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

2. IENG 486: Statistical Quality & Process Control
11/21/2018
Assignment:
Reading:
CH5: 5.3 (already read & 5.4)
Start on CH6: all except & 6.4
Homework 4:
Textbook Problems CH5: 9, 11, 13, 23, & 24
11/21/2018
IENG 486: Statistical Quality & Process Control
(c) , D.H. Jensen & R. C. Wurl

3. 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) , D.H. Jensen & R. C. Wurl

4. 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) , D.H. Jensen & R. C. Wurl

5. 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) , D.H. Jensen & R. C. Wurl

6. 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) , D.H. Jensen & R. C. Wurl

7. 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) , D.H. Jensen & R. C. Wurl

8. 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) , D.H. Jensen & R. C. Wurl

9. 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) , D.H. Jensen & R. C. Wurl

10. 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) , D.H. Jensen & R. C. Wurl

11. 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