On stochastic ordering and control charts for traﬃc intensity

Morais, Manuel Cabral; Pacheco, Antònio

doi:10.1080/07474946.2016.1238266

Cited by 4 publications

(3 citation statements)

References 7 publications

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“…These features of the GINAR(1) process and the associated results are comparable to the ones derived by (Morais [ 21 ] Section 3.2) and Morais and Pacheco [ 8 , 28 ].…”

Section: Discussionsupporting

confidence: 88%

Two Features of the GINAR(1) Process and Their Impact on the Run-Length Performance of Geometric Control Charts

Morais

2023

Entropy

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The geometric first-order integer-valued autoregressive process (GINAR(1)) can be particularly useful to model relevant discrete-valued time series, namely in statistical process control. We resort to stochastic ordering to prove that the GINAR(1) process is a discrete-time Markov chain governed by a totally positive order 2 (TP2) transition matrix.Stochastic ordering is also used to compare transition matrices referring to pairs of GINAR(1) processes with different values of the marginal mean. We assess and illustrate the implications of these two stochastic ordering results, namely on the properties of the run length of geometric charts for monitoring GINAR(1) counts.

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“…These features of the GINAR(1) process and the associated results are comparable to the ones derived by (Morais [ 21 ] Section 3.2) and Morais and Pacheco [ 8 , 28 ].…”

Section: Discussionsupporting

confidence: 88%

Two Features of the GINAR(1) Process and Their Impact on the Run-Length Performance of Geometric Control Charts

Morais

2023

Entropy

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“…Santos [14,Chapter 2] and Santos, Morais and Pacheco [15] capitalize on the Markov chain approach [5] to compute several RL related measures for the X n ,X n and W n charts, and extend the analysis in [10] to a broader set of To provide a more thorough answer to the question When it comes to detection speed, does it pay off to use the control statistic W n that requires more bookkeeping than the discrete statistics X n andX n ?…”

Section: Control Statistic Chartmentioning

confidence: 99%

“…For an unintentionally biased, most likely incomplete and somewhat overlapping reviews of the monitoring of the traffic intensity of queueing systems and other stochastic systems the reader is referred for instance to [10], [14,Section 1.7] and [15].…”

Section: Introductionmentioning

confidence: 99%

Comparing Short and Long-Memory Charts to Monitor the Traffic Intensity of Single Server Queues

Santos

Morais

Pacheco

2019

Stochastics and Quality Control

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The traffic intensity (ρ) is a vital parameter of queueing systems because it is a measure of the average occupancy of a server. Consequently, it influences their operational performance, namely queue lengths and waiting times. Moreover, since many computer, production and transportation systems are frequently modelled as queueing systems, it is crucial to use control charts to detect changes in ρ. In this paper, we pay particular attention to control charts meant to detect increases in the traffic intensity, namely: a short-memory chart based on the waiting time of the n-th arriving customer; two long-memory charts with more sophisticated control statistics, and the two cumulative sum (CUSUM) charts proposed by Chen and Zhou (2015). We confront the performances of these charts in terms of some run length related performance metrics and under different out-of-control scenarios. Extensive results are provided to give the quality control practitioner a concrete idea about the performance of these charts.

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On ARL-Unbiased Charts to Monitor the Traffic Intensity of a Single Server Queue

Morais

Knoth

2018

Frontiers in Statistical Quality Control 12

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On stochastic ordering and control charts for traﬃc intensity

Cited by 4 publications

References 7 publications

Two Features of the GINAR(1) Process and Their Impact on the Run-Length Performance of Geometric Control Charts

Two Features of the GINAR(1) Process and Their Impact on the Run-Length Performance of Geometric Control Charts

Comparing Short and Long-Memory Charts to Monitor the Traffic Intensity of Single Server Queues

On ARL-Unbiased Charts to Monitor the Traffic Intensity of a Single Server Queue

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