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Cumulative Sum (cumulative + sum)

Distribution by Scientific Domains
Mathematics and Statistics25%

Selected Abstracts

A Cumulative Sum scheme for monitoring frequency and size of an event

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 6 2010
Zhang Wu
Abstract This article proposes a Cumulative Sum (CUSUM) scheme, called the TC-CUSUM scheme, for monitoring a negative or hazardous event. This scheme is developed using a two-dimensional Markov model. It is able to check both the time interval (T) between occurrences of the event and the size (C) of each occurrence. For example, a traffic accident may be defined as an event, and the number of injured victims in each case is the event size. Our studies show that the TC-CUSUM scheme is several times more effective than many existing charts for event monitoring, so that cost or loss incurred by an event can be reduced by using this scheme. Moreover, the TC-CUSUM scheme performs more uniformly than other charts for detecting both T shift and C shift, as well as the joint shift in T and C. The improvement in the performance is achieved because of the use of the CUSUM feature and the simultaneous monitoring of T and C. The TC-CUSUM scheme can be applied in manufacturing systems, and especially in non-manufacturing sectors (e.g. supply chain management, health-care industry, disaster management, and security control). Copyright © 2009 John Wiley & Sons, Ltd. [source]

Asymmetric adjustment and nonlinear dynamics in real exchange rates

INTERNATIONAL JOURNAL OF FINANCE & ECONOMICS, Issue 1 2005
Hyginus Leon
Abstract This paper examines whether deviations from PPP are stationary in the presence of nonlinearity, and whether the adjustment towards PPP is symmetric from above and below. Using alternative nonlinear models, our results support mean reversion and asymmetric adjustment dynamics. We find differences in magnitudes, frequencies and durations of the deviations of exchange rates from fixed and time-varying thresholds, both between over-appreciations and over-depreciations and between developed and developing countries. In particular, the average cumulative sum of deviations during periods when exchange rates are below forecasts is twice that during periods of over-appreciation and larger for developing than advanced countries. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Model-Free CUSUM Methods for Person Fit

JOURNAL OF EDUCATIONAL MEASUREMENT, Issue 4 2009
Ronald D. Armstrong
This article demonstrates the use of a new class of model-free cumulative sum (CUSUM) statistics to detect person fit given the responses to a linear test. The fundamental statistic being accumulated is the likelihood ratio of two probabilities. The detection performance of this CUSUM scheme is compared to other model-free person-fit statistics found in the literature as well as an adaptation of another CUSUM approach. The study used both simulated responses and real response data from a large-scale standardized admission test. [source]

Estimating the Change Point of a Poisson Rate Parameter with a Linear Trend Disturbance

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 4 2006
Marcus B. Perry
Abstract Knowing when a process changed would simplify the search and identification of the special cause. In this paper, we compare the maximum likelihood estimator (MLE) of the process change point designed for linear trends to the MLE of the process change point designed for step changes when a linear trend disturbance is present. We conclude that the MLE of the process change point designed for linear trends outperforms the MLE designed for step changes when a linear trend disturbance is present. We also present an approach based on the likelihood function for estimating a confidence set for the process change point. We study the performance of this estimator when it is used with a cumulative sum (CUSUM) control chart and make direct performance comparisons with the estimated confidence sets obtained from the MLE for step changes. The results show that better confidence can be obtained using the MLE for linear trends when a linear trend disturbance is present. Copyright © 2005 John Wiley & Sons, Ltd. [source]

A magnitude-robust control chart for monitoring and estimating step changes for normal process means

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 6 2002
Joseph J. Pignatiello Jr
Abstract Statistical process control charts are intended to assist operators of a usually stable system in monitoring whether a change has occurred in the process. When a change does occur, the control chart should detect it quickly. If the operator can also be provided information that aids in the search for the special cause, then critical off-line time can be saved. We investigate a process-monitoring tool that not only provides speedy detection regardless of the magnitude of the process shift, but also supplies useful change point statistics. A likelihood ratio approach can be used to develop a control chart for permanent step change shifts of a normal process mean. The average run length performance for this chart is compared to that of several cumulative sum (CUSUM) charts. Our performance comparisons show that this chart performs better than any one CUSUM chart over an entire range of potential shift magnitudes. The likelihood ratio approach also provides point and interval estimates for the time and magnitude of the process shift. These crucial change-point diagnostics can greatly enhance special cause investigation. Copyright © 2002 John Wiley & Sons, Ltd. [source]

TWO-PASS CUSUM TO IDENTIFY AGE-CLUSTER OUTBREAKS

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 3 2010
Ross Sparks
Summary The paper introduces a two-pass adaptive cumulative sum (CUSUM) statistic to identify age clusters (age grouping) that significantly contribute to epidemics or unusually high counts. If epidemiologists know that an epidemic is confined to a narrow age group, then this information not only makes it clear where to target the epidemiological effort but also helps them decide whether to respond. It is much easier to control an epidemic that starts in a narrow age range of the population, such as pre-school children, than an epidemic that is not confined demographically or geographically. [source]

Model-Checking Techniques Based on Cumulative Residuals

BIOMETRICS, Issue 1 2002
D. Y. Lin
Summary. Residuals have long been used for graphical and numerical examinations of the adequacy of regression models. Conventional residual analysis based on the plots of raw residuals or their smoothed curves is highly subjective, whereas most numerical goodness-of-fit tests provide little information about the nature of model misspecification. In this paper, we develop objective and informative model-checking techniques by taking the cumulative sums of residuals over certain coordinates (e.g., covariates or fitted values) or by considering some related aggregates of residuals, such as moving sums and moving averages. For a variety of statistical models and data structures, including generalized linear models with independent or dependent observations, the distributions of these stochastic processes under the assumed model can be approximated by the distributions of certain zero-mean Gaussian processes whose realizations can be easily generated by computer simulation. Each observed process can then be compared, both graphically and numerically, with a number of realizations from the Gaussian process. Such comparisons enable one to assess objectively whether a trend seen in a residual plot reflects model misspecification or natural variation. The proposed techniques are particularly useful in checking the functional form of a covariate and the link function. Illustrations with several medical studies are provided. [source]

Monitoring of nosocomial invasive aspergillosis and early evidence of an outbreak using cumulative sum tests (CUSUM)

CLINICAL MICROBIOLOGY AND INFECTION, Issue 9 2010
J. Menotti
Clin Microbiol Infect 2010; 16: 1368,1374 Abstract In order to provide a statistically based evaluation of the incidence of invasive aspergillosis (IA) over time, we applied the cumulative sums (CUSUM) methodology, which was developed for quality control and has already been applied for the surveillance of hospital-acquired infections. Cases of IA were recorded during a 5-year period. Incidence rates of cases assumed to be hospital-acquired, i.e. nosocomial IA (NIA), were analysed using CUSUM tests. Relationships between NIA, fungal contamination and construction or renovation work were tested using time-series methods. Between January 2002 and December 2006, 81 cases of NIA were recorded. CUSUM analysis of NIA incidence showed no significant deviation from the expected monthly number of cases until August 2005, and then the CUSUM crossed the decision limit, i.e. identified a significant increase in NIA as compared with the reference period (January 2002 to December 2004). Up to April 2006, the learning-curve CUSUM stayed over its limit, supporting an ongoing outbreak involving 24 patients, and then it significantly decreased in May 2006. Follow-up after May 2006 indicated no out-of-control situation, supporting a return to the baseline situation. In haematology wards, significant links were found between NIA incidence and fungal contamination of several sites at each ward (mainly unprotected common sites). An environmental source of contamination could be suspected, but no significant relationship was found between NIA incidence and ongoing construction or renovation. In conclusion, the CUSUM test proved to be well suited for real-time monitoring of NIA and for early identification and follow-up of an outbreak. [source]