Abstract
The exponentially weighted moving average (EWMA) X-bar chart with the variable-sampling-interval (VSI) feature is usually scrutinized under the assumption of known process parameters. However, in practice, process parameters are usually unknown, and they need to be estimated from the in-control Phase-I data set. With this in mind, this article proposes the VSI EWMA X-bar chart in which the process parameters are estimated. A Markov Chain approach is adopted to derive the run-length properties of the VSI EWMA X-bar chart with estimated process parameters. The standard deviation of the average time to signal (SDATS) is employed to measure the practitioner-to-practitioner variation in the control chart’s performance. This variation occurs because different Phase-I datasets are used among practitioners to estimate the process parameters. Based on the SDATS criterion, this article provides recommendations regarding the minimum number of required Phase-I samples. For an optimum implementation, this article develops two optimization algorithms for the VSI EWMA X-bar chart with estimated process parameters, i.e., by minimizing the (i) out-of-control expected value of the average time to signal (AATS) and (ii) out-of-control expected value of the AATS (EAATS) for the cases of deterministic and unknown shift sizes, respectively. With the implementation of these new design procedures, the VSI EWMA X-bar chart with estimated process parameters is not only able to achieve a desirable in-control performance, but it is also able to quickly detect changes in the process.
Original language | English |
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Pages (from-to) | 1237-1265 |
Number of pages | 29 |
Journal | Journal of Testing and Evaluation |
Volume | 49 |
Issue number | 2 |
Early online date | 11 Jun 2019 |
DOIs | |
Publication status | Published - Jun 2019 |
Keywords
- Expected value of the average time to signal
- Known and unknown shift sizes
- Optimization design
- Parameter estimation
- Standard deviation of the average time to signal
- Standard deviation of the time to signal
ASJC Scopus subject areas
- General Materials Science
- Mechanics of Materials
- Mechanical Engineering