Hi all. I'm trying to calculate how frequently an employer would need to perform random drug testing in order to achieve a desired probability of detecting a drug user within a certain time.
Here's the relevant facts:
There is no upper or lower limit to the frequency of testing. Subjects can be tested every day if required, or once a year.
If a subject is using drugs it will be evident on testing for 4 days...that is, the day of use and the next 3 days.
I need to achieve a 99.9% chance of detecting drug use within a 60 day period.
So, here is the question....how frequently (on average) should drug testing be applied in order to achieve this 99.9% chance of detection within 60 days? I'm not talking about a regular, fixed schedule of testing - rather it will be random, with a given probability of testing each day.
If someone could give me a formula to apply, or even the priniciples used to derive a formula this would be most helpful, because then I could experiment with the numbers a bit myself.
Thanks in advance !