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vincent, a quality control manager at an outdoor apparel manufacturing company, studies and monitors quality using r-charts. he discovers a quality problem with the construction of zippers. vincent proposes that 25 samples of eight observations each be collected on a daily basis. he plans to prepare an r-chart to monitor the variation in the size of the zippers. the data collected shows that the mean length of the zippers is 15 inches and the average range is 0.5 inches. if d3 for the r-chart is 0.136, the lower control limit (lclr) for the r-chart will be: a. less than or equal to 1. b. more than 1 but less than or equal to 2. c. more than 2 but less than or equal to 3. d. more than 4.



Answer :

lowest control limit (LCL^{R} ) for R chart is equal to 0.068 inches

and 0.068 is less than 1 .So the correct answer is( A) less than or equal  to 1 .

What is  lowest control limit?

The lower control limit on a control chart is a line that runs parallel to the centerline and denotes the value below which any particular data point would be deemed to be outside statistical control due to special cause variation.

Total sample = 25

sample size =  8 observation

mean length of the zippers = 15 inches

average range = 0.5 inches

D3 for R chart = 0.136

Formula =  [tex]LCL^{R}[/tex] = D₃ R

        Put the values

              R = 0.5 Inches

             D₃ = 0.136

LCL^{R} =  D₃ R

            = 0.136 * 0.5 = 0.068  inches

Thus lowest control limit (LCL^{R} ) for R chart is equal to 0.068 inches

and 0.068 is less than 1 .

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