Experimental designs for autoregressive models applied to industrial maintenance

• Optimal experimental design theory is applied to AR models to reduce costs.
• The first observation has an important impact on any optimal design.
• Either the lack of precision or small starting observations claim for large times.
• Reasonable optimal times were obtained relaxing slightly the efficiency.
• Optimal designs were computed in a predictive maintenance context.

Some time series applications require data which are either expensive or technically difficult to obtain. In such cases scheduling the points in time at which the information should be collected is of paramount importance in order to optimize the resources available. In this paper time series models are studied from a new perspective, consisting in the use of Optimal Experimental Design setup to obtain the best times to take measurements, with the principal aim of saving costs or discarding useless information. The model and the covariance function are expressed in an explicit form to apply the usual techniques of Optimal Experimental Design. Optimal designs for various approaches are computed and their efficiencies are compared. The methods working in an application of industrial maintenance of a critical piece of equipment at a petrochemical plant are shown. This simple model allows explicit calculations in order to show openly the procedure to find the correlation structure, needed for computing the optimal experimental design. In this sense the techniques used in this paper to compute optimal designs may be transferred to other situations following the ideas of the paper, but taking into account the increasing difficulty of the procedure for more complex models.