A quality control inspector at the Beautiful Shampoo Company has taken three sam

Question

A quality control inspector at the Beautiful Shampoo Company has taken three samples with four observations each of the volume of shampoo bottles filled. The data collected by the inspector and the computed means are shown here:

Samples of Shampoo Bottle Volume in Ounces

20.0

A quality control inspector at the Beautiful Shampoo Company has taken three samples with four observations each of the volume of shampoo bottles filled. The data collected by the inspector and the computed means are shown here:

Samples of Shampoo Bottle Volume in Ounces

Observation 1 2 3 1 19.7 19.7 19.7 2 20.6 20.2 18.7 3 18.9 18.9 21.6 4 20.8 20.7 20.0 Mean 20.0If the standard deviation of the shampoo bottle-filling operation is 0.2 ounces, use the information in the table to develop control limits of 3 standard deviations for the operation: (a) CL, (b) UCL, (c) LCL. 19.875

20.0

Explanation / Answer

Overall Average = (20+19.875+20)/3 = 19.96 ; n = 4

Therefore (a) Central line (CL) = 19.96

(b) UCL (Upper control limit)

standard deviation = 0.2 ounces

UCL = CL (Overall Avg) + 3 / ( n = 4)

UCL = 19.96+ 3 (0.2) / ( n = 4) = 19.96 + 0.3 = 20.26

(c) LCL = CL (Overall Avg) - 3 / ( n = 4)

              = 19.96 - 3 (0.2) / ( n = 4) = 19.96 - 0.3 = 19.66

Sample Number Observations(Ounces) 1 2 3 4 Avg. Value (X) 1 19.7 20.6 18.9 20.8 20.0 2 19.7 20.2 18.9 20.7 19.875 3 19.7 18.7 21.6 20.0 20.0

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