I wouldn’t say that classic survival models are not directly applicable to this kind of analysis but some of their key features can be incorporated into an appropriate model.

Firstly you have to confront the observational model of consumption. Let’s say that each observation is comprised of the current time, the previous time, and the observed (continuous) amount of credits at each. In order to specify an observational model we have to reason about how people are consuming their credits: do they consume a similar amount regardless of how much they left or are their “rationing effects” where people tend to use a fixed percentage of what remains.

If consumption rate is fixed then one might consider a truncated observational model like

c_{n} \sim \pi(\max(0, c_{n - 1} - \rho), \phi)

where \pi is a density function over the positive real line in a location parameterization and \rho quantifies a consistent consumption rate across all times. Or if one assumed a constant rate of consumption then they'd have to take the time between observations \tau_{n, n -1}$ into account,

c_{n} \sim \pi(\max(0, c_{n - 1} - \rho \cdot \tau_{n, n -1}), \phi).

On the other hand if consumption is conditional then one might consider

\frac{c_{n}}{c_{n - 1}} \sim \pi(\omega, \phi)

where \pi might for example be a beta density function in a location parameterization (such as the `beta_proportional`

in Stan) and `\omega`

quantifies a proportional consumption of what it left.

One could build upon these simple models by allowing the behavior to change with time, for example by allowing \rho and \omega to vary with n or by building a hidden Markov model where consumers can shift between different behaviors at different times.

Anyway there are a lot of modeling opportunities in an application like this but which is most productive will depend on the particular details of the application. For a workshop it often helps to work with simulated data so that you can fix those details to be relatively simple, but even then I find it productive to give the audience a hint of the complexity that might arise in more realistic settings.