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Economic Design of a Variable Sampling Rate X-bar Chart

Summary: [This abstract is based on the authors' abstract.] An economic model is developed for a variable sampling rate (VSR) Shewhart X-bar chart in which sample size and sampling interval for the next sample depend on the current sample mean. The model expresses long-run cost per hour of the VSR chart as a function of: design parameters of the chart; process parameters that describe process behavior; and cost parameters associated with operation of the chart. This model can be used to quantify cost reduction of operating the VSR chart instead of a traditional chart with a fixed sampling rate. The cost reduction can range from modest to substantial, depending on the process and cost parameters. The model also can be used to gain insight into VSR chart design for applications. It is shown that the same threshold limit can be used for both sample size and sampling interval with little increase in cost. It also is shown that in most cases it is best to design the VSR chart with a very low false alarm rate.

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  • Topics: Sampling
  • Keywords: Control charts,X-bar control charts,Sampling interval,Sample size
  • Author: Park, Changsoon; Reynolds, Marion R., Jr.
  • Journal: Journal of Quality Technology