lecture8 - MIT OpenCourseWare http:/ocw.mit.edu 2.830J /...

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MIT OpenCourseWare http://ocw.mit.edu 2.830J / 6.780J / ESD.63J Control of Manufacturing Processes (SMA 6303) Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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1 M anufacturing Control of Manufacturing Processes Subject 2.830/6.780/ESD.63 Spring 2008 Lecture #8 Process Capability & Alternative SPC Methods March 4, 2008
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2 M anufacturing Agenda • Control Chart Review – hypothesis tests: α, β and n – control charts: α , β , n , and average run length (ARL) • Process Capability • Advanced Control Chart Concepts
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3 M anufacturing • How often will the data exceed the ±3 σ limits if Δμ x = 0? Prob( x > μ x + 3 σ x ) + Pr ob ( x < μ x 3 x ) = 3 /1000 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 -4 -3 -2 -1 0 1 2 3 4 μ+ 3 σ −3σ Average Run Length
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4 M anufacturing • Consider a real shift of Δμ x : • How many samples before we can expect to detect the shift on the xbar chart? 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 2 3 4 5 6 7 8 9 1 01 11 21 31 41 51 61 71 81 92 0 Sample Number Detecting Mean Shifts: Chart Sensitivity
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5 M anufacturing • How often will the data exceed the ±3 σ limits if Δμ x = +1 σ ? p e 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 -4 -3 -2 -1 0 1 2 3 4 Actual Distribution Δμ 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 -4 -3 -2 -1 0 1 2 3 4 μ +3σ −3σ Assumed Distribution Average Run Length Prob( x > μ x + 2 σ x ) + Prob( x < μ x 4 x ) = 0.023 + 0.001 = 24 /1000
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6 M anufacturing Definition • Average Run Length (arl): Number of runs (or samples) before we can expect a limit to be exceeded = 1/p e –fo r Δμ = 0 arl = 3/1000 = 333 samples r Δμ = 1 σ arl = 24/1000 = 42 samples Even with a mean shift as large as 1 σ , it could take 42 samples before we know it!!!
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7 M anufacturing • Assume the same Δμ = 1 σ – Note that Δμ is an absolute value • If we increase n, the Variance of xbar decreases: • So our ± 3 σ limits move closer together σ x = x n Effect of Sample Size n on ARL
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8 M anufacturing 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 -4 -3 -2 -1 0 1 2 3 4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 -4 -3 -2 -1 0 1 2 3 4 New Distribution 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 -4 -3 -2 -1 0 1 2 3 4 μ +3σ −3σ Original Distribution ARL Example p e +3σ∗ −3σ∗ new limits Δμ same absolute shift As n increases p e increases so ARL decreases
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9 M anufacturing Another Use of the Statistical Process Model: The Manufacturing -Design Interface • We now have an empirical model of the process 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 -4 -3 -2 -1 0 1 2 3 4 μ+ 3 σ −3σ How “good” is the process? Is it capable of producing what we need?
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10 M anufacturing Process Capability • Assume Process is In-control • Described fully by xbar and s • Compare to Design Specifications – Tolerances – Quality Loss
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11 M anufacturing Tolerances : Upper and Lower Limits Characteristic Dimension Target x* Upper Specification Limit USL Lower Specification Limit LSL Design Specifications
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12 M anufacturing Quality Loss : Penalty for Any Deviation from Target QLF = L*(x-x*) 2 Design Specifications x*=target How to How to Calibrate?
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This note was uploaded on 09/24/2010 for the course MECHE 2.830J taught by Professor Davidhardt during the Spring '08 term at MIT.

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lecture8 - MIT OpenCourseWare http:/ocw.mit.edu 2.830J /...

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