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- Title
Design and implementation of q <sup>th</sup> quantile‐unbiased t<sub>r</sub> ‐chart for monitoring times between events.
- Authors
Kumar, Nirpeksh; Baranwal, Amita
- Abstract
The times between events control charts have been proposed in literature for statistical monitoring of high‐yield processes by observing the waiting times up to rth (r ≥ 1 ) non‐conforming items or defects. The average run length (ARL) is the most widely used performance measure to evaluate the chart's performance, but in recent years, it has been subjected to criticisms. Because the run length distribution is highly skewed and hence, the ARL is not necessarily a typical value of the run length. Thus, evaluation of the control chart based on ARL alone could be misleading. In this paper, the quantiles of run length distribution are considered, instead of ARL, to design the tr‐chart. Further, we eliminate the bias in qth quantile function of the tr‐chart for both the known and unknown parameter case. In particular, the MRL‐unbiased tr‐chart is discussed in detail and compared with the ARL‐unbiased tr‐chart. It is found that the MRL‐unbiased tr‐chart outperforms than the corresponding ARL‐unbiased chart in unknown parameter case. It is also found that the proposed chart requires less phase I observations than that of the earlier studies has been suggested.
- Subjects
STATISTICAL process control; QUALITY control charts; CRYSTAL structure; MICROSTRUCTURE; QUANTILE regression
- Publication
Quality & Reliability Engineering International, 2019, Vol 35, Issue 4, p1061
- ISSN
0748-8017
- Publication type
Article
- DOI
10.1002/qre.2445