Evaluation of the run-length distribution for a combined Shewhart-EWMA control chart

Authors:
Giovanna Capizzi;Guido Masarotto
Affiliations:
Department of Statistical Sciences, University of Padua, Padova, Italy 35121;Department of Statistical Sciences, University of Padua, Padova, Italy 35121
Venue:
Statistics and Computing
Year:
2010

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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 Clenshaw-Curtis product-integration 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.