Mathematical models are formulated for the possible onset and growth in subsystem degradation. The model recognizes that the time of onset of a degrading trend may be random, and hence initially unknown, and that the trend magnitude is also initially unknown. The trend magnitude will become better known as more data are accumulated. Maximum likelihood and Bayesian statistical procedures to estimate the time of onset and the trend magnitude are presented. A cost model is formulated to develop procedures (which recognize the uncertainty concerning the time of onset and trend magnitude) to determine estimated costs and the associated risks of upgrading the subsystem at different times in the future. Results of simulation studies of the procedures are presented.... Changepoint problems, Maximum likelihood, Bayesian procedures, Cost of system upgrade.