This section describes the computations for the prediction intervals in the Reliability Forecast platform. Unlike plug-in intervals, prediction intervals take into account the parameter estimate variability. The computations for prediction intervals depend on the setting of the Use Approximate Distribution option.
When the Use Approximate Distribution option is selected, the Poisson distribution is used to approximate the sequential and cumulative forecasts. A simulation generates empirical distributions for the sequential and cumulative forecasts. This empirical distribution is then used to define the prediction intervals based on lower and upper quantiles. This method is appropriate when the rule of thumb of using Poisson approximation is satisfied.
For more information about computing prediction intervals in a warranty forecasting system, see Liu and Wang (2013).