# lognormal process time, output rate distribution

#### KurtVH

##### New Member
For a project of factory lay out we have given an assembly time of 20 min and stdev of 5 min. distribution type is not given but assumed lognormal (since normal is infeasable because of the possibility of negative assembly times).

At what rate do the products exit the assembly station?for example in 1 hour: what are the number of products produced?what is the type of probability distribution?average and stdev?(Is of course a function of the time interval you choose)

Thx

#### BGM

##### TS Contributor
If the product assembly one by one in series, then you have to deal with the sum of independent log-normal process time which is very complicated. (You can take approximations if you want of course)

Your question is related to some sort of renewal theory. By the elementary renewal theorem, the long-term average output rate is equal to the reciprocal of the mean holding time. In your case, the mean holding time is 20 min, and therefore the long term average output rate is 0.05 per min, or 3 per hour as expected.