Numerical Experiments on the Application of Markov Chain Monte Carlo for the Establishment of Calibration Intervals

Abstract

This study presented a new approach for conducting measurement reliability analysis and establishing calibration intervals based on Markov chain Monte Carlo (MCMC). Calibration records following the Weibull and lognormal reliability models were generated under various calibration conditions, and they were used to test the validity of the method proposed in this study. Numerical experiments were used to obtain the estimates for the measurement reliability model, and the optimum calibration interval was obtained for the simulated calibration records. The results showed that the measurement reliability models obtained using the MCMC method were consistent with those obtained using the S3 method, which is considered to be the most advanced approach. In particular, both methods exhibited strong agreement in the estimation of calibration records simulated under the renew-if-failed policy. The MCMC method allows sampling to estimate the distribution, and this feature can be employed to calculate the uncertainty of the measurement reliability model and the optimal calibration interval. This uncertainty provides the reliability of the estimation and is expected to help manage the risk of establishing the calibration interval and maintaining measurement quality.