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1) Upper Control Limit?

2) Lower Control Limit?

Sampling 4 pieces of precision-cut wire (to be used in computer assembly) every hour for the past 24 hours has produced the following results: Hour R Hour x R Hour x R Hour x 1 3.35 0.767 2.95 0.58 13 3.21 0.80 19 3.41 1.66 2 3.20 88 2.75 1.0814 2.93 1.36 20 2.79 104 3 3.12 43 9 3.12 0.6615 3.22 1.06 212.55 1.03 4 3.29 1.31 10 2.75 1.33 16 274 0.55 22 3.28 0.41 5 3.07 122 2.83 1.12 7 2.86 1.48 23 3.04 1.58 6 2.76 0.42 12 3.07 0.3518 2.84 1.29242.64 0.92 Based on the sampling done, the control limits for 3-sigma x chart are (round all intermediate calculations to three decimal places before proceeding with further calculations) Upper Control Limit (UCL)nches (round your response to three decimal places).

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Answer #1

From the data provided:

Mean of Xbar = Xbar-bar = Sum of all Xbar / Number of samples = 71.77/24 = 2.990

Rbar = Mean of R = Sum of R values / Number of samples = 24.62/24 = 1.025

Given that , sample size = n = 4

The relevant values of constants for n = 4 will be :

A2 = 0.729

Therefore, control limits for Xbar chart :

Upper Control Limit = UCLx = Xbar + A2.Rbar = 2.990 + 0.729 x 1.025 = 2.990 + 0.747= 3.737 inches

Lower Control Limit = LCLx = Xbar – A2.Rbar = 2.990 – 0.729 x 1.025 = 2.990 – 0.747 = 2.243 inches

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