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Lecture_11_14

# Lecture_11_14 - Lecture of Nov 14 HW#9 due on today HW#10...

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1 Lecture of Nov 14 Lecture of Nov 14 HW#9 due on today. HW#10 assigned and due Nov 21.

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2 Example 5.2 Example 5.2 A normally distributed quality characteristic is monitored through use of an x-bar and an R chart. These charts have the following parameters ( n =4): LCL=0 LCL=614 CL=8.236 CL=620 UCL=18.795 UCL=626 R chart x -bar chart (a) What is the type-II error when detect a shift in the process mean to 610. Find the average run length for the chart. (b) What is the probability of detecting the shift in (a) by at least the third sample after the shift?
3 Example 5.2 (continued) Example 5.2 (continued) • Read information from the charts -- being able to do so is critical. Part (a) β -error and ARL 1

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4 Example 5.2 (continued) Example 5.2 (continued) Part (b)
5 Individual Individual x x Chart and Chart and Moving Range Chart Moving Range Chart When n = 1 , each sample has only a single observation. Then, x x x x x L LCL CL L UCL σ µ = µ = σ + µ = x x x x become become , x i 1 2 m x 1 x 2 x m = x R = R s = s x ... ... • Follow the general model for control chart, w = x , we can estimate µ x from x . How about σ x ?

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6 Individual Individual x x Chart and Chart and Moving Range Chart Moving Range Chart Then, cannot be subsequently used in the control limits because computing them requires at least two observations in each sample.
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