Fishing for Errors in an Ocean Rather than a Pond

In the internet age, a proliferation of services appear on the web. Errors in using the internet service or app are dynamically introduced as new devices/interfaces/software are produced and are found to be incompatible with an app that is perfectly good for other devices. The number of users who can detect various errors changes dynamically: for instance, there may be new adopters of the software over time. It may also happen that an old user might upgrade and thus run into new incompatibility errors. Allowing new users and errors to enter dynamically poses considerable modeling and estimation difficulties. In the era of Big Data, methods for dynamically updating as new observations arise are important. Traditional models for detecting errors have generally assumed a finite number of errors. We provide a general model that allows for a procedure for finding maximum likelihood estimators of key parameters where the number of errors and the number of users can change.