approximation effects on control charts for process monitoring

in statistical quality control a very widely used measure is average run length (arl) which may be worked out by different methods like integral equation, approximations, and monte carlo simulations. the arl measure and the other related measures are of major significance in every type of production process. an omission in its computation (and hence its related measures such as extra quadratic loss (eql)) may cause a loss. this necessitates great care in the choice of its evaluation method. this article will deal with this issue using some approximation methods and the monte carlo simulations. the discrepancies among the results will be examined to highlight the deficiencies of using approximation methods in quality control techniques.