In maintenance planning a crucial question is when some asset should be maintained. As preventive maintenance often needs outages it is necessary to predict the condition of an asset until the next possible outage. The degradation of the condition can be modelled by a linear function. One method of estimating the condition is linear regression, which requires a number of measured values for different times and gives an interval within which the asset will reach a condition when it should be maintained [1]. A more sophisticated calculation of the uncertainty of the regression is presented based on [2, section 9.1].

Another method is martingale theory [3, chapter 24], which serves to deduce a formula for the time such that there is a probability of less than a given $\alpha$ that the condition has reached 0 before that time. The formula contains an integral, which is evaluated numerically for different values of the measurement variance and the variance of the Brownian motion, which must be estimated by knowing the maximum and the minimum degradation per time interval. Then just one measured value is needed together with an estimate of the variance.

The two methods are compared, especially with regard to the size of the confidence interval of the time when the condition reaches a predefined level. The application for the methods is the development of so called health indices for the assets in an engineering system, which should tell which asset need maintenance first. We present some requirements for a health index and check how the different predictions fulfil these requirements.

References

[1] S.E. Rudd, V.M. Catterson, S.D.J. McArthur, and C. Johnstone. Circuit breaker prognostics using SF6 data. In IEEE Power and Energy Society General Meeting, Detroit, MI, United States, 2011.

[2] Bernard W. Lindgren. Statistical theory. Macmillan, New York, 2nd edition, 1968.

[3] Jean Jacod and Philip Protter. Probability essentials. Springer-Verlag, Berlin, 2000.