^{a}and Jørn Vatn

^{b}

^{a}xingheng.liu@ntnu.no

^{b}jorn.vatn@ntnu.no

Stochastic processes are widely used to describe continuous degradations, among which the monotonically increasing degradation is most common. However, in practice, the observed degradation path is often perturbed with undesired noise due to sensor or measurement errors. When the noise is Gaussian distributed with constant variance, different approaches such as Monte Carlo integral, Gibbs sampler, and Genz transform can be used to estimate model parameters. In this paper, we show the limitations of Genz transform and the consequences of its inappropriate use. We also improve the Gibbs sampler by proposing an enhanced rejection sampling algorithm. In the presence of noise, the calculation of likelihood functions involves multivariate normal integrals. Genz transform converts the original integration domain into a unit hypercube. Compared to the Monte Carlo integral, Genz transform is more efficient since it avoids sampling from the domain outside the integration limits. However, suppose during a time interval, the hidden degradation growth is negligible compared to the noise. In that case, we can prove that there is an accumulating error between the observed path and the sampled paths obtained using Genz transform, and the error cannot be eliminated once it appears. This results in an incorrect evaluation of the expected likelihood, biased estimates of model parameters, and erroneous prediction of the degradation growth.