IENG 486: Statistical Quality & Process Control Basic Control Charts 11/21/2018 IENG 486 - Lecture 12 Basic Control Charts 11/21/2018 IENG 486: Statistical Quality & Process Control (c) 2002 - 2009, D.H. Jensen & R. C. Wurl

IENG 486: Statistical Quality & Process Control 11/21/2018 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 11/21/2018 IENG 486: Statistical Quality & Process Control (c) 2002 - 2009, D.H. Jensen & R. C. Wurl

General Model: Shewhart Control Chart IENG 486: Statistical Quality & Process Control 11/21/2018 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 11/21/2018 IENG 486: Statistical Quality & Process Control (c) 2002 - 2009, D.H. Jensen & R. C. Wurl

IENG 486: Statistical Quality & Process Control 11/21/2018 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 11/21/2018 IENG 486: Statistical Quality & Process Control (c) 2002 - 2009, D.H. Jensen & R. C. Wurl

Symptoms of Two Common Sampling Mistakes IENG 486: Statistical Quality & Process Control 11/21/2018 Symptoms of Two Common Sampling Mistakes Data points hug centerline – Stratification indicating sample averages are not normally distributed Data points hug control limits – Mixing 11/21/2018 IENG 486: Statistical Quality & Process Control (c) 2002 - 2009, D.H. Jensen & R. C. Wurl

Stratification – Sample Averages Hug Centerline IENG 486: Statistical Quality & Process Control 11/21/2018 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 11/21/2018 IENG 486: Statistical Quality & Process Control (c) 2002 - 2009, D.H. Jensen & R. C. Wurl

Stratification – Why Does It Happen? IENG 486: Statistical Quality & Process Control 11/21/2018 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 11/21/2018 IENG 486: Statistical Quality & Process Control (c) 2002 - 2009, D.H. Jensen & R. C. Wurl

Mixing – Sample Averages Hug Control Limits IENG 486: Statistical Quality & Process Control 11/21/2018 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 parts Old and new machines have different means Sample size = 4: All parts are mixed together Symptom: Data points hug control limits samples 1 & 2 samples 3 & 4 11/21/2018 IENG 486: Statistical Quality & Process Control (c) 2002 - 2009, D.H. Jensen & R. C. Wurl

What to do if there is evidence of stratification or mixing IENG 486: Statistical Quality & Process Control 11/21/2018 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 11/21/2018 IENG 486: Statistical Quality & Process Control (c) 2002 - 2009, D.H. Jensen & R. C. Wurl

Why Monitor Both Process Mean and Process Variability? IENG 486: Statistical Quality & Process Control 11/21/2018 Why Monitor Both Process Mean and Process Variability? Process Over Time Control Charts X-bar R X-bar R X-bar R 11/21/2018 IENG 486: Statistical Quality & Process Control (c) 2002 - 2009, D.H. Jensen & R. C. Wurl

IENG 486: Statistical Quality & Process Control Teminology 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 11/21/2018 IENG 486: Statistical Quality & Process Control