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Online monitoring of stationary ordinal time series
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AI
C
Christian Weiß*O
Osama SwidanM
Murat Caner Testik DOI：10.1080/00224065.2026.2667338.png)
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Abstract
En 中文
Except a few, the majority of the literature on monitoring ordinal data consider independent and identically distributed processes, where samples of data are collected sequentially in time. However, stationary ordinal processes exhibiting serial dependence are also common in many real-world process monitoring applications. This study proposes three classes of novel control charts for monitoring serially dependent stationary ordinal processes. Instead of sample statistics, individual observations are utilized. Exponentially weighted moving-average smoothing of a sequence of estimates is used for estimating the probability mass (cumulative distribution) function of the process. Defined real-valued functions of the probability mass (cumulative distribution) estimates are then used as the statistic plotted on the control charts. The methods are designed to be sensitive to a shift in the marginal distribution. Average run length performance of the control charts are computed under a comprehensive set of data-generating process models, which are inspired by real-world examples and exhibit quite different serial dependence structures. The performances of the proposed control charts are evaluated and compared to provide recommendations for implementations. The results show that the class of demerit-type charts generally perform better than the others. To illustrate the application and interpretation of the proposed methods, a real-world data example on monitoring of heating, ventilation, and air conditioning systems in passenger rail coaches is discussed.
Keywords:
attributes control charts
average run length
exponentially weighted moving average
individuals control charts
stationary ordinal time series
statistical process monitoring
Journal
IF:
2.2
Papers:
57
Citations:
2.9K
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Cited Papers