To detect outbreaks of diseases in public health, several control charts have been proposed in the literature. In this context, the usual generalized linear model may be fitted for counts under a Negative Binomial distribution with a logarithm link function and the population size included as offset to model hospitalization rates. Different statistics are used to build CUSUM control charts to monitor daily hospitalizations and their performances are compared in simulation studies. The main contribution of the current paper is to consider different statistics based on transformations and the deviance residual to build control charts to monitor counts with seasonality effects and evaluate all the assumptions of the monitored statistics. The monitoring of daily number of hospital admissions due to respiratory diseases for people aged over 65 years in the city São Paulo-Brazil is considered as an illustration of the current proposal.

Cumulative sum control charts have been used for health surveillance due to its efficiency to detect soon small shifts in the monitored series. However, these charts may fail when data are autocorrelated. An alternative procedure is to build a control chart based on the residuals after fitting autoregressive moving average models, but these models usually assume Gaussian distribution for the residuals. In practical health surveillance, count series can be modeled by Poisson or Negative Binomial regression, this last to control overdispersion. To include serial correlations, generalized autoregressive moving average models are proposed. The main contribution of the current article is to measure the impact, in terms of average run length on the performance of cumulative sum charts when the serial correlation is neglected in the regression model. Different statistics based on transformations, the deviance residual, and the likelihood ratio are used to build cumulative sum control charts to monitor counts with time varying means, including trend and seasonal effects. The monitoring of the weekly number of hospital admissions due to respiratory diseases for people aged over 65 years in the city São Paulo-Brazil is considered as an illustration of the current method.

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Exponentially weighted moving average (EWMA) charts and cumulative sum (CUSUM) control charts based on fitting a generalized linear model (GLM) to estimate the time‐varying mean of the process have been used for health surveillance due to its efficiency to detect soon small shifts in count data as morbidity or mortality rates. However, in these proposals, the serial correlation is usually omitted implying that the charts may fail. In this paper, generalized autoregressive moving average (GARMA) models that include lagged terms to model the autocorrelation are proposed to analyze the performance of regression EWMA control charts based on fitting of GLM models with negative binomial distribution for monitoring time series. The main contributions of the current paper are two new statistics based on the likelihood function to be monitored and three procedures to build one‐sided EWMA charts and to measure the impact on the performance of these EWMA charts when the serial correlation is neglected in the regression model. For the simulated scenarios, the statistics based on the likelihood and the winsorized EWMA presented the best performance. Also, a real data analysis detected outbreaks in the hospitalization time series due to respiratory diseases of elderly people in São Paulo city.

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