Please use this identifier to cite or link to this item: https://doi.org/10.1080/03610920600728450
Title: CUSUM chart with transformed exponential data
Authors: Liu, J.Y.
Xie, M. 
Goh, T.N. 
Keywords: ARL
Control charts
CUSUM
Time between events
Transformation
Issue Date: 1-Oct-2006
Source: Liu, J.Y., Xie, M., Goh, T.N. (2006-10-01). CUSUM chart with transformed exponential data. Communications in Statistics - Theory and Methods 35 (10) : 1829-1843. ScholarBank@NUS Repository. https://doi.org/10.1080/03610920600728450
Abstract: Time Between Events (TBE) charts were proposed to monitor the time between events occur based on exponential distribution, and have been shown to be more effective than monitoring the fraction non conforming directly. In this article, we consider monitoring the TBE data with CUSUM scheme by transformation. The idea behind it is to transform the TBE data to normal, and then apply the CUSUM scheme for the approximate normal data. Several simple transformation methods are examined. The calculation of Average Run Length (ARL) with Markov chain approach is described. Comparative studies on the ARL performance show that the transformed CUSUM is superior to the X-MR (Moving Range) chart with transformation, the Cumulative Quantity Control (CQC) chart, and have comparable performance with exponential CUSUM charts. The design procedures of optimal CUSUM chart are also presented. This study provides another possible alternative for monitoring TBE data with easy design procedures and relatively good performance.
Source Title: Communications in Statistics - Theory and Methods
URI: http://scholarbank.nus.edu.sg/handle/10635/72310
ISSN: 03610926
DOI: 10.1080/03610920600728450
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