The combined use of data and expert estimates in population variability analysis

Bayesian population variability analysis, also known as the first stage in two-stage Bayesian updating [IEEE Trans. Power Appar. Syst. PAS-102 (1983) 195] or hierarchical Bayes [Bayesian reliability analysis, 1991], is an estimation procedure for the assessment of the variability of reliability measures among a group of similar systems. Variability distributions resulting from this form of analysis find application as generic prior distributions in system-specific Bayesian reliability assessments. This paper presents an extension of the Bayesian approach to population variability analysis, which concerns the introduction of sources estimates (e.g. engineering judgment) as one of the forms of evidence used in the construction of population variability distributions. The paper presents the model, and illustrates its behavior by means of a practical example.