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Control charts with random interarrival times between successive samplings
Author(s) -
Koutras Markos V.,
Rakitzis Athanasios C.
Publication year - 2018
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2358
Subject(s) - control chart , chart , computer science , control limits , statistic , statistical process control , poisson distribution , statistics , sampling (signal processing) , random variable , x bar chart , algorithm , process (computing) , shewhart individuals control chart , \bar x and r chart , mathematics , ewma chart , detector , operating system , telecommunications
In the classical setup used in process monitoring, the times between the collection of successive plotted samples are considered as nonrandom. However, in several real‐life applications, it seems plausible to assume that the time needed to collect the necessary information for plotting a point in the control chart has a stochastic nature. Under this scenario, instead of focusing on the number of points plotted on the chart until an out‐of‐control signal is initiated, the appropriate statistic to look at is the total time until a signal is generated. If we denote by L the run length of a control chart and by Y t , t = 1,2,…, the times between successive plotted points, then the compound random variable S L = ∑ t = 1 LY t expresses the time to signal of a monitoring scheme, under a particular sampling policy. In this paper, we illustrate how S L can be exploited to study various charts that are suitable for monitoring Poisson observations. We provide some results for the exact distribution of S L that may facilitate the task of the performance assessment of a control chart with random plotting times; illustrations and several numerical comparisons that are useful for quality control experts who wish to practice them are presented, and finally, an illustrative example elucidating the implementation of the proposed model is also provided.