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Effectiveness of phase I applications for identifying randomly scattered out‐of‐control observations and estimating control chart parameters
Author(s) -
Testik Murat Caner,
Weiß Christian H.,
Koca Yesim,
Testik Ozlem Muge
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.2239
Subject(s) - control chart , control limits , shewhart individuals control chart , chart , computer science , statistics , x bar chart , control (management) , statistical process control , set (abstract data type) , ewma chart , process (computing) , sampling (signal processing) , mathematics , artificial intelligence , filter (signal processing) , computer vision , operating system , programming language
Estimation of unknown process parameters with fixed‐size samples are studied in the following. The standard textbook approach for phase I control chart implementation with a Shewhart control chart is evaluated for the case of normally distributed independent observations with random sampling. Thex ¯ − s charts are simultaneously implemented by generating observations that have a given percentage of randomly scattered out‐of‐control observations. Simulating the phase I steps, where out‐of‐control samples are detected iteratively by determining trial control limits, identifying samples exceeding these limits, and revising the control limits, the standard practice is evaluated in terms of both detection performance and quality of parameter estimates. It is shown that standard phase I control chart implementations with 3‐σ‐limits may perform very poorly in identifying true out‐of‐control observations and providing a reference set of in‐control observations for estimation in some practical settings. A chart design with 2‐σ‐limits is recommended for a successful phase I analysis.