In this work we will provide a monitoring scheme for the mean of an autocorrelated process which can experience bidirectional jumps of random size and occurrence and has a steady state. Our interest focuses in the start up phase and short-run scenarios, where traditional SPC techniques fail to provide formal testing. Furthermore, we will provide a framework where prior information regarding the process can be employed. These will be achieved by adopting a Bayesian sequentially updated scheme that will allow inference in an online fashion. The performance of the proposed model will be compared against other methods which can be applied in similar settings. A simulation study along with a real data application from the dairy business will conclude this work. Supplemental files are available online, with technical details and the code for applying the proposed methodology in R.
Bibliographical noteFunding Information:
We would like to express our gratitude to the editorial staff and two referees for a number of valuable suggestions which improved the manuscript. Also we would like to thank Joanna Lukas of the Department of Animal Science, University of Minnesota for providing the MUN data used in the example. This work was partially supported under NSF grant DMS 0306304.
- Bayesian statistical process control
- Normal mixtures
- Online inference
- Short runs