Curing the misbehavior of reservoir capacity statistics by controlling shortfall during failures using the modified sequent peak algorithm

In a recent article, Pretto et al. [1997] found that certain statistics of storage capacity estimates, for example, mean and higher quantiles, obtained using a behavior analysis do misbehave for medium record lengths in that they exhibit a hump in their functional relationships with the data record length. Further, this upward bias was observed to disappear at longer record lengths. Pretto et al. proffered several reasons for this apparently anomalous behavior. In this paper, we investigate another reason that we suspect might also be causing behavior analysis storage estimates to misbehave. In particular, we use a modified sequent peak methodology, which, unlike a behavior analysis, enables the analyst to restrict the amount of water shortfall during any failure period to fixed amounts. The results show that when the shortfall is made the same for all failure periods, the hump in the storage capacity statistics versus length of record functions largely disappears.