Trouble Shooting by Bayesian Networks

Hans-J. Lenz, Freie Univ. Berlin, Germany

Friday 3 February 2006

In the middle nineties an East-German gas oven manufacturer produced about 120.000 units, which were uniformly badly designed, manufactured, and shipped all over the country. One gas oven exploded. Note, that the sample size is n=1.

At the same day, the manufacturer's management instantaneously established a task force for fixing the problem within 24 hours. The author was recruited as a well-known expert in statistical technology. Its main objective was risk assessment and identification of trouble maker households.

As for this kind of problems nearly no data are at hand - for goodness sake! - there does not exist a (well defined) likelihood function. Consequently, human expert knowledge was heavily utilized and transformed into prior probabilities linked to a (rather simple) Bayesian network model, which enabled the task force members to set-up an intuitively well understandable cause-effect model of the domain of interest.

The model was carefully used for various scenarios for risk assessment, especially for a worst case scenario. This was used to identify households with an un-normal high risk. Using the know-how of the plumbers involved in the installation of all ovens about the household characteristics (conditions and factors of the risk of corrosion), the task force was successful in identifying the real trouble makers with minimum error rates. The technicians repaired all contaminated tubes just in time. No further accident was ever reported.

We describe the modelling process, we shortly summarize the well-known theory of Bayesian Belief Networks, and we illuminate the semi-automatic identification process of the trouble-making households and ovens.