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Survival analysis is a statistical method used to analyze time-to-event data, often employed in fields such as medicine, engineering, and social sciences. One of the key challenges in survival analysis is dealing with incomplete data, a phenomenon known as "censoring." Censoring occurs when the event of interest (such as death, relapse, or system failure) has not occurred for some individuals by the end of the study period or is otherwise unobservable, and it might have many different...
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Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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Related Experiment Video

Updated: Nov 10, 2025

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
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Monitoring the Zero-Inflated Time Series Model of Counts with Random Coefficient.

Cong Li1, Shuai Cui1, Dehui Wang1,2

  • 1School of Mathematics, Jilin University, Changchun 130012, China.

Entropy (Basel, Switzerland)
|April 3, 2021
PubMed
Summary

This study introduces a new control chart for monitoring changes in autocorrelated count data. The method effectively detects shifts in mean and correlation, outperforming traditional approaches.

Keywords:
CUSUM control chartINAR-type time seriesrandom survival ratestatistical process monitoringzero-inflation

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Area of Science:

  • Statistical Process Control
  • Time Series Analysis
  • Count Data Modeling

Background:

  • Monitoring zero-inflated autocorrelated count data presents challenges for traditional statistical process control methods.
  • Existing methods may not adequately capture the complexities of time series data with excess zeros and autocorrelation.
  • The integer-valued time series model with random survival rate offers a potential framework for addressing these complexities.

Purpose of the Study:

  • To develop and validate an efficient control charting procedure for detecting mean and correlation changes in zero-inflated autocorrelated count data.
  • To provide practical guidelines for the design and implementation of the proposed control chart.
  • To compare the performance of the new method against conventional control charting procedures.

Main Methods:

  • Construction of a cumulative sum (CUSUM) control chart tailored for integer-valued time series models with random survival rates.
  • Derivation of analytical methods for calculating the average run length (ARL) and standard deviation of the run length (SDRL).
  • Utilization of designs of experiments for extensive computational validation and performance assessment.

Main Results:

  • The proposed CUSUM control chart demonstrates effectiveness in monitoring mean and correlation shifts in the specified data type.
  • Calculations for ARL and SDRL provide a basis for chart design and performance evaluation.
  • Extensive simulations confirm the validity and efficiency of the developed method.

Conclusions:

  • The novel control charting method offers a robust approach for process monitoring of zero-inflated autocorrelated count data.
  • The CUSUM chart provides superior performance compared to conventional methods in detecting critical process changes.
  • The study's findings are illustrated through a real-world application analyzing monthly drug crime data in Pittsburgh.