Control charts based on the Poisson distribution are commonly used to monitor count data in attributes. However, the Poisson distribution is based on the underlying equidispersion assumption that is limiting as discussed by different researchers in the literature. Therefore, a generalized control chart is required that can be used to monitor both overdispersed and underdispersed count data. This article reviews the methods to implement for dispersed count data and present ideas for future work in this area. A comprehensive literature review for researchers and practitioners is presented in this article. Copyright © 2014 John Wiley & Sons, Ltd.

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Food chain contamination by soil cadmium (Cd) through vegetable consumption poses a threat to human health. Therefore, an understanding is needed on the relationship between the phytoavailability of Cd in soils and its uptake in edible tissues of vegetables. The purpose of this study was to establish soil Cd thresholds of representative Chinese soils based on dietary toxicity to humans and develop a model to evaluate the phytoavailability of Cd to Pak choi (Brassica chinensis L.) based on soil properties. Mehlich-3 extractable Cd thresholds were more suitable for Stagnic Anthrosols, Calcareous, Ustic Cambosols, Typic Haplustalfs, Udic Ferrisols and Periudic Argosols with values of 0.30, 0.25, 0.18, 0.16, 0.15 and 0.03 mg kg−1, respectively, while total Cd is adequate threshold for Mollisols with a value of 0.86 mg kg−1. A stepwise regression model indicated that Cd phytoavailability to Pak choi was significantly influenced by soil pH, organic matter, total Zinc and Cd concentrations in soil. Therefore, since Cd accumulation in Pak choi varied with soil characteristics, they should be considered while assessing the environmental quality of soils to ensure the hygienically safe food production.

The study proposes a Shewhart-type control chart, namely an MD chart, based on average absolute deviations taken from the median, for monitoring changes (especially moderate and large changes -a major concern of Shewhart control charts) in process dispersion assuming normality of the quality characteristic to be monitored. The design structure of the proposed MD chart is developed and its comparison is made with those of two well-known dispersion control charts, namely the R and S charts. Using power curves as a performance measure, it has been observed that the design structure of the proposed MD chart is more powerful than that of the R chart and is very close competitor to that of the S chart, in terms of discriminatory power for detecting shifts in the process dispersion. The non-normality effect is also examined on design structures of the three charts, and it has been observed that the design structure of the proposed MD chart is least affected by departure from normality.

The Conway-Maxwell-Poisson distribution can be used to model under-dispersed or over-dispersed count data. This study proposes a flexible and generalized attribute exponentially weighted moving average (EWMA), namely GEWMA, control chart for monitoring count data. The proposed EWMA chart is based on the Conway-Maxwell-Poisson distribution. The performance of the proposed chart is evaluated in terms of run length (RL) characteristics such as average RL, median RL, and standard deviation of the RL distribution. The average RL of the proposed GEWMA chart is compared with Sellers chart. The sensitivity of the standard Poisson EWMA (PEWMA) chart is also studied and compared with the proposed GEWMA chart for under-dispersed or over-dispersed data. It has been observed that the PEWMA chart is very sensitive for under-dispersed or over-dispersed data while the proposed GEWMA is very robust. Finally, the generalization of the proposed chart to the Bernoulli EWMA, PEWMA, and geometric EWMA charts is also studied using someone simulated data sets.