Effect of neglecting autocorrelation in regression EWMA charts for monitoring count time series

Abstract

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.

Early Detection of SARS-CoV-2 Epidemic Waves: Lessons from the Syndromic Surveillance in Lombardy, Italy

“…One of the most popular methods used for the early detection of a respiratory syndrome outbreak is the residual chart model known as the cumulative sum (CUSUM) [14,15]. Similar methods received less attention from public health agencies [16], although some of them (e.g., the exponentially weighted moving average (EWMA) chart) are characterized by exciting properties and greater flexibility compared to the CUSUM residual chart [17,18].…”

Monitoring the Zero-Inflated Time Series Model of Counts with Random Coefficient

“…The essential assumption underlying the design of CUSUM charts is that the process observations are independent (Montgomery [ 31 ], Alencar, Ho and Albarracin [ 32 ], Bourguignon, Medeiros, Fernandes and Ho [ 33 ]). While the violation of this major assumption seriously affects the monitoring performance of the charts (Harris and Ross [ 34 ], Triantafyllopoulos and Bersimis [ 35 ], Albarracin, Alencar and Ho [ 36 ]). Some authors have studied the performance of CUSUM charts for some integer-valued models (Weiß and Testik [ 23 ], Weiß and Testik [ 24 ], Yontay, Weiß, Testik and Bayindir [ 25 ], Rakitzis, Weiß and Castagliola [ 26 ], Li, Wang and Sun [ 27 ], Lee and Kim [ 37 ], Lee, Kim and Kim [ 38 ]).…”

Simulation approach for assessing the performance of the γEWMA control chart

“…The effect of parameter estimation on the control chart performance has been studied in the literature. These studies have concluded that the effects of parameter estimation on the control chart properties should not be ignored (Crowder and Wiel, 2014;Dawod et al, 2017;Esparza Albarracin et al, 2018;Jensen et al, 2006;Lucas and Saccucci, 1990;Reynolds and Lu, 1997;Saleh et al, 2013).…”

“…In referring to control chart performance, in the literature, it has been evaluated using indicators that were derived from the Run-Length (RL). These indicators include the Average-Run-Length (ARL), the Standard-Deviation-Run-Length (SDRL), and the Median-Run-Length (MRL) (B. C. Khoo et al, 2015;Borror et al, 1999;Dawod et al, 2017;Esparza Albarracin et al, 2018;Human et al, 2011;Jones et al, 2001). For instance, it is desirable for the ARL to be large if no assignable cause has occurred, and small if one out-of-control condition has occurred.…”