APME_5 - Applied Probability Methods for Engineers Slide...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Applied Probability Methods for Engineers Slide Set 5
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Chapter 16 Quality Control Methods
Background image of page 2
Statistical Process Control A control chart is a useful visual tool for observing an important measurement over time Used to detect when something unusual occurs in a measurable process
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Control Charts Drift in average value: Increase in variation:
Background image of page 4
Control Limits How do we know when a process is out of control? Control limits: Upper Control Limit (UCL) and Lower Control Limit (LCL) Hypothesis test: H 0 : process is in control H A : process is out of control 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) 3 sigma control limits often used α = 1 – 0.9974 = 0.0026
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Note on Six Sigma Six Sigma is actually a set of total quality management (TQM) principles and practices Six Sigma was started at Motorola Processes operating at the six sigma level produce less than 3.4 defects per one million opportunities 3.4 does not correspond to our 0.0026 α value What is going on? Six Sigma permits a 1.5 standard deviation shift in the mean One tail α associated with z = 4.5 equals 0.0000034
Background image of page 6
Piston Head Example In control process produces piston heads with radius values with a mean of μ 0 = 30.00 mm and standard deviation σ = 0.05 mm Suppose we take samples of size n and look at the sample mean to determine whether the process is in control Sample mean has expected value μ 0 and standard deviation σ/ n Control chart has center line at μ 0 = 30.00 mm, and LCL and UCL equal to μ 0 - 3σ/ n and μ 0 + 3σ/ n
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Piston Head Example If sample size n = 5, then LCL = 30 – 3 × 0.05/ 5; UCL = 30 + 3 × 0.05/ 5 LCL = 29.933; UCL = 30.067 Probability of Type I error = 1 – P(29.933 ≤ X ≤ 30.067) = 1 – P(-3 ≤ Z ≤ 3) = 0.0026
Background image of page 8
Control Charts 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
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Control Chart Properties Recall the definition of Type II error:
Background image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 35

APME_5 - Applied Probability Methods for Engineers Slide...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online