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- Title
New EWMA t charts for process mean.
- Authors
Haq, Abdul; Riasat, Raheel; Khoo, Michael B. C.
- Abstract
In practice, the process standard deviation is usually unknown or is estimated inaccurately. The X¯$\bar{X}$‐type charts, such as the exponentially weighted moving average (EWMA) X¯$\bar{X}$ chart, which works under the assumption that the process standard deviation is either known or it is estimated accurately, may not perform well when the process standard deviation is actually unknown or estimated inaccurately. To address the aforesaid setback of the EWMA‐X¯$\bar{X}$ chart, the EWMA‐t chart was developed for monitoring the process mean when errors in estimating the process standard deviation occur or when the standard deviation is unknown. In this paper, new EWMA‐t charts, which are also robust against estimation errors in the process standard deviation and are applicable when the standard deviation is unknown, are developed for detecting mean shifts of a normal process. The new EWMA‐t charts are developed using the newly derived t‐statistics, based on the fixed sampling interval (FSI) and variable sampling interval (VSI) features. The new FSI/VSI EWMA‐t charts are found to outperform the existing FSI/VSI EWMA‐t chart, in terms of the zero‐state (ZS) and steady‐state (SS) average, median and standard deviation of the run‐length (SDRL)/time‐to‐signal criteria, for various shift sizes in the process mean, values of smoothing parameter and shift sizes in the process standard deviation. The application of the existing and new FSI/VSI‐EWMA‐t charts for detecting increases and decreases in the process mean is demonstrated with the automobile piston rings dataset.
- Subjects
QUALITY control charts; STANDARD deviations; PISTON rings; STATISTICAL process control; MOVING average process; MONTE Carlo method
- Publication
Quality & Reliability Engineering International, 2022, Vol 38, Issue 8, p4247
- ISSN
0748-8017
- Publication type
Article
- DOI
10.1002/qre.3205