Title: Designing of CUSUM chart with transformed Rayleigh distributed data

Authors: Dushyant Tyagi; Bhupendra Singh

Addresses: Department of Mathematics and Statistics, DSMNR University, Lucknow-226017, India ' Department of Statistics, Ch. Charan Singh University, Meerut-250004, India

Abstract: In this paper, the CUSUM chart has been proposed to monitor the small shift in production process when the quality characteristic follows Rayleigh distribution. To achieve approximate normality of the Rayleigh distributed data, Nelson transformation method is used. The efficiency of CUSUM chart in detecting small shift in the process as compared to traditional Shewhart chart is demonstrated through a simulated study. Parameters for proposed chart has been determined for varying true mean at fix 'in control mean' and 'in control ARL'. Table of k and h values are provided to assist quality control engineers for designing an optimal CUSUM chart to detect δσ shift.

Keywords: Shewhart mean charts; CUSUM charts; Rayleigh distribution; average run length; ARL; Monte Carlo simulation; control charts; statistical process control; SPC; production processes; Nelson transformation; control chart design.

DOI: 10.1504/IJQET.2016.081641

International Journal of Quality Engineering and Technology, 2016 Vol.6 No.1/2, pp.82 - 92

Received: 13 Jan 2016
Accepted: 29 Oct 2016

Published online: 17 Jan 2017 *

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