Colorant change prediction

A prediction server, comprising:

• one or more processors;
• and
• data storage configured to store computer-readable instructions that, when executed by the one or more processors, cause the prediction server to perform tasks comprising:
• receiving a request to predict colorant usage for a first printing device;
• determining a first plurality of functions to predict colorant usage for the first printing device, wherein the first plurality of functions comprise a plurality of linear functions and a plurality of non-linear functions, and wherein the first plurality of functions are based on one or more colorant-usage rates that indicate historical rates of change in colorant used by a plurality of printing devices that include the first printing device;
• determining a prediction of colorant usage for the first printing device using the first plurality of functions based on combining an estimate of the plurality of linear functions weighted by a first weight with an estimate of the plurality of non-linear functions weighted by a second weight that is less than the first weight;
• and
• providing an output involving the prediction of colorant usage for the first printing device comprising an estimated time before replacing colorant for the first printing device without replacement, wherein the prediction of colorant usage further comprises a confidence interval indicating a range of time related to the estimated time before replacing colorant for the first printing device.

An article of manufacture comprising non-transitory data storage storing at least computer-readable instructions that, when executed by one or more processors of a prediction server, cause the prediction server to perform tasks comprising:

• receiving a request to predict colorant usage for a first printing device;
• determining a first plurality of functions to predict colorant usage for the first printing device, wherein the first plurality of functions comprise a plurality of linear functions and a plurality of non-linear functions, and wherein the first plurality of functions are based on one or more colorant-usage rates that indicate historical rates of change in colorant used by a plurality of printing devices that include the first printing device;
• determining a prediction of colorant usage for the first printing device using the first plurality of functions based on combining an estimate of the plurality of linear functions weighted by a first weight with an estimate of the plurality of non-linear functions weighted by a second weight that is less than the first weight;
• and
• providing an output involving the prediction of colorant usage for the first printing device comprising an estimated time before replacing colorant for the first printing device without replacement, wherein the prediction of colorant usage further comprises a confidence interval indicating a range of time related to the estimated time before replacing colorant for the first printing device.