RESUMEN
The EWMA Sign control chart is an efficient tool for monitoring shifts in a process regardless the observations' underlying distribution. Recent studies have shown that, for nonparametric control charts, due to the discrete nature of the statistics being used (such as the Sign statistic), it is impossible to accurately compute their Run Length properties using Markov chain or integral equation methods. In this work, a modified nonparametric Phase II EWMA chart based on the Sign statistic is proposed and its exact Run Length properties are discussed. A continuous transformation of the Sign statistic, combined with the classical Markov Chain method, is used for the determination of the chart's in- and out-of-control Run Length properties. Additionally, we show that when ties occur due to measurement rounding-off errors, the EWMA Sign control chart is no longer distribution-free and a Bernoulli trial approach is discussed to handle the occurrence of ties and makes the proposed chart almost distribution-free. Finally, an illustrative example is provided to show the practical implementation of our proposed chart.
RESUMEN
In the context of public health surveillance, the aim is to monitor the occurrence of health-related events. Among them, statistical process monitoring focuses very often on the monitoring of rates and proportions (i.e. values in (0,1)) such as the proportion of patients with a specific disease. A popular control chart that is able to detect quickly small to moderate shifts in process parameters is the exponentially weighed moving average control chart. There are various models that are used to describe values in (0,1). However, especially in the case of rare health events, zero values occur very frequently which, for example, denote the absence of the disease. In this paper, we study the performance and the statistical design of exponentially weighed moving average control charts for monitoring proportions that arise in a health-related framework. The proposed chart is based on the zero-inflated Beta distribution, a mixed (discrete-continuous) distribution, suitable for modelling data in [0,1). We use a Markov chain method to study the run length distribution of the exponentially weighed moving average chart. Also, we investigate the statistical design as well as the performance of the proposed charts. Comparisons with a Shewhart-type chart are also given. Finally, we provide an example for the practical implementation of the proposed charts.
Asunto(s)
Atención a la Salud , Vigilancia en Salud Pública , Humanos , Cadenas de MarkovRESUMEN
In this work, we study upper-sided cumulative sum control charts that are suitable for monitoring geometrically inflated Poisson processes. We assume that a process is properly described by a two-parameter extension of the zero-inflated Poisson distribution, which can be used for modeling count data with an excessive number of zero and non-zero values. Two different upper-sided cumulative sum-type schemes are considered, both suitable for the detection of increasing shifts in the average of the process. Aspects of their statistical design are discussed and their performance is compared under various out-of-control situations. Changes in both parameters of the process are considered. Finally, the monitoring of the monthly cases of poliomyelitis in the USA is given as an illustrative example.