Abstract
We use the Fredholm type integral equations method to derive explicit formulas for the Average Run Length (ARL) in some special cases. In particular, we derive a closed form representation for the ARL of Cumulative Sum (CUSUM) chart when the random observations have hyperexponential distribution. For Exponentially Weighed Moving Average (EWMA) chart we solve the corresponding ARL integral equation when the observations have the Laplace distribution. The explicit formulas obviously takes less computational time than the other methods, e.g. Monte Carlo simulation or numerical integration.
Original language | English |
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Pages (from-to) | 253-265 |
Number of pages | 13 |
Journal | East-West Journal of Mathematics |
Volume | 2010 |
Issue number | Special edition |
Publication status | Published - 2010 |
Keywords
- integral equations
- CUSUM technique
- numerical integration