Title: Design and implementation of ARL-unbiased CCC_r-chart for monitoring high-yield processes

Authors: Nirpeksh Kumar; Ranjeet Kumar Singh

Addresses: Department of Statistics, Banaras Hindu University, Varanasi 221005, India ' Department of Mathematics, Adamas University, West Bengal, India

Abstract: In this paper, we consider the -charts for monitoring the high-quality processes considering the cumulative counts of conforming (CCC) items up to the r^th non-conforming one. But the charts perform poorly in detection of small downward shifts in the fraction non-conforming because of their undesirable ARL-biased property. In this paper, we eliminate the ARL-biasedness property and propose the ARL-unbiased charts using the notion of uniformly most powerful unbiased (UMPU) test to ensure that a user will get an OOC signal more quickly than a false alarm for the shifts in both upward and downward directions. The performance of the proposed chart is also compared with the existing ARL-unbiased CCC chart and it is found that the former has an improved ability of detecting shifts in the fraction non-conforming over the latter. An illustrative example is given and a summary and conclusions are offered.

Keywords: average run length; ARL; ARL-unbiased; control chart; high-yield processes; in-control performance; out-of-control performance; geometric distribution; fraction non-conforming; uniformly most powerful unbiased; UMPU; UMPU test.

DOI: 10.1504/IJQET.2022.123492

International Journal of Quality Engineering and Technology, 2022 Vol.8 No.4, pp.351 - 365

Received: 17 Jun 2020
Accepted: 24 Jun 2021
Published online: 23 Jun 2022 *