A hierarchical approach to the study of the exponential failure model

The exponential failure model is studied from the hierarchical point of view. The parameter of the exponential is considered as a random variable with a gamma function as a prior. Futhermore, the scale parameter of the gamma prior isassumed to be a random variable with known hyperprior. Under these assumptions estimators are derived for the exponential parameter and reliability function. Monte Carlo simulation is utilized to compare the various estimators.