A Gray System Modeling Approach to the Prediction of Calibration Intervals

Abstract

This paper discusses a class of data-preprocessed statistical models for evaluating the optimal calibration interval of a measuring instrument. These models are based on the assumption that the calibration status of a measuring instrument can be predicted using the instrument's historical calibration data. On the basis of the gray threshold value prediction method, a series of historical calibration data are preprocessed so that a monotone-increasing series of data points will be created. Then, the first-order gray model, exponential regression, linear regression, and general polynomial regression are applied to fit the series of preprocessed data points to predict the time at which the measured value of the instrument will be outside of the allowable tolerance range. The effectiveness of each developed model was evaluated through the actual data collected in a calibration laboratory. Results demonstrate that the gray threshold value prediction based on second-order polynomial model, a modified autoregressive model, is the best method for forecasting the calibration interval of a measuring instrument.