Statistical Control of Multiple-Stream Processes: A Shewhart Control Chart for Each Stream

ABSTRACT

Shewhart control charts for multiple stream processes (MSP) are studied in this article, including control limits, correlation influence, and average run lengths. Graphs are presented to aid in the design of control charts. Subgroups of one unit per stream or partial samples were taken. An example based on industry data is presented and analyzed to show the application and a comparison with other well-known methodologies for statistical control of MSP.

Keywords:

• ARL
• correlation
• multiple stream processes
• partial sampling
• Shewhart control charts

ACKNOWLEDGMENTS

The authors acknowledge Ms. Elena Saccone and Michael Hellmer for their help with English language issues.

Notes

^a For the set of MSP Shewhart control charts (one for each stream), when ±3σ _T control limits for each stream are used, and there is no correlation between them.

Process is out of control when one or more charts showed a point outside control limits.

^b In σ _T units, calculated limits for MSP Shewhart control charts (one for each stream), in order to maintain type I error probability at 0.0027, when ρ = 0.

^a The estimated values were calculated from 53 units for each stream. The machine was set to a target value of 0.700 g.

^b Stream #13.

^c Stream #5.