Reliability estimation through the linear mixed effects model

The linear model with random intercept and random slope is considered to assess degradation and reliability of a component or a system. For the case of known variance and covariance components of the above model, bias and standard error (SE) of the estimator of the time-to-failure distribution are examined through the Taylor's series expansion, Gaussian quadrature method and the simulation procedure. The simulation procedure is also considered when the variance and covariance components are estimated. Information from practical situations is used to examine the biases and SEs.