I'd like to define our app user churn, Generally, people will define their app user churn by some simply way, like: if the user do not logon continually 7 days or 1 month, we will define them churn user. So is there a better way?
The churn rate is users the ratio of active users that stop being active after a given period.
The churn rate for application user is exactly the one used for other cases, like employees. However, when dealing with employees it is clear whether the employee is active, The problem with application users is the identification that they are no longer active.
What you can do is to identify a period of in activity after which, the vast majority of these user never return.
For example, take the users that were active during January of the previous year and were not active for 7 days since then. If 99% of them were not active for the rest of the year than 7 days are a good indication of being in active.
The suitable period is usually determined by the domain (e.g., some applications are used in periods longer than 7 days) and the required confidence level (99%, 90%). Note that you don't want to be too safe because if you'll decide that a user is inactive only after 2 years, this definition will prevent you from identifying users that are practicality lost and take actions to reduce the churn rate.
Two small amendments to the previous complete answer.
You may classify the churn based on cause, this is typically active and passive churn. In your case this will be churn due to inactivity and churn due to lock account by the administrator.
To handle the uncertainty of the inactivity churn, you may introduce a measure called dechurn (probably not a stable term), measuring the reactivation of a churned user.