Precision Manufacturers employ Ron Wood, an MBA student. One of his first assign

Question

Precision Manufacturers employ Ron Wood, an MBA student. One of his first assignments is to introduce quality initiatives in the production of shafts used in engine lathes. Attached to the machine producing shafts is an X-bar chart and R chart for monitoring diameter of shafts. The present control chart has Center Line (mean X) = 2.5 inches, and three standard deviation control limits of UCL = 2.518 inches and LCL = 2.482 inches.

In his enthusiasm for reducing inspection costs, he decides to reduce the current sample size of 20 units designated on the chart to 10 units. Compute the revised control limits for X-bar chart and R-chart for the new sample size.

Explanation / Answer

R = UCL - LCL = 2.518 - 2.482 = 0.036 inches

R-bar = 0.036/10 = 0.0036 inches

UCL - R chart = R-bar x D4 = 0.0036 * 1.777 =  0.0063

LCL -R chart = R-bar x D3 = 0.0036 * 0.223 = 0.008

D3 and D4 are constants at n = 10

UCL - X Bar =  X-bar-bar + (A2 x R-bar) = 2.5+ 0.308*0.0036 = 2.5011

LCL - X Bar =  X-bar-bar - (A2 x R-bar) = 2.5 - 0.308*0.0036 = 2.498

A2 = constant = 0.308 at n =10

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