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The guaranteed adaptive c ‐charts with estimated parameter
Author(s) -
Vakilian Fatemeh,
Amiri Amirhossein,
Faraz Alireza
Publication year - 2018
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2342
Subject(s) - control chart , bootstrapping (finance) , statistics , variable (mathematics) , computer science , ewma chart , sampling (signal processing) , sample size determination , adaptive sampling , mathematics , process (computing) , econometrics , monte carlo method , mathematical analysis , filter (signal processing) , computer vision , operating system
The performance of control charts with estimated parameters in Phase II depends on the accuracy of parameter estimation in Phase I. Estimation accuracy depends on the amount of data. Simulation results show that no realistic number of Phase I samples is available to ensure that the in‐control performance of control charts with estimated parameters is close to cases where the parameters are known. In this paper, the bootstrapping method is applied to adjust the control and warning limits of c ‐charts with adaptive sampling schemes, such as variable sample size, variable sampling intervals, and variable parameters. The adjusted charts guarantee that the in‐control average adjusted time to signal is more than a certain amount with a predefined probability. In addition, the performance of the adjusted adaptive c ‐charts is compared with the commonly used approach to design adaptive c ‐charts.