Methods and systems of determining a failure copula for a consumable are disclosed. Multiple consumable levels for a consumable and multiple timestamps are received from a device. Each timestamp is associated with one of the consumable levels. The consumable levels are ordered into a time-ordered sequence based on the associated timestamps. For at least one consumable level in the time-ordered sequence, a computing device determines a value associated with the consumable level based on at least one earlier and at least one later consumable level in the time-ordered sequence. The computing device identifies historical consumable replacement(s) based on the values associated with the consumable levels in the time-ordered sequence and determines one or more consumable lifetimes and one or more consumable yields based on the historical consumable replacement(s). The computing device determines a failure copula based on the one or more consumable lifetimes and consumable yields.
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