A new double sampling X¯ control chart for monitoring an abrupt change in the process location

Abstract

This paper develops a new double sampling (DS) monitoring scheme, namely, the side-sensitive DS $\overline{X}$ chart, to monitor the process mean. The operational procedure is presented first followed by the exact form of the probability of the in-control process under the normality assumption. Finally, the performance of the new scheme is investigated by minimizing the out-of-control average run-length and extra quadratic loss function. It was observed that the proposed chart presents a better overall performance than the existing DS $\overline{X}$ chart. An illustrative example is given to facilitate the design and implementation of the new chart.

Keywords:

• DS control chart; Statistical process monitoring; Side-sensitive DS scheme; Overall performance measures; Run length distribution

Acknowledgments

The authors thank the Department of Statistics, Masters and Doctorate (MD) bursary and the Extended Science Path-way (ESP) stream at the University of South Africa (UNISA) for their support. The authors also thank Mr. Sandile Shongwe for his valuable comments.

Funding

Marien Graham's research was funded by the National Research Foundation (NRF) [reference: PR_IFR190111407337, UID: 114814].