A Simple Method for Studying Run – Length Distributions of Exponentially Weighted Moving Average Charts

Crowder, Stephen V.

doi:10.1080/00401706.1987.10488267

Cited by 127 publications

(106 citation statements)

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“…The EWMA method has been widely studied in the literature, mostly for various shifts in the mean in a stochastic process of normally distributed variables (Roberts (1959); Robinson and Ho (1978); Crowder (1987); Crowder (1989); Lucas and Saccucci (1990); Srivastava and Wu (1993); Chandrasekaran, English, and Disney (1995); Srivastava and Wu (1997); Schone, Schmid, and Knoth (1999); Steiner (1999); Chan and Zhang (2000) and Frisen and Sones son (2001)). However, the EWMA method has also been studied in many other situations.…”

Section: Different Types Of Ewma Methodsmentioning

confidence: 99%

“…This was done for both the one-sided and two-sided EWMAa in discrete time. Crowder (1987) used integral equations to evaluate the properties of the run length distribution in discrete time for the two-sided EWMAa. In Crowder (1989) optimal values of the weight parameter A, to minimize the ARLI for a fixed ARLo, together with a design strategy of the method, was proposed, based on the results in Crowder (1987).…”

Section: Different Types Of Ewma Methodsmentioning

confidence: 99%

“…Crowder (1987) used integral equations to evaluate the properties of the run length distribution in discrete time for the two-sided EWMAa. In Crowder (1989) optimal values of the weight parameter A, to minimize the ARLI for a fixed ARLo, together with a design strategy of the method, was proposed, based on the results in Crowder (1987). Lucas and Saccucci (1990) used another approach to find the optimal value of A, for the same situation as by Crowder (1989).…”

Section: Different Types Of Ewma Methodsmentioning

confidence: 99%

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Evaluations of some Exponentially Weighted Moving Average methods

Sonesson¹

2003

Journal of Applied Statistics

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SUMMARYSeveral versions of the EWMA (Exponentially Weighted Moving Average) method for monitoring a process with the aim of detecting a shift in the mean are studied both for the onesided and the two-sided case. The effects of using barriers for the one-sided alarm statistic are also studied. One important issue is the effect of different types of alarm limits. Different measures of evaluation are considered such as the expected delay, the ARLI, the probability of successful detection and the predictive value of an alarm to give a broad picture of the features of the methods. Results are presented both for a fixed ARLO and a fixed probability of a false alarm. The differences highlight the essential problem of how to define comparability between surveillance methods. The results are from a large-scale simulation study. Special attention is given to the effect on the confidence in the final results by the stochastic variation in the calibration of the methods. It appears that important differences from an inferential point of view exist between the one-and two-sided versions of the methods. It is demonstrated that the method, usually considered as a convenient approximation, is to be preferred over the exact version in many respects.

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Section: Different Types Of Ewma Methodsmentioning

confidence: 99%

Section: Different Types Of Ewma Methodsmentioning

confidence: 99%

Section: Different Types Of Ewma Methodsmentioning

confidence: 99%

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Evaluations of some Exponentially Weighted Moving Average methods

Sonesson¹

2003

Journal of Applied Statistics

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“…This method has also been used to obtain the run-length properties of the combined Shewhart-EWMA (CSEWMA) control chart (Lucas and Saccucci, 1990). Following the second approach, a continuos characterization of the process is directly used (Crowder, 1987). Then, solutions of the corresponding integral equations and integral recurrence relations are approximated numerically.…”

Section: Introductionmentioning

confidence: 99%

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

Capizzi

Masarotto

2009

Stat Comput

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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.

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“…Sweet (1986) proposed two models to construct simultaneous control charts to monitor the mean and the variance of a process using the EWMA. Crowder (1987Crowder ( & 1989 provided average run length (ARL) tables and graphs for the selection of the optimum values of the EWMA control chart parameters in the design of an EWMA chart. Ng & Case (1989) sample mean, sample range and moving range statistics.…”

Section: Introductionmentioning

confidence: 99%