1 Chapter 6 Statistical Process Control (SPC)

2 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

xxx xx µ ( x-µ) The Standard Deviation

River Crossing Problem RiverABC Average2.5 Range255 St Dev

5 Inferential Statistics Population (N) Parameters Samples (n) Statistics 1. Central Tendency: 2. Dispersion:

6 The Normal (Gaussian) Curve -3  -2  -1  +1  +2  +3  68.26% 95.46% 99.73%

7 Red Bead Experiment

8 Types of Control Charts Quality Characteristic n>6 Variable Attribute Type of Attribute Constant sample size? Constant sampling unit? p-chart np-chart u-chart c-chart X and MR chart X-bar and R chart X-bar and s chart DefectiveDefect Yes No n>1

9 Data Information 1.Central Tendency 2.Dispersion 3.Shape Action Stats Decision No Action

10 The Shape of the Data Distribution mean = median = mode mode mean median Skewed to the right (positively skewed) median mode mean Skewed to the left (negatively skewed) “Box-and-Whisker” Plot Pearsonian Coefficient of Skewness

11 Control Charts +3σ Average -3σ Common Cause (Chance or Random) Special Cause (Assignable) Special Cause (Assignable)

12 Central Limit Theorem Standard Error of the Mean Population (individual) Distribution Sample (x-bar) Distribution μ

13 X-Bar and R Example X-Double Bar X-Bar R-Bar R Rational Subgroup Subgroup Interval

14 X-Bar and R Control Chart Limits nA2A2 D4D4 d2d UCL x-Bar (.577 x.00483) =.1676 LCL x-Bar (.577 x.00483) =.1621 UCL R x =.0102

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16 Attribute Control Chart Limits DefectivesDefects Changing Sample Size Fixed Sample Size

17 n *n-bar = p p-bar= p-Chart Example UCL p LCL p *Note: Use n-bar if all n’s are within 20% of n-bar

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19 The α and β on Control Charts +3σ Average -3σ α = β β β

20 Out of Control Patterns 2 of 3 successive points outside 2  4 of 5 successive points outside 1  8 successive points same side of centerline -3  33 22 11 -1  -2  Average

21 Control Chart Patterns Gradual Trend “Freaks” Sudden Shifts Cycles Instability “Hugging” Centerline“Hugging Control Limits”

22 Six Sigma Process Capability C p k = ppm USLLSL  1.5  C p = ppm

23 Cause and Effect Diagram a.k.a. Ishikawa Diagram, Fishbone Diagram Process PersonProcedures MaterialEquipment BCA

24 Pareto Chart a.k.a. 80/20 Rule Vital Few Trivial (Useful) Many

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29 Taguchi Loss Function The Taguchi Loss Function: L (x) = k (x-T) 2 Loss ($) Traditional Loss Function: Loss ($)

30 Response Curves Most “Robust” Setting