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

Author(s)

Esparza Albarracin, Orlando Yesid ^[1] ; Alencar, Airlane Pereira ^[1] ; Ho, Linda Lee ^[2]

Affiliation

^[1] Univ Sao Paulo, IME, Dept Stat, Sao Paulo - Brazil

^[2] Univ Sao Paulo, EP, Dept Prod Engn, Sao Paulo - Brazil

• Document type: Journal article
• Source: QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL; v. 34, n. 8, p. 1752-1762, DEC 2018.
• Web of Science Citations: 0

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 Sao Paulo city. (AU)

• FAPESP's process: 13/00506-1 - Time series, wavelets and functional data analysis
• Grantee: Pedro Alberto Morettin
• Support Opportunities: Research Projects - Thematic Grants