Computations for Plug-In Intervals
This section describes the computations for the plug-in intervals in the Reliability Forecast platform. The plug-in interval uses the estimate of the reliability forecast in place of the true parameter to compute the interval. The interval is based on lower and upper percentiles of the distribution of the estimate. Plug-in intervals do not take into account the uncertainty of the parameter estimate. This type of interval provides an exploratory tool to evaluate the variability associated with the forecast. The intervals are appropriate for actual forecasting, assuming that the parameter estimate is accurate.
The point estimates for the sequential and cumulative forecasts are nonidentical binomial random variables. Because the theoretical percentiles are difficult to obtain, the percentiles that define the interval are approximated with a Poisson distribution.
To find the 100×αth percentile of the Poisson distribution, find the closest integer x that satisfies the following equation:
where X is a Poisson random variable.
For more information about computing plug-in intervals in a warranty forecasting system, see Liu and Wang (2013).