolehlivosti

graf zorbazující interval spolehlivosti pro hodnotu x

Replikovaný model

minque2

empirické pokrytí

konfidence

graf pásu spolehlivosti

graf zorbazující interval spolehlivosti pro hodnotu x

Srovnání

graf porovná intervaly spolehlivosti pro hodnotu x

Polynomická kalibrace

simulační studie

Metoda maximální věrohodnosti

logaritmická věrohodnostní funkce

výpočet odhadu vektoru parametrů

empirické pokrytí

konfidence5

graf pásu spolehlivosti

graf zorbazující interval spolehlivosti pro hodnotu x

pás

MITAV 2017

funkce použité pro simulace v článku

funtion used for simulation to postconference proceedings

Data

dotaznik