Average run length by numerical integral equation method for exponentially weighted moving average control chart when data are symmetric and asymmetric distributions
Abstract:
The main purpose of this paper is to approximate the Average Run Length (ARL)
of Exponentially Weighted Moving Average (EWMA) control chart using the Numerical
Integral Equations (NIE) methods when observations are exponential, laplace, logistic
and pareto distributions. The Numerical Integral Equations (NIE) techniques to
approximate Average Run Length (ARL) are Simpsons rule, Midpoint rule, Trapezoidal
rule and Gauss-Legendre Quadrature rule. In addition, the numerical results obtained
from the NIE methods are compared with results obtained from Monte Carlo
Simulations (MC) technique. The results show that the ARL from the NIE methods by
Simpsons rule, Midpoint rule, Trapezoidal rule and Gauss-Legendre quadrature rule
are close to the MC method with an absolute percentage difference less than 5%. In
addition, the NIE method can reduce in the computational time better than the MC
method.