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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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Problem 8-1. µ 0 = 1050; σ = 25; δ = 1 σ ; K = ( δ /2) σ = (1/2)25 = 12.5; H = 5 σ = 5(25) = 125 (a) MTB > Stat > Control Charts > Time-Weighted Charts > CUSUM Sample Cumulat ive Sum 20 18 16 14 12 10 8 6 4 2 1250 1000 750 500 250 0 0 UCL=125 LCL=-125 CUSUM Chart of Molecular Weight ( Ex8-1mole) target = 1050, std dev = 25, k = 0.5, h = 5 The process signals out of control at observation 10. The point at which the assignable cause occurred can be determined by counting the number of increasing plot points. The assignable cause occurred after observation 10 – 3 = 7. (b) σ ˆ = MR2 d 2 = 38.8421/1.128 = 34.4345 equation 5-6. No. The estimate used for σ is much smaller than that from the data. 8- 2
Problem 8-2. MTB > Stat > Control Charts > Time-Weighted Charts > CUSUM Sample Cumulat ive Sum 20 18 16 14 12 10 8 6 4 2 50 40 30 20 10 0 0 UCL=5 LCL= -5 CUSUM Chart of Standardized Molecular Weight ( Ex8-2std) target = 1050, std dev = 25, k = 0.5, h = 5 The process signals out of control at observation 10. The assignable cause occurred after observation 10 – 3 = 7.

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