Premium
The performance of X ¯ control charts for large non‐normally distributed datasets
Author(s) -
Huberts Leo C.E.,
Schoonhoven Marit,
Goedhart Rob,
Diko Mandla D.,
Does Ronald J.M.M.
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.2287
Subject(s) - control chart , control limits , shewhart individuals control chart , x bar chart , sample (material) , computer science , chart , control (management) , statistics , limit (mathematics) , \bar x and r chart , ewma chart , mathematics , process (computing) , artificial intelligence , mathematical analysis , chemistry , chromatography , operating system
Because of digitalization, many organizations possess large datasets. Furthermore, measurement data are often not normally distributed. However, when samples are sufficiently large, the central limit theorem may be used for the sample means. In this article, we evaluate the use of the central limit theorem for various distributions and sample sizes, as well as its effects on the performance of a Shewhart control chart for these large non‐normally distributed datasets. To this end, we use the sample means as individual observations and a Shewhart control chart for individual observations to monitor processes. We study the unconditional performance, expressed as the expectation of the in‐control average run length (ARL), as well as the conditional performance, expressed as the probability that the control chart based on estimated parameters will have a lower in‐control ARL than a specified desired in‐control ARL. We use recently developed factors to correct the control limits to obtain a specified conditional or unconditional in‐control performance. The results in this paper indicate that the X ¯ control chart should be applied with caution, even with large sample sizes.