Benefits of a Bayesian approach to anomaly and failure investigations

It is often the case in failure and anomaly investigations that data is either limited or so wide ranging that it is difficult to bring focus to a key root cause. For this reason, a disciplined approach incorporating root cause trees (Ishikawa Diagrams) is usually taken to develop and track root cause hypotheses and analyses. During the investigation, statistical tools can be used to evaluate various hypotheses of failure. However, in many cases, there is limited failure data and it is often necessary to set up accelerated life tests involving many samples in order to induce failures under controlled conditions so that a statistically significant population of failures can be obtained. Root cause is sometimes achieved only after extensive and expensive efforts to reduce the number of root cause hypotheses. Other times, root cause investigations are truncated to "most probable cause" based on the evidence available and expert opinion. Bayesian analysis allows test or observation data to be combined with prior information to produce a posterior estimate of likelihood. It can be a tool that provides a number of benefits to the root cause determination process. The first benefit is to provide an estimate of the likelihood that certain hypotheses are true based on the limited data available. This can provide useful direction to the failure investigation. For example, it can provide an indication as to where more data collection might be valuable, i.e., tests of most likely hypothesis as opposed to tests of all hypotheses in a root cause analysis. It also can provide a way to assess the incremental impact of data as it becomes available to the decision making process. Another benefit is to organize the logic, once root cause has been determined, that can lead to a more quantitative measure of the likelihood of a future failure. This latter benefit can help guide the decision making processes necessary for determining what corrective action (if any) might be necessary. Thi- s paper provides an elementary introduction to a Bayesian approach to data analysis for anomaly and failure investigations and provides a number of worked examples illustrating its utility.