Estimation of the correlation among destructively measured variables

Abstract

This paper uses the Gibbs sampler for the proof-loading problem which arises when the correlation is to be estimated between two variables that can only be measured destructively. (In this problem, the characteristics whose correlation is of interest are typically called modes.) One of the common approaches to estimating the correlation is as follows: Load a unit in mode 1 up to an established maximum load. If the unit fails, record its mode 1 strength as variable 1. If it does not fail, load the unit in mode 2 until failure and record its mode 2 strength as variable 2. In this problem and its variants, censoring is used, and a closed-form solution for an estimate of the correlation is typically not available. We propose to use the Gibbs sampler for estimating the correlation. This provides a conceptually simple approach that is readily implemented on a computer. Furthermore, it is easy to modify our approach to deal with variants and generalizations of the proof-loading procedure described above.

Keywords:

• Bayesian statistics
• censoring
• Gibbs sampling
• normal distribution
• proof-loading