Multivariate control charts to monitor the monthly frequency of vehicle robberies in Sao Paulo city

In this paper, vectors of the deviance residuals (after fitting a STARMA model) are used to build MCUSUM and MEWMA control charts to monitor multivariate space-time count series. Chart parameters are estimated by simulation to meet a desired in-control average run length and to minimize out-of-control average run length. A complementary simulation study is performed to measure the impact of the omission of the spatial dependencies on the performance of the control charts. Results highlight that false alarms will be signaled much earlier on average. For illustrative purposes, consider the data set of the monthly rates of vehicle robberies registered in 93 police districts located in sao Paulo City (Brazil). Data from January 2001 to December 2013 are used to fit the STARMA model. Chart parameters are searched by simulation and used to draw the control charts to monitor observed vehicle robberies from January 2014 to April 2016. The control charts signal as out-of-control for almost all months of 2014 and the beginning of 2015. An exploratory analysis is used to identify which districts are responsible for these signals. In the case of omission of spatial dependencies, in the current application, these control charts will give false alarms on average 2.5 (MEWMA) and 7 months (MCUSUM) earlier due to this fault. (C) 2018 Elsevier B.V. All rights reserved.