Analytic and Numerical Solutions of ARL of CUSUM Procedure for Exponentially Distributed Observations
Keywords:
Average Run Length, CUSUM, exponential distribution, integral equationAbstract
This paper aims at deriving the explicit expressions of the Average Run Length (ARL) for a negative Cumulative Sum (CUSUM) chart for a lower-sided case when observations are from exponential distribution. ARL is found using two approaches; Integral Equation (IE) and Numerical Integral Equation (NI). The comparison for accuracy of results for explicit expression have been solved with the Integral Equation approach, while, the numerical approximations have been solved with the Numerical Integral equation, which both tend to an acceptable agreement. The computational time obtained from the NI approach is significantly longer than that obtained from the IE approach.