The Variable Sampling Interval (VSI) in an Analysis of Taguchi's On-line Quality Monitoring Procedure for Variables

Abstract

The procedure of on-line process control for variables proposed by Taguchi consists of inspecting the mth item (a single item) of every m items produced and deciding, at each inspection, whether the mean value is increased or not. If the value of the monitored statistic is outside of the control limits, one decides the process is out-of-control and the production is stopped for adjustment; otherwise, it continues. In this article, a variable sampling interval (with a longer L and a shorter m ≤ L) chart with two set of limits is used. These limits are the warning (±W) and the control (±C), where W ≤ C. The process is stopped for adjustment when an observation falls outside of the control limits or a sequence of h observations falls between the warning limits and the control limits. The longer sample interval is used after an adjustment or when an observation falls inside the warning limits; otherwise, the short sampling interval is used. The properties of an ergodic Markov chain are used to evaluate the time (in units) that the process remains in-control and out-of-control, with the aim of building an economic–statistical model. The parameters (the sampling intervals m and L, the control limits W and C and the length of run h) are optimized by minimizing the cost function with constraints on the average run lengths (ARLs) and the conformity fraction. The performance of the current proposal is more economical than the decision taken based on a sequence of length h = 1, L = m, and W = C, which is the model employed in earlier studies. A numerical example illustrates the proposed procedure.

Keywords:

• Markov chain
• On-line process control
• Sequence of inspections
• Variable interval sampling
• Quality control by variables
• Warning limit

Mathematics Subject Classification:

• Primary 62P30, 60J10
• Secondary 90B25

Acknowledgments

The authors would like to acknowledge the suggestions from the anonymous reviewers, which greatly contributed to the readability of this article. We would also like to thank CNPq and Fapesp for the financial support for this research.