A simple algorithm is introduced for computing the run length distribution of a monitoring scheme combining a Shewhart chart with an Exponentially Weighted Moving Average control chart. The algorithm is based on the numerical approximation of the integral equations and integral recurrence relations related to the run-length distribution. In particular, a modified Clenshaw-Curtis quadrature rule is applied for handling discontinuities in the integrand function due to the simultaneous use of the two control schemes. The proposed algorithm, implemented in R and publicy available, compares favourably with the Markov chain approach originally used to approximate the run length properties of the combined Shewhart-EWMA.
Evaluation of the Run-Length Distribution for a Combined Shewhart-EWMA Control Chart
Masarotto, Guido;Capizzi, Giovanna
2007
Abstract
A simple algorithm is introduced for computing the run length distribution of a monitoring scheme combining a Shewhart chart with an Exponentially Weighted Moving Average control chart. The algorithm is based on the numerical approximation of the integral equations and integral recurrence relations related to the run-length distribution. In particular, a modified Clenshaw-Curtis quadrature rule is applied for handling discontinuities in the integrand function due to the simultaneous use of the two control schemes. The proposed algorithm, implemented in R and publicy available, compares favourably with the Markov chain approach originally used to approximate the run length properties of the combined Shewhart-EWMA.File | Dimensione | Formato | |
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