Binomial CUSUM Research Articles

제1형의 우측중도절단된 와이블 수명자료를 관리하는 이항 누적합 관리도

제1형의 우측중도절단된 와이블 수명자료를 관리하는 이항 누적합 관리도

Assessment of Several Algorithms for Outbreak Detection using Bovine Meat Inspection Data for Syndromic Surveillance: A Pilot Study on Whole Carcass Condemnation Rate

Slaughterhouses are a potential source of data which is under-used for cattle health monitoring. The objective of this work was to assess the performance of several algorithms for outbreak detection based on weekly proportions of whole carcass condemnation. Data from 177,098 cattle slaughtered in one French slaughterhouse from 2005 to 2009 were used. The Shewart p chart, one-sided confidence interval of a negative binomial regression model, and EWMA and CUSUM on residuals of a negative binomial model were investigated. The highest sensitivity was obtained using negative binomial regression and the highest specificity using CUSUM or EWMA.

Run Length Distribution of CUSUM Control Schemes for Negative Binominal Processes

The CUSUM control scheme is an important tool in detecting the quality of goods or services. It is used in many industries for rapid detection of many industrial processes. The average run length (ARL) and distribution of run length and standard deviation of run length (SDRL) are the essential characteristics in constructing a control chart and are also important indexes for comparing performance with other control charts. Until now, no theoretic derivation for the run length and its standard deviation underlying negative binominal distribution for the CUSUM scheme have been developed. In this paper, an analytic method for steady state average run length as well as SDRL and two-sided ARL and SDRL with different control statistics is developed for negative binomial CUSUM (NB CUSUM). To decrease computer memory requirements and computing time, a sparse matrix operation method is also proposed to obtain the run length when conducting the Markov chain method. This analytic method makes the computations of run length for one-sided and two-sided NB CUSUM schemes easier. A real numerical example also shows the analytic results are consistent with the simulation results.

Aplicação de um gráfico cusum binomial no monitoramento de um indicador de água potável

A proposta deste artigo é analisar a aplicação de um gráfico de somas acumuladas (CUSUM) binomial no monitoramento da presença de coliformes totais, um indicador biológico para verificar a qualidade da água de abastecimento em um processo de tratamento de água. A série analisada é proveniente de uma estação de tratamento de água e corresponde ao período de 2007 a 2009, com frequência mensal. O tratamento estatístico dos dados foi realizado no GNU R, com desenvolvimento de rotinas para aproximar o limite superior do gráfico CUSUM binomial. Além disso, foi realizado um estudo comparativo para investigar se existe diferença significativa quanto à sensibilidade existente entre a aplicação do referido gráfico e o tradicional gráfico do tipo Shewhart, geralmente aplicado em monitoramento de processos. Os resultados demonstraram que este estudo foi fundamental para definir a melhor opção entre os gráficos para a análise estatística deste processo.

A comparison of weighted CUSUM procedures for monitoring process proportions with varying sample sizes

The conventional binomial CUSUM chart is an efficient tool for monitoring changes in fraction nonconforming when the sample size is fixed. However, it is less efficient in the case with varying sample sizes as the mean number of the nonconforming items is changing over time in this case. In order to deal with the varying mean of the binomial observations, this paper extends the idea of weighted CUSUM (WCUSUM) technique for monitoring fraction nonconforming under varying sample sizes. The comparison results with the traditional binomial CUSUM method and combined Shewhart-CUSUM method favour the proposed method. An example is used to illustrate the application of the proposed method.

Optimal average sample number of the SPRT chart for monitoring fraction nonconforming

The Sequential Probability Ratio Test (SPRT) control chart is a powerful tool for monitoring manufacturing processes. It is highly suitable for the applications where testing is destructive or very expensive, such as the automobile airbags test. This article studies the effect of the Average Sample Number (ASN) (i.e., the average sample size) on the chart’s performance. A design algorithm is proposed to develop the optimal SPRT chart for monitoring the fraction nonconforming p of Bernoulli processes. By optimizing the ASN and other charting parameters, the average detection speed of the SPRT chart is almost doubled. It is also found that the optimal SPRT chart significantly outperforms the optimal np and binomial CUSUM charts, in terms of Average Number of Defectives (AND), under different combinations of the design specifications. It is observed that the SPRT chart using a relatively smaller ASN and a shorter sampling interval (h) has a higher overall detection effectiveness.

Outbreak detection algorithms for seasonal disease data: a case study using ross river virus disease

BackgroundDetection of outbreaks is an important part of disease surveillance. Although many algorithms have been designed for detecting outbreaks, few have been specifically assessed against diseases that have distinct seasonal incidence patterns, such as those caused by vector-borne pathogens.MethodsWe applied five previously reported outbreak detection algorithms to Ross River virus (RRV) disease data (1991-2007) for the four local government areas (LGAs) of Brisbane, Emerald, Redland and Townsville in Queensland, Australia. The methods used were the Early Aberration Reporting System (EARS) C1, C2 and C3 methods, negative binomial cusum (NBC), historical limits method (HLM), Poisson outbreak detection (POD) method and the purely temporal SaTScan analysis. Seasonally-adjusted variants of the NBC and SaTScan methods were developed. Some of the algorithms were applied using a range of parameter values, resulting in 17 variants of the five algorithms.ResultsThe 9,188 RRV disease notifications that occurred in the four selected regions over the study period showed marked seasonality, which adversely affected the performance of some of the outbreak detection algorithms. Most of the methods examined were able to detect the same major events. The exception was the seasonally-adjusted NBC methods that detected an excess of short signals. The NBC, POD and temporal SaTScan algorithms were the only methods that consistently had high true positive rates and low false positive and false negative rates across the four study areas. The timeliness of outbreak signals generated by each method was also compared but there was no consistency across outbreaks and LGAs.ConclusionsThis study has highlighted several issues associated with applying outbreak detection algorithms to seasonal disease data. In lieu of a true gold standard, a quantitative comparison is difficult and caution should be taken when interpreting the true positives, false positives, sensitivity and specificity.

Disease surveillance using a hidden Markov model

BackgroundRoutine surveillance of disease notification data can enable the early detection of localised disease outbreaks. Although hidden Markov models (HMMs) have been recognised as an appropriate method to model disease surveillance data, they have been rarely applied in public health practice. We aimed to develop and evaluate a simple flexible HMM for disease surveillance which is suitable for use with sparse small area count data and requires little baseline data.MethodsA Bayesian HMM was designed to monitor routinely collected notifiable disease data that are aggregated by residential postcode. Semi-synthetic data were used to evaluate the algorithm and compare outbreak detection performance with the established Early Aberration Reporting System (EARS) algorithms and a negative binomial cusum.ResultsAlgorithm performance varied according to the desired false alarm rate for surveillance. At false alarm rates around 0.05, the cusum-based algorithms provided the best overall outbreak detection performance, having similar sensitivity to the HMMs and a shorter average time to detection. At false alarm rates around 0.01, the HMM algorithms provided the best overall outbreak detection performance, having higher sensitivity than the cusum-based Methods and a generally shorter time to detection for larger outbreaks. Overall, the 14-day HMM had a significantly greater area under the receiver operator characteristic curve than the EARS C3 and 7-day negative binomial cusum algorithms.ConclusionOur findings suggest that the HMM provides an effective method for the surveillance of sparse small area notifiable disease data at low false alarm rates. Further investigations are required to evaluation algorithm performance across other diseases and surveillance contexts.

A binomial CUSUM chart for detecting large shifts in fraction nonconforming

This article studies a unique feature of the binomial CUSUM chart in which the difference (d t −d 0) is replaced by (d t −d 0)2 in the formulation of the cumulative sum C t (where d t and d 0 are the actual and in-control numbers of nonconforming units, respectively, in a sample). Performance studies are reported and the results reveal that this new feature is able to increase the detection effectiveness when fraction nonconforming p becomes three to four times as large as the in-control value p 0. The design of the new binomial CUSUM chart is presented along with the calculation of the in-control and out-of-control Average Run Lengths (ARL0 and ARL1).

Applying cusum-based methods for the detection of outbreaks of Ross River virus disease in Western Australia

BackgroundThe automated monitoring of routinely collected disease surveillance data has the potential to ensure that important changes in disease incidence are promptly recognised. However, few studies have established whether the signals produced by automated monitoring methods correspond with events considered by epidemiologists to be of public health importance. This study investigates the correspondence between retrospective epidemiological evaluation of notifications of Ross River virus (RRv) disease in Western Australia, and the signals produced by two cumulative sum (cusum)-based automated monitoring methods.MethodsRRv disease case notification data between 1991 and 2004 were assessed retrospectively by two experienced epidemiologists, and the timing of identified outbreaks was compared with signals generated from two different types of cusum-based automated monitoring algorithms; the three Early Aberration Reporting System (EARS) cusum algorithms (C1, C2 and C3), and a negative binomial cusum.ResultsWe found the negative binomial cusum to have a significantly greater area under the receiver operator characteristic curve when compared with the EARS algorithms, suggesting that the negative binomial cusum has a greater level of agreement with epidemiological opinion than the EARS algorithms with respect to the existence of outbreaks of RRv disease, particularly at low false alarm rates. However, the performance of individual EARS and negative binomial cusum algorithms were not significantly different when timeliness was also incorporated into the area under the curve analyses.ConclusionOur retrospective analysis of historical data suggests that, compared with the EARS algorithms, the negative binomial cusum provides greater sensitivity for the detection of outbreaks of RRv disease at low false alarm levels, and decreased timeliness early in the outbreak period. Prospective studies are required to investigate the potential usefulness of these algorithms in practice.

ESTIMATION OF THE CHANGE POINT OF THE PROCESS FRACTION NONCONFORMING IN SPC APPLICATIONS

Knowing when a process has changed would simplify the search for and identification of the special cause. In this paper, we compare the maximum likelihood estimator (MLE) of the process change point (that is, when the process changed) to built-in change point estimators from binomial CUSUM and EWMA control charts. We conclude that it is better to use the maximum likelihood change point estimator when a CUSUM or EWMA control chart signals a change in the process fraction nonconforming. The results show that the MLE provides process engineers with an accurate and useful estimate of the last subgroup from the unchanged process.

Sample size and the Binomial CUSUM Control Chart: the case of 100% inspection

The Binomial CUSUM is used to monitor the fraction defective (p) of a repetitive process, particularly for detecting small to moderate shifts. The number of defectives from each sample is used to update the monitoring CUSUM. When 100% inspection is in progress, the question arises as to how many sequential observations should be grouped together in forming successive samples. The tabular form of the CUSUM has three parameters: the sample size n, the reference value k, and the decision interval h, and these parameters are usually chosen using statistical or economic-statistical criteria, which are based on Average Run Length (ARL). Unlike earlier studies, this investigation uses steady-state ARL rather than zero-state ARL, and the occurrence of the shift can be anywhere within a sample. The principal finding is that there is a significant gain in the performance of the CUSUM when the sample size (n) is set at one, and this CUSUM might be termed the Bernoulli CUSUM. The advantage of using n=1 is greater for larger shifts and for smaller values of in-control ARL.