(redirected here from mathoverflow.net) Hello,

At work I was asked the probability of a user hitting an outage on the website. I have some following metrics. Total system downtime = 500,000 seconds a year. Total amount of seconds a year = 31,556,926 seconds. Thus, p of system down = 0.159 or 1.59% We can also assume that downtime occurs evenly for a period of approximately 2 hours per week.

Now, here is the tricky part. We have a metric for amount of total users attempting to use the service = 16,000,000 during the same time-frame. However, these are subdivided, in the total time spent using the service. So, lets say we have 7,000,000 users that spend between 0 - 30 seconds attempting to use the service. So for these users what is the probability of hitting the system when it is unavailable? (We can assume an average of 15 seconds spent total if this simplifies things)

I looked up odds ratios and risk factors, but I am not sure how to calculate the probability of the event occurring at all.

Thanks in advance!

P.S. I was given a possible answer, at https://mathoverflow.net/questions/52816/probability-calculation-system-uptime-likelihood-of-occurence and was following the advice on posting the question in the most appropriate forum.