Missing Covariates : a Bayesian Approach

John C. Naylor Tony Pettit y Abstract Data on observed fault rates in an industrial process together with values of selected covariates, ordered through time, is analysed. The record of covariate values is incomplete for operational reasons and a particular feature of the analysis is dealing with these missing values. Of practical interest is the selection of covariates which might in uence the fault rate, with respect to possible future monitoring or control of the process. 1 The Problem The data to be modelled and analysed is observed defect rates for castings of one type produced at The Southern Cross Foundry during a period of a few weeks in 1989. Of the three types of defect noted only one (`blisters') will be considered as this is, for this casting type, the most serious possible defect. The data is recorded for several days on which this particular product was cast, includes values for covariates relating to the mold sand used, together with a record of the time and date of production. For a fuller description of the industrial situation and of possible covariates and their measurement see [3, 4]. The occurrence of defects has been recorded only as a percentage rate, 100 p say. The maximum run size for this type of casting is 250 but shorter runs are possible for a variety of reasons and it is likely that there is considerable variation in sample size for p. It is not then possible to consider models for p based on, for example, the binomial distribution. In any case, exploratory analysis suggests the variation in observed values for p is much greater than would be expected for a simple binomial model with Deparment of Mathematics, Statistics and O.R., Nottingham Trent University, Nottingham, UK. yHead of Department of Mathematics, Queensland University of Technology, Brisbane, Queensland, Australia. o o oo o