Aspen Plastics produces plastic bottles to customer order. The quality inspector

Question

Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottie machine and measures the outside diameter of the bottle neck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions (in.) from the last six samples are Bottle Sample 0.622 0.599 0.607 0.622 0.598 0.589 0.585 0.614 0.602 0.612 0.599 0.593 0.622 0.589 0.595 0.572 0.588 0.583 0.603 0.571 0.590 0.581 0.583 0.606 Click the icon to view the table of factors for calculating three-sigma limits for the x-chart and R-chart. Assume that only these six samples are sufficient, and use the data to determine control limits for an R- and an x-chart. Compute the range R and the sample mean x for each sample. (Enter your responses rounded fo three decimal places.) Bottle Sample 0.622 0.599 0.607 0.622 0.598 0.599 0.588 0.583 0.589 0.585 0.614 0.602 0.612 0.622 0.589 0.595 0.572 0.603 0.571 0.590 0.581 0.037 0.043 0.017 0.050 0.608 0.593 0.599 0.597 0.593 0.583 0.606 CLR equals inches and the LCLR equals inches. Enter your esponses unded to three deci al pla es "your answer fr LCLR The egative enter this e asa The UCL, equasnches and the LCL equalsinches. (Enter your responses rounded to three decimal places.)

Explanation / Answer

To be calculated:

(a) Upper control limit (UCLr) and Lower control limit (LCLr)

(b) Upper control limit (UCLx) and Lower control limit (LCLx)

Given values:

Number of samples = 6

Sample size, n = 4

Solution:

From the given information, X-bar and R is calculated as below:

X-bar = Sum of Averages of observations / Total number of samples

Range = Highest observed value - Lowest observed value

X-bar = (0.608 + 0.593 + 0.599 + 0.597 + 0.592 + 0.593) / 6 = 0.597

R-bar = (0.037 + 0.043 + 0.017 + 0.050 + 0.016 + 0.023) / 6 = 0.031

(a) UCLr and LCLr are calculated as;

UCLr = D4 x R-bar

LCLr = D3 x R-bar

From the table of 3-sigma limits, for n = 4;

A2 = 0.729

D3 = 0

D4 = 2.282

UCLr = 2.282 x 0.031

UCLr = 0.071 inches

LCLr = 0 x 0.031

LCLr = 0 inches

(b) UCLx and LCLx are calculated as;

UCLx = X-bar + (A2 x R-bar)

LCLx = X-bar - (A2 x R-bar)

UCLx = 0.597 + (0.729 x 0.031)

UCLx = 0.620 inches

LCLx = 0.597 - (0.729 x 0.031)

LCLx = 0.574 inches

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