Question

A rum producer monitors the position of its label on the bottle by sampling two bottles from each batch. One quantity measured is the distance from the bottom of the bottle neck to the top of the label. The process mean should be μ = 1.6 inches. Past experience indicates that the distance varies with σ = 0.15 inch. (a) The mean distance x for each batch sample is plotted on an x control chart. Calculate the center line and control limits for this chart. (Round your answers to three decimal places.) CL = in LCL = in UCL = in (b) The sample standard deviation s for each batch's sample is plotted on an s control chart. What are the center line and control limits for this chart? (Round your answers to four decimal places.) CL = in LCL = in UCL = in

Answer 1

a)

sample mean x̅ =			1.6
population std deviation σ =			0.15
sample size n   =			2
control line (CL) = x̅=			1.6
upper control limit =x̅+3*σ/√n =			1.92
lower control limit =x̅+3*σ/√n =			1.28

b)

average std deviation s̅ =			0.15
sample size n   =			2
for sample size n=2, criitcal value of constant C4 =					0.7979
upper control limit =s̅+3(s̅/c4)*(√(1-c42)) =					0.490
lower control limit =max(s̅-3(s̅/c4)*(√(1-c42)),0) =					0.000