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Design and implementation of q th quantile‐unbiased t r ‐chart for monitoring times between events
Author(s) -
Kumar Nirpeksh,
Baranwal Amita
Publication year - 2019
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2445
Subject(s) - quantile , chart , control chart , statistics , x bar chart , mathematics , control limits , function (biology) , algorithm , computer science , process (computing) , evolutionary biology , biology , operating system
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 r th ( 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 t r ‐chart. Further, we eliminate the bias in q th quantile function of the t r ‐chart for both the known and unknown parameter case. In particular, the MRL‐unbiased t r ‐chart is discussed in detail and compared with the ARL‐unbiased t r ‐chart. It is found that the MRL‐unbiased t r ‐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.