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## Chapter 6 Statistical Process Control (SPC)

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**Chapter 6**Statistical Process Control (SPC)**Descriptive Statistics**1.Measures of Central Tendencies (Location) • Mean • Median = The middle value • Mode - The most frequent number 2. Measures of Dispersion (Spread) • Range R=Maximum-Minimum • Standard Deviation • Variance**x**x x x x 1 2 3 4 5 6 7 8 µ The Standard Deviation (x-µ)**68.26%**95.46% 99.73% The Normal (Gaussian) Curve -3-2-1+1+2+3**Types of Control Charts**Quality Characteristic Attribute Variable Type of Attribute X and MR chart No n>1 Defective Defect Yes Constant sample size? Constant sampling unit? Yes Yes No X-bar and R chart n>6 Yes No np-chart No c-chart X-bar and s chart p-chart u-chart**Data**Stats • Information • Central Tendency • Dispersion • Shape No Action Decision Action**median**median mode mode mean mean Skewed to the right (positively skewed) Skewed to the left (negatively skewed) The Shape of the Data Distribution • “Box-and-Whisker” Plot mean = median = mode • Pearsonian Coefficient of Skewness**Special Cause**(Assignable) Control Charts Special Cause (Assignable) +3σ Average -3σ Common Cause (Chance or Random)**Standard Error of the Mean**Central Limit Theorem Sample (x-bar) Distribution Population (individual) Distribution μ**X-Bar and R Example**Rational Subgroup Subgroup Interval**p-Chart Example***Note: Use n-bar if all n’s are within 20% of n-bar**β**β β The α and β on Control Charts α = .00135 +3σ Average -3σ α = .00135**3**2 1 Average -1 -2 Out of Control Patterns 8 successive points same side of centerline 2 of 3 successive points outside 2 -3 4 of 5 successive points outside 1 **Control Chart Patterns**Instability “Freaks” Gradual Trend Sudden Shifts Cycles “Hugging” Centerline “Hugging Control Limits”**Six Sigma Process Capability**1.5 Cp = 2.0 .54 ppm Cpk = 1.5 3.4 ppm LSL USL**Cause and Effect Diagrama.k.a. Ishikawa Diagram, Fishbone**Diagram Person Procedures A B C Process Material Equipment**Vital Few**Trivial (Useful) Many Pareto Charta.k.a. 80/20 Rule**The Taguchi Loss Function:**L (x) = k (x-T)2 Loss ($) .480 .500 .520 Traditional Loss Function: Loss ($) .480 .500 .520 Taguchi Loss Function**Most “Robust” Setting**Response Curves