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04/10/2018, 14:00 — 15:00 — Room P3.10, Mathematics Building

Manuel Cabral Morais, *CEMAT & DM, Instituto Superior Técnico, Universidade de Lisboa*

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A thinning-based EWMA chart to monitor counts: some preliminary results

Shewhart control charts are known to be somewhat insensitive to shifts of small and moderate size. Expectedly, alternative control schemes such as the cumulative sum (CUSUM) and the exponentially weighted moving average (EWMA) charts have been proposed to speed up the detection of such shifts.

The novel chart we propose relies on a EWMA control statistic where the usual scalar product is replaced by what we call a fractional binomial thinning to avoid the typical over smoothing ascribable to ceiling, rounding, and flooring operations. The properties of this discrete statistic are, to a moderate extent, similar to the ones of its continuous EWMA counterpart and the run length (RL) performance of the associated chart can be computed exactly using the Markov chain approach for independent and identically distributed (i.i.d.) counts. Moreover, this chart is set in such way that: the average run length (ARL) curve attains a maximum in the in-control situation, i.e., the chart is ARL- unbiased; and the in-control ARL is equal to a pre-specified value.

We use the R statistical software to provide compelling illustrations of this unconventional EWMA chart and to compare its RL performance with the ones of a few competing control charts for the mean of i.i.d. Poisson counts.

### Keywords

Average run length; Exponentially weighted moving average; Fractional binomial thinning; Statistical process control.