Designing of CUSUM chart with transformed Rayleigh distributed data

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.