Abstract
Memory-type control charts are widely used for monitoring small to moderate shifts in the process parameter(s). In the present article, we present an exponentiated exponentially weighted moving average (Exp-EWMA) control chart that weights the past observations of a process using an exponentiated function. We evaluated the run-length characteristics of the Exp-EWMA chart via Monte Carlo simulations. A comparison study versus the CUSUM, EWMA and extended EWMA (EEWMA) charts under similar in-control (IC) run-length properties demonstrates that the Exp-EWMA chart is more effective for detecting small and, under certain circumstances, moderate shifts for both the zero-state and steady-state cases. Moreover, the Exp-EWMA chart has better zero-state out-of-control (OOC) performance than an EWMA chart with smoothing parameter equal to the limit to the infinity of the exponentiated function, while the two charts perform similarly for the steady-state case. Finally, it is shown that the Exp-EWMA chart is more IC robust than its competitors under several non-normal distributions. Two examples are provided to explain the implementation of the proposed chart.
Original language | English |
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Pages (from-to) | 3853-3891 |
Number of pages | 39 |
Journal | Statistical Papers |
Volume | 65 |
Issue number | 6 |
DOIs | |
State | Published - Aug 2024 |
Scopus Subject Areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
Keywords
- Exp-EWMA chart
- Monte Carlo simulation
- Run-length distribution
- Steady-state
- Zero-state