APME_5 - Applied Probability Methods for Engineers Slide...

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Click to edit Master subtitle style Applied Probability Methods for Engineers Slide Set 5

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Click to edit Master subtitle style Chapter 16 Quality Control Methods
Statistical Process Control n A control chart is a useful visual tool for observing an important measurement over time n Used to detect when something unusual occurs in a measurable process

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Control Charts Drift in average value: Increase in variation:
Control Limits n How do we know when a process is out of control? n Control limits: Upper Control Limit (UCL) and Lower Control Limit (LCL) n Hypothesis test: n H0: process is in control n HA: process is out of control n Type I error: α associated with hypothesis test (Type I error is probability of observing point outside control limits when it is actually in control) n 3 sigma control limits often used n α = 1 – 0.9974 = 0.0026

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Note on Six Sigma n Six Sigma is actually a set of total quality management (TQM) principles and practices n Six Sigma was started at Motorola n Processes operating at the six sigma level produce less than 3.4 defects per one million opportunities n 3.4 does not correspond to our 0.0026 α value n What is going on? n Six Sigma permits a 1.5 standard deviation shift in the mean n One tail α associated with z = 4.5 equals 0.0000034
Piston Head Example n In control process produces piston heads with radius values with a mean of μ0 = 30.00 mm and standard deviation σ = 0.05 mm n Suppose we take samples of size n and look at the sample mean to determine whether the process is in control n Sample mean has expected value μ0 and standard deviation σ/= n n Control chart has center line at μ0 = 30.00 mm, and LCL and UCL equal to μ0 - 3σ/& n and μ0 + 3σ/& n

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Piston Head Example n If sample size n = 5, then n LCL = 30 – 3& 0.05/; 5; UCL = 30 + n LCL = 29.933; UCL = 30.067 n Probability of Type I error = 1 – P(29.933 ≤ X ≤ 30.067) = 1 – P(-3 ≤ Z ≤ 3) = 0.0026
Control Charts n Even if a process is within the control limits, we can detect problems when a series of consecutive points lies completely above or below the center line

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This note was uploaded on 10/27/2010 for the course ESI 6321 taught by Professor Josephgeunes during the Spring '07 term at University of Florida.

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APME_5 - Applied Probability Methods for Engineers Slide...

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