International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749

Designing an Effective Combined Shewhart-CUSUM Control Scheme with Exponentially Distributed Data

Dushyant Tyagi
Department of Mathematics and Statistics, Dr. Shakuntala Misra National Rehabilitation University, Lucknow-226017, India.


Received on May 13, 2019
Accepted on July 24, 2019


In this paper, the Combined Shewhart-CUSUM control scheme has been proposed to monitor the production process when the quality characteristic follows exponential distribution to quickly detect the shift in the process. The simulated values of ARL are determined after the transformation of the data into approximate normal distribution by Nelson transformation method and adding Shewhart control limits to existing CUSUM Control Chart. Scheme parameters (value of k and h) and out of control ARL are calculated at various shift and at various in-control ARL. Parameters are also calculated to detect δ standard deviation shifts, which may be helpful to the quality control practitioners in designing the Combined Shewhart-CUSUM scheme when data is highly skewed.

Keywords- Combined Shewhart-CUSUM scheme, Exponential distribution, Average runs length, Monte Carlo simulation.


Tyagi, D. (2019). Designing an Effective Combined Shewhart-CUSUM Control Scheme with Exponentially Distributed Data. International Journal of Mathematical, Engineering and Management Sciences, 4(5), 1277-1286.

Conflict of Interest

The authors confirm that there is no conflict of interest to declare for this publication.


The author would like to express his sincere thanks to the referees for their valuable suggestions towards the improvement of the paper. The author is also grateful to Prof. Bhupendra Singh, Department of Statistics, C. C. S. University, Meerut for continuous guidance and University Grants Commission, Government of India for financial support for the work.


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