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Understanding Shewhart Control Charts for Process Control

Learn about Shewhart Control Charts, rational subgroups, causes of common sampling mistakes, and how to address stratification and mixing in process control. Explore monitoring process mean and variability in statistical quality control.

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Understanding Shewhart Control Charts for Process Control

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  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

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