Sandra García-Bustos, Nadia Cárdenas-Escobar, Ana Debón and César Pincay
The study aims to design a control chart based on an exponentially weighted moving average (EWMA) chart of Pearson's residuals of a model of negative binomial regression in order…
Abstract
Purpose
The study aims to design a control chart based on an exponentially weighted moving average (EWMA) chart of Pearson's residuals of a model of negative binomial regression in order to detect possible anomalies in mortality data.
Design/methodology/approach
In order to evaluate the performance of the proposed chart, the authors have considered official historical records of death of children of Ecuador. A negative binomial regression model was fitted to the data, and a chart of the Pearson residuals was designed. The parameters of the chart were obtained by simulation, as well as the performances of the charts related to changes in the mean of death.
Findings
When the chart was plotted, outliers were detected in the deaths of children in the years 1990–1995, 2001–2006, 2013–2015, which could show that there are underreporting or an excessive growth in mortality. In the analysis of performances, the value of λ = 0.05 presented the fastest detection of changes in the mean death.
Originality/value
The proposed charts present better performances in relation to EWMA charts for deviance residuals, with a remarkable advantage of the Pearson residuals, which are much easier to interpret and calculate. Finally, the authors would like to point out that although this paper only applies control charts to Ecuadorian infant mortality, the methodology can be used to calculate mortality in any geographical area or to detect outbreaks of infectious diseases.
Details
Keywords
Sandra García-Bustos, Joseph León and María Nela Pastuizaca
This research proposes a multivariate control chart, whose parameters are optimized using genetic algorithms (GA) in order to accelerate the detection of a change in the vector of…
Abstract
Purpose
This research proposes a multivariate control chart, whose parameters are optimized using genetic algorithms (GA) in order to accelerate the detection of a change in the vector of means.
Design/methodology/approach
This chart is based on a variation of the Hotelling T2 chart using a sampling scheme called generalized multiple dependent state sampling. For the analysis of performances of this chart, the out-of-control average run length (ARL) values were used for different scenarios. In this comparison, it was considered the classic Hotelling T2 chart and the T2 chart using the scheme called multiple dependent state sampling.
Findings
It was observed that the new chart with its optimized parameters is more efficient to detect an out-of-control process. Additionally, a sensitivity analysis was performed, and it was concluded that the best yields are obtained when the change to be considered in the optimization is small. An application in the resolution of a real problem is given.
Originality/value
In this research, a multivariate control chart is proposed based on the Hotelling T2 statistic but adding a sampling scheme. This makes this control chart more efficient than the classic T2 chart because the new chart not only uses the current information of the T2 statistic but also conditions the decision to consider a process as “in- control” on the statistic's previous information. The practitioner can obtain the optimal parameters of this new chart through a friendly program developed by the authors.