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Evaluation of Shewhart time‐between‐events‐and‐amplitude control charts for correlated data
Author(s) -
Rahali Dorra,
Castagliola Philippe,
Taleb Hassen,
Khoo Michael Boon Chong
Publication year - 2021
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.2731
Subject(s) - control chart , weibull distribution , statistics , amplitude , mathematics , exponential function , exponential distribution , gamma distribution , shewhart individuals control chart , distribution (mathematics) , computer science , ewma chart , physics , mathematical analysis , process (computing) , quantum mechanics , operating system
In recent years, several techniques based on control charts have been developed for the simultaneous monitoring of the time interval T and the amplitude X of events, known as time‐between‐events‐and‐amplitude (TBEA) charts. However, the vast majority of the existing works have some limitations. First, they usually focus on statistics based on the ratioX T , and second, they only investigate a reduced number of potential distributions, that is, the exponential distribution for T and the normal distribution for X . Moreover, until now, very few research papers have considered the potential dependence between T and X . In this paper, we investigate three different statistics, denoted as Z 1 , Z 2 , and Z 3 , for monitoring TBEA data in the case of three potential distributions (gamma, normal, and Weibull), for both T and X , using copulas as a mechanism to model the dependence. An illustrative example considering times between machine breakdowns and associated maintenance illustrates the use of TBEA control charts.