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Chapter 1: Q2BSC (page 1)

Notation and Terminology Consider process data consisting of the amounts (oz) of Coke in randomly selected cans of regular Coke. The process is to be monitored with \(\bar x\)and R control charts based on samples of 50 cans randomly selected each day for 20 consecutive days of production. What are x and R control charts, and what do \(\bar x,\bar R\), UCL, and LCL denote?

Short Answer

Expert verified

\(\bar x\)-chart is the sample mean control chart, used to monitor sample means.

R-chart is the range control chart, used to monitor the variation in process.

\(\bar x,\bar R\) are centerlines of two charts where the former represents the mean of all sample means and later represents the mean of all sample ranges.

UCL and LCL are the upper and lower control limit respectively.

Step by step solution

01

Given information

The process data is recorded from 50 randomly selected cans containingcoke for 20 days. It is monitored using two control charts; \(\bar x,R\)-charts.

02

Define the control charts

Control charts are visual depictions of certain statistical measure taken from all the samples over the time period.The control charts would include three other measures other than the observations:

  • Centerline\(\left( {\bar R\;or\; \bar x} \right)\)
  • Lower control limit (LCL)
  • Upper control limit (UCL)

In case of \(\bar x\)-charts, the measure under study is sample mean and the corresponding centerline value \( \bar x\)is the mean of all sample means. The chart is used to monitor the means.

In case of \(R\)-charts, the measure under study is range of the samples and the corresponding centerline value \(\bar R\) is the mean of all sample range measures. The chart is used to monitor the variation.

03

Describe the notations

The UCL and LCL are lower and upper control limits of the charts,, computed in a way that 99.7% of the observations fall within the range of two limits in any of the two control charts.

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