Run Length definition and distribution?

Hi,

I am not sure how old your post may be.

Anyhow, the run length RL is a random variable, hence it has a distribution, which itself has a mean, called the average run length ARL. Hence ARL and RL are not to be mistaken.

For a gaussian property, assuming you track it using say an Xbar shewhart chart, the RL will have a geometric distribution, however this is certainly not the case for all control variables (eg. EWMA, CuSUM), and will not be the case for a non-gaussian property.

I hope this helps.

Regards,

Florent