A nonparametric cumulative sum scheme based on sequential ranks and adaptive control limits

2015 ◽  
Author(s):  
Michael Lang ◽  
Abdelhak M. Zoubir
Keyword(s):  
Adaptive Control ◽  
Cumulative Sum ◽  
Control Limits

A new risk-adjusted Bernoulli cumulative sum chart for monitoring binary health data

2016 ◽  
Vol 25 (6) ◽  
pp. 2704-2713 ◽  
Author(s):  
Giuseppe Rossi ◽  
Simone Del Sarto ◽  
Marco Marchi
Keyword(s):  
Simple Formula ◽  
Efficient Solution ◽  
Real Data ◽  
Health Data ◽  
Data Sets ◽  
Cumulative Sum ◽  
Baseline Incidence ◽  
Health Event ◽  
Control Limits ◽  
Underlying Risk

To monitor a health event in patients with a specific risk of developing the event, a risk-adjusted cumulative sum chart is needed. The risk-adjusted cumulative sum chart proposed in the literature has some limitations. Setting appropriate control limits is not straightforward, there is no simple formula for constructing them, and they remain sensitive to changes in the underlying risk distribution and the baseline incidence rate. To overcome these limits, we propose a new risk-adjusted Bernoulli cumulative sum chart as a simple and efficient solution. Analyses of simulated and real data sets illustrate the performance and usefulness of the proposed procedure.

On a unified approach to the analysis of two-sided cumulative sum control schemes with headstarts

1985 ◽  
Vol 17 (3) ◽  
pp. 562-593 ◽  
Author(s):  
Emmanuel Yashchin
Keyword(s):  
Length Distribution ◽  
Sufficient Conditions ◽  
Unified Approach ◽  
Cumulative Sum ◽  
Control Schemes ◽  
The Laplace Transform ◽  
Run Length Distribution ◽  
Cumulative Sum Control ◽  
Necessary And Sufficient ◽  
Control Limits

The necessary and sufficient conditions for various modes of interactions of the upper and lower schemes with headstarts are derived. The expression for the Laplace transform of the run-length distribution (for both interacting and non-interacting schemes) is obtained and used to develop a method of analysis for general two-sided cumulative sum schemes with headstarts. The results are shown to be relevant in the case when the schemes are supplemented by Shewhart’s control limits.

On a unified approach to the analysis of two-sided cumulative sum control schemes with headstarts

1985 ◽  
Vol 17 (03) ◽  
pp. 562-593 ◽  
Author(s):  
Emmanuel Yashchin
Keyword(s):  
Length Distribution ◽  
Sufficient Conditions ◽  
Unified Approach ◽  
Cumulative Sum ◽  
Control Schemes ◽  
The Laplace Transform ◽  
Run Length Distribution ◽  
Cumulative Sum Control ◽  
Necessary And Sufficient ◽  
Control Limits

The necessary and sufficient conditions for various modes of interactions of the upper and lower schemes with headstarts are derived. The expression for the Laplace transform of the run-length distribution (for both interacting and non-interacting schemes) is obtained and used to develop a method of analysis for general two-sided cumulative sum schemes with headstarts. The results are shown to be relevant in the case when the schemes are supplemented by Shewhart’s control limits.

scholarly journals Cumulative Sum Chart Modeled under the Presence of Outliers

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 269 ◽  
Author(s):  
Nasir Abbas ◽  
Mu’azu Ramat Abujiya ◽  
Muhammad Riaz ◽  
Tahir Mahmood
Keyword(s):  
Phase I ◽  
Phase Ii ◽  
Estimation Error ◽  
Signal Strength ◽  
Received Signal Strength ◽  
Cusum Chart ◽  
Cumulative Sum ◽  
Run Length ◽  
Design Structure ◽  
Control Limits

Cumulative sum control charts that are based on the estimated control limits are extensively used in practice. Such control limits are often characterized by a Phase I estimation error. The presence of these errors can cause a change in the location and/or width of control limits resulting in a deprived performance of the control chart. In this study, we introduce a non-parametric Tukey’s outlier detection model in the design structure of a two-sided cumulative sum (CUSUM) chart with estimated parameters for process monitoring. Using Monte Carlo simulations, we studied the estimation effect on the performance of the CUSUM chart in terms of the average run length and the standard deviation of the run length. We found the new design structure is more stable in the presence of outliers and requires fewer amounts of Phase I observations to stabilize the run-length performance. Finally, a numerical example and practical application of the proposed scheme are demonstrated using a dataset from healthcare surveillance where received signal strength of individuals’ movement is the variable of interest. The implementation of classical CUSUM shows that a shift detection in Phase II that received signal strength data is indeed masked/delayed if there are outliers in Phase I data. On the contrary, the proposed chart omits the Phase I outliers and gives a timely signal in Phase II.

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