Lec 10 - Xbar and R Charts

# Lec 10 - Xbar and R Charts - Variables Control Charts...

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Variables Control Charts: Constructing X and R Charts BACKGROUND MATERIAL: Statistics of the Range R, range is a sample statistic if X 1 , X 2 , … are iid Normal then R has following relationship to σ σ = R / d 2 where d 2 (given n) comes from Table A.2 (p. 789 Devor) n=2…15 Here is a good way to estimate σ from control chart data Compute R i from subsample i=1. ..m Compute R Estimate: / σ= R d 2

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Example of Computing Ranges Sub i X 1 X 2 X 3 X 4 X i R i R i / d 2 S i 1 25.6 25.8 32.4 33.8 29.40 8.2 3.983 4.3 2 33.2 28.2 26.2 31.4 29.75 7.0 3.400 3.1 ... 25 d 2 = 2.059 for n=4 observations in the range R = 7.8 Use R to estimate σ : / σ= R d 2 = 7.8 / 2.059 = 4.34 recall pooled estimate of variance. 2
Computing Control Limits for X Charts n observations per subsample (n is small, say 3-8) m subsamples (m is at least 25) for subsample i, compute X i and R i , i=1. ..m compute: X and R from initial data X X R R i i m i i m = = = = 1 1 3

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Initial Control Limits CL = X UCL X n X R d n X A R = + = + = + 3 3 2 2 σ / LCL X A R = - 2 (A 2 in Table - as a function of n) 4
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Lec 10 - Xbar and R Charts - Variables Control Charts...

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