CUSUM ARL - Conditional or Unconditional?

Abstract: The behavior of CUSUM charts depends strongly on how they are initialized. Recent work has suggested that self-starting CUSUM methods retain some dependence on their very first readings, and introduced the concept of "conditional average run length" (CARL) -- the average run length conditioned on the first few process readings -- as a result of which is it claimed that different practitioners using the same methodology could experience different ARLs because of the random differences in their earliest readings. We cast doubt on whether CARL is relevant to practitioners who use self-starting methods and argue that the unconditional ARL is the relevant measure there.