The combined Shewhart-CUSUM sign charts

Abstract

A Shewhart control chart is highly effective for detecting large process shifts, however, it is relatively less sensitive to the small shifts. A CUSUM chart is more efficient than a Shewhart chart for detecting small process shifts but it is inferior to that for detecting the large ones. This paper proposes the nonparametric combined Shewhart-CUSUM (CSC) control charts based on the sign statistic. By appropriately choosing the design parameters, a CSC chart exhibits a trade-off statistical performance between that of the Shewhart and CUSUM sign charts. That is, its performance lies between the performances of the Shewhart and CUSUM sign charts for detecting a process shift of any size. The expressions for the zero-state and steady-state average run lengths of the CSC chart are obtained using a Markov chain approach. An example illustrating the implementation of this chart is provided.

Keywords:

• Nonparametric control chart
• sign statistic
• zero-state average run length
• steady-state average run length

Acknowledgment

The authors are grateful to the reviewers for their critical comments and suggestions, which have greatly improved the content and presentation of the paper.

Additional information

Funding

Dadasaheb G. Godase’s work was supported by Department of Science and Technology through INSPIRE fellowship (IF160684). Shashibhushan B. Mahadik’s work was supported in part by University Grants Commission, New Delhi through Special Assistance Programme (F.520/8/DRS-I/2016(SAP-I)).