Statistical Quality & Process Control 2/18/2019 IENG 486 - Lecture 09 Examples of Hypothesis Tests: Anthropometric Data and Intro to the Seven Tools of Ishikawa 2/18/2019 IENG 486: Statistical Quality & Process Control (c) 2002 - 2009, D.H. Jensen & R. C. Wurl

Statistical Quality & Process Control 2/18/2019 Assignment: Preparation: Print Hypothesis Test Tables from Materials page Have this available in class …or exam! Reading: Chapter 5: 5.1 through 5.2, and 5.4 - only these portions are on Exam I HW 3: CH 5: # 5, 26, 27 Review for Exam I 2/18/2019 IENG 486: Statistical Quality & Process Control (c) 2002 - 2009, D.H. Jensen & R. C. Wurl

Grip Strength Data Results R-L Side, Equal Variance Dominant Hand Means Comparison: L = x1 = 129.4, S12 = 2788, n1 = 34 people R = x2 = 104.0, S22 = 1225, n2 = 20 people Sp = 47.1, v = 52 Two-Sided Test at  = .05 HA: There is a difference Test: Is | t0 | > t.025, 52? |1.91| > 2.021 - NO! Keep the Null Hypothesis: There is NOT a difference btwn L & R ! 2/18/2019 IENG 486: Statistical Quality & Process Control

Grip Strength Data Results R-L Side, No Assumptions Dom. Hand Means Comparison: L = x1 = 129.4, S12 = 2788, n1 = 34 people R = x2 = 104.0, S22 = 1225, n2 = 20 people v = 51 Two-Sided Test at  = .05 HA: There is a difference Test: Is | t0 | > t.025, 51? |2.12| > 2.021 - YES! Reject the Null Hypothesis: There IS a difference btwn L & R! Why is this wimpy test significant when the other wasn’t? ANS: Check the equal variance assumption! 2/18/2019 IENG 486: Statistical Quality & Process Control

Grip Strength Data Results Unknown 0 Variances Comparison: S12 = 2788 n1 = 34, v1 = 33 S22 = 1225 n2 = 20, v2 = 19 Two-Sided Test at  = .10 HA: There is a difference Test: Is F0 > F.05, 33, 19? 2.276 > 2.07 - YES! (if not, also check F1– /2, 33, 19) Reject the Null Hypothesis: There IS a difference in variance! At  = .05, this test is just barely not significant (Should also have checked for Normality with Normal Prob. Plot) 2/18/2019 IENG 486: Statistical Quality & Process Control

Statistical Quality Improvement Goal: Control and Reduction of Variation Causes of Variation: Chance Causes / Common Causes In Statistical Control Natural variation / background noise Assignable Causes / Special Causes Out of Statistical Control Things we can do something about - IF we act quickly! Both can cause defects – because specifications are often set regardless of process capabilities! 2/18/2019 IENG 486: Statistical Quality & Process Control

Ishikawa’s “Magnificent Seven” Tools The Seven Tools are: Histogram / Stem & Leaf Diagram Cause & Effect (Fishbone) Diagram Defect Concentration Diagram Check Sheet Scatter (Plot) Diagram Pareto Chart Control Chart - covered after exam! The tools were not invented by Ishikawa, but were very successfully put into methodical use by him The first six are used before starting to use the seventh They are also reused when needed to find an assignable cause 2/18/2019 IENG 486: Statistical Quality & Process Control

Ishikawa’s Tools: Histogram A histogram is a bar chart that takes the shape of the distribution of the data. The process for creating a histogram depends on the purpose for making the histogram. One purpose of a histogram is to see the shape of a distribution. To do this, we would like to have as much data as possible, and use a fine resolution. A second purpose of a histogram is to observe the frequency with which a class of problems occurs. The resolution is controlled by the number of problem classes. – see Pareto Chart slide! 2/18/2019 IENG 486: Statistical Quality & Process Control

Ishikawa’s Tools: Fishbone Diagram Cause & Effect diagram constructed by brainstorming Identified problem at the “head” Connects potential causes along the spine Sub-causes are listed along the major “bones” Man Material Method Machine Environment 2/18/2019 IENG 486: Statistical Quality & Process Control

Cause & Effect Diagram, Cont. The purpose of the cause and effect diagram is to obtain as many potential influencers of a process, so that the problem solving can take a more directed approach. Material Machine Man Method Environment Skill Level Low RPM Orifice Clogs Dusty Humidity Poor Conductor Attention Level Poor Mixing Travel Limits Temperature Worn Parts Poor Vendor Bad Paint 2/18/2019 IENG 486: Statistical Quality & Process Control

Ishikawa’s Tools: Defect Diagram A defect concentration diagram graphically records the frequency of a defect with respect to product location. Obtain a digital photo or multi-view part print showing all product faces. Operator tallies the number and location of defects as they occur on the diagram. 2/18/2019 IENG 486: Statistical Quality & Process Control

Ishikawa’s Tools: Check Sheet Title Header Info: Date, Time, Location, Operator, etc. Types of Errors Times of Occurrence (periodic) Type of Error Statistics Time of Occurrence Statistics Overall Statistics Instructions, settings, comments, etc. Raw Data recorded here Check sheets are used to collect data (values or pieces of information) in a consistent manner. List each of the known / possible problems Record each occurrence including time-orientation. 2/18/2019 IENG 486: Statistical Quality & Process Control

Ishikawa’s Tools: Scatter Plot A scatter plot shows the relationship between any two variables of interest: Plot one variable along the X-axis and the other along the Y-axis The presence of a relationship can be inferred or ruled out, but it cannot determine if a cause and effect relationship exists Y X 2/18/2019 IENG 486: Statistical Quality & Process Control

Ishikawa’s Tools: Pareto Chart 80% of any problem is the result of 20% of the potential causes Histogram categories are sorted by the magnitude of the bar A line graph is overlaid, and depicts the cumulative proportion of defects Quickly identifies where to focus efforts 2/18/2019 IENG 486: Statistical Quality & Process Control

Use of Ishikawa’s Tools Reduce Variability Identify Special Causes - Good (Incorporate) Improving Process Capability and Performance Characterize Stable Process Capability Head Off Shifts in Location, Spread Identify Special Causes - Bad (Remove) Continually Improve the System Statistical Quality Control and Improvement Time Center the Process LSL 0 USL Removing special causes of variation Preparation for: hypothesis tests control charts process improvement 2/18/2019 IENG 486: Statistical Quality & Process Control