Abstract
The run sum X- control chart is usually investigated under the assumption of known process parameters. In practice, process parameters are rarely known and they need to be estimated from an in-control Phase I dataset. However, different practitioners use different numbers of Phase I samples to estimate the process parameters. As a result, the commonly used performance measure, ie, the average run length becomes a random variable. In this study, we present a run sum X- control chart with estimated process parameters and use the standard deviation of the average run length to evaluate the average of the average run length performance of the run sum X- chart when process parameters are estimated. Based on the standard deviation of the average run length criterion, the number of Phase I samples required by the estimated process parameter-based run sum X- chart to have an average of the average run length performance close to that obtained under the assumption of known process parameters is recommended.
Original language | English |
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Pages (from-to) | 1885–1899 |
Number of pages | 15 |
Journal | Quality and Reliability Engineering International |
Volume | 33 |
Issue number | 8 |
Early online date | 17 Apr 2017 |
DOIs | |
Publication status | Published - 28 Nov 2017 |
Keywords
- Average of the average run length
- Average run length
- Parameter estimation
- Run sum X chart
- Standard deviation of the average run length
ASJC Scopus subject areas
- Safety, Risk, Reliability and Quality
- Management Science and Operations Research