ARL Estimation of the Control Chart of Log Likelihood Ratios’ Sum for Markov Sequence | Zendy

Yi Guo | Zendy; Lei Gao | Zendy; Yan Zhu | Zendy

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ARL Estimation of the Control Chart of Log Likelihood Ratios’ Sum for Markov Sequence

Author(s) -

Yi Guo,

Lei Gao,

Yan Zhu

Publication year - 2021

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2021/6649949

Subject(s) - mathematics , markov chain , control chart , control limits , limit (mathematics) , sequence (biology) , statistics , equivalence (formal languages) , statistic , combinatorics , discrete mathematics , process (computing) , computer science , mathematical analysis , genetics , operating system , biology

To evaluate the surveillance performance of a control chart with the charting statistic of the sum of log likelihood ratios in the statistical process control (SPC), in this paper, we give the proof procedure based on Markov chains for the asymptotic estimation of the average run length (ARL) for this kind of chart. The out-of-control ARL 1 is approximately equal to 1 for any fixed in-control ARL 0 with a negative control limit. By the equivalence between limit distribution of a sum and that of a suprema sum of Markov chain, we derive the estimation of ARL 1 with a large enough positive control limit. Numerical experiments are conducted to confirm our results.

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