IENG 486 - Lecture 12

1. IENG 486 - Lecture 12 Basic Control Charts IENG 486: Statistical Quality & Process Control

2. Assignment: • Reading: • CH5: 5.3 (already read 5.1-5.2 & 5.4) • Start on CH6: all except 6.3.2 & 6.4 • Homework 4: • Textbook Problems CH5: 9, 11, 13, 23, & 24 IENG 486: Statistical Quality & Process Control

3. General Model:Shewhart Control Chart • Suppose x is some quality characteristic, and w is a sample statistic of x. • Suppose mean of w is μw and std dev of w is σw, then: • UCL = μw + Lσw • CL = μw • UCL = μw – Lσw • where L is the “distance” of the control limits from the center line, and expressed in multiples (units) of the standard deviation of the statistic, i.e. sw. • This type of chart is called a Shewhart Control Chart IENG 486: Statistical Quality & Process Control

4. Rational Subgroups • Subgroups/Samples should be selected so that if assignable causes are present: • Chance for differences between samples is maximized • Chance for differences within a sample is minimized • Use consecutive units of production • Keep sample size small so that: • New events won’t occur during sampling • Inspection is not too expensive • But size is large enough that x is normally distributed IENG 486: Statistical Quality & Process Control

5. Symptoms of Two Common Sampling Mistakes • Data points hug centerline –Stratification indicating sample averages are not normally distributed • Data points hug control limits –Mixing indicating sample averages are not normally distributed IENG 486: Statistical Quality & Process Control

6. Stratification – Sample Averages Hug Centerline • Quality Characteristic: • Amount of liquid filled into a container. • Machine: • 4 heads fill 4 containers simultaneously. • Each head has a slightly different mean • Sample: select 4 bottles, 1 bottle ea. from heads 1, 2, 3, and 4 • Symptom: data points hug centerline indicating sample averages are not normally distributed IENG 486: Statistical Quality & Process Control

7. Stratification – Why Does It Happen? • Each head has a different mean. • Why do points hug centerline? • Ans: Estimate of s is wrong • So … the Control Charts limits are too wide • And … the data points hug centerline because the scaling to detect a shift in process mean is off IENG 486: Statistical Quality & Process Control

8. samples 1 & 2 samples 3 & 4 Mixing – Sample Averages Hug Control Limits • Quality Characteristic: • Dimension of a part • 2 Similar Machines: • Old one: produces 40% of parts New one: produces 60% of partsOld and new machines have different means • Sample size = 4: • All parts are mixed together • Symptom: Data points hug control limits IENG 486: Statistical Quality & Process Control

9. What to do if there is evidence of stratification or mixing • Examine your sampling procedure • Make separate control charts for each filling head (or machine) • Problem: It may not be obvious that samples are stratified or mixed IENG 486: Statistical Quality & Process Control

10. X-bar X-bar X-bar R R R Why Monitor Both Process Mean and Process Variability? Process Over Time Control Charts IENG 486: Statistical Quality & Process Control

11. Causes of Variation: Assignable Causes Keep the process from operating predictably Things that we can do something about Common Causes Random, inherent variation in the process Meaning of Control: In Specification Meets customer constraints on product In Statistical Control No Assignable Causes of variation present in the process Teminology IENG 486: Statistical Quality & Process Control