Chapter 6 - Part 1
description
Transcript of Chapter 6 - Part 1
Chapter 6 - Part 1Chapter 6 - Part 1
Introduction to SPC
Proactive approaches to qualityProactive approaches to quality Design of Experiments Statistical Process Control
Design of ExperimentsDesign of Experiments Tool for designing quality into a product or
service at the design before production begins.
Quality is designed into product or service by finding the levels of inputs that maximizes customer satisfaction.
How should we design a laptop? What battery and processor speed?
Longer battery life but slower speed? Faster speed but shorter battery life?
Design of ExperimentsDesign of Experiments When is best room size and color when
designing a hotel? In designing a new drink, what carbonation
and sugar levels maximize taste? Carbonation and sugar levels that maximizes
taste become the ???
Example of Designed ExperimentExample of Designed Experiment Sugar and carbonation (factors) are each at
two levels High Low
Experiment is called a 2 x 2 factorial experiment, where there are two factors, each at two levels.
Example of Designed ExperimentExample of Designed Experiment Potential customers rate all possible design
combinations. Taste is rated on a scale of 1 to 10, with 10
being best. Are there significant differences between
mean taste scores for all pairs of design combinations?
Are changes in the mean taste score more sensitive to changes in sugar or carbonation?
Factorial ExperimentFactorial Experiment
Sugar Carbonation Focus Group 1
Focus Group 2
Mean Taste Score
L L 4 6 5.0
H L 9 2 5.5
L H 9 8 8.5
H H 8 1 4.5
Factorial Experiment - graphFactorial Experiment - graph
SugarCarbonation L H
L 5 5.5H 8.5 4.5
0
2
4
6
8
10
L H
Carbonation
Mea
n Ta
ste
Scor
e
Sugar = L
Sugar = H
Carbonation vs. SugarCarbonation vs. Sugar
ConclusionConclusion Best combination of inputs is
Low Sugar High Carbonation
At low level of carbonation, an increase in sugar does not appear to result in a statistically significant gain in the mean taste score.
If carbonation is a the high level, a decrease in sugar results in a statistically significant gain in the mean taste score.
This combination not only maximizes taste, but will lower cost of production if ????
Statistical Process Control (SPC)Statistical Process Control (SPC) Tool for predicting future performance of a
process. Main tools of SPC are control charts. Control charts make it possible to detect
problems early enough to take corrective action on the process before too many defective units are produced.
Control charts are proactive because action is taken on the process, and not on the output, to prevent defects from being produced.
Control ChartsControl Charts Allow us to detect earlier shifts in the mean
and/or variance of the quality characteristic of a product or service.
Control charts have an upper control limit (UCL) and a lower control limit (LCL).
Control limits are set at 3 standard deviations above and below the estimated mean of the quality characteristic, called the estimated process mean.
SPC vs. DOESPC vs. DOE If design of experiments is used to determine target levels, then control charts can be used to determine if process is operating on target.
If it is, control charts can be used to detect early shifts from target.
If process is not on target, control charts can be used to determine if corrective action to adjust process mean to target is effective.
Control ChartsControl Charts Control charts rely on sample inspection, not
mass inspection. We may take a sample of 5 invoices every day to
check for errors, or A sample of 5 bottles of a soft drink each hour to
estimate the average number of ounces in a bottle.
The samples are used to Estimate the process mean and to Compute the control limits
The control limits, the estimated process mean and the means of all the sample means are plotted on the control chart.
Control ChartControl Chart
.50
.40
.30
.20
.10
00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
UCL
LCL
Mean
Hour
Frac
tion
Def
ectiv
e
QC) of 3(Std QC ofMean UCL
QC) of 3(Std QC ofMean LCL
Control ChartsControl Charts In addition to detecting shifts in the process
mean and/or variation, control charts allow us to determine what sources of variation are in the process.
There are two sources of variation: Special causes Random variation (common causes)
Random variation always exists in any process. Special causes of variation may or may not exits.
Random variation (Common Causes)Random variation (Common Causes) Inherent in any process Due to many causes, each contribution a
small amount to the total random variation Occurs within 3 standard deviations of mean
(3-sigma limits)
Special CausesSpecial Causes Not inherent in the process Occur when something unusual happens Unusual event can be good or bad
If good, make it part of process If bad, eliminate it
What Sources of Variation are What Sources of Variation are Present?Present?
If all the sample means fall randomly within the control limits, the variation between the sample means is due to random causes or variation.
If at least one sample mean falls beyond the control limits, the variation is due to special or assignable causes of variation.
Statistical ControlStatistical Control If there are no special causes of variation in the process, the process is said to be in statistical control, or “in control.” Process mean (and/or variance) is stable
and hence predictable. The sample means will vary randomly
around the unknown process mean.
Sample number
UCL
LCL1 2 3 4
.00135
.00135
Statistical Control – Stable ProcessStatistical Control – Stable Process
Statistical Control – Stable ProcessStatistical Control – Stable Process Since all the sample means come the same
stable distribution, each sample mean is an estimate of the process mean.
Rather than using each sample mean as an estimate of the process mean, we can get a better estimate the mean of the process by ???
Process Out of ControlProcess Out of Control If one or more special causes of variation are present, the process is “out-of-control.” Process behaves erratically It is unstable and no longer predictable. It is therefore impossible to get a good
estimate of the process mean.
UCL
LCL
Mean
Hour
Sam
ple
mea
nProcess in ControlProcess in Control
All the sample mean fall randomly within the control limits This variation is due to random causes.
UCL
LCL
Mean
Hour
Sam
ple
mea
n
Process that is Out of ControlProcess that is Out of Control
All the sample mean fall within the control limits, but pattern is not random. It is a predictable trend. Source of variation is due to a special cause.
Hour
Sam
ple
mea
n UCL
LCL
Mean
All the sample mean fall within the control limits, but pattern is not random. It is a predictable cyclical pattern. Source of variation is due to a special cause.
Process that is Out of ControlProcess that is Out of Control
UCL
LCL
Mean
Hour
Process out of ControlProcess out of ControlOne point beyond the control limit. Variation beyond control limits is due to unusual or special (assignable) causes
Responsibility for Corrective ActionResponsibility for Corrective Action Knowing what sources of variation are
present in the process allows us to determine who is responsible for taking corrective action to fix or improve the process.
Removing or institutionalizing special causes— the worker
Reducing random variation – management
An Offer You Can’t RefuseAn Offer You Can’t Refuse I claim I have a fair coin—50/50 chance of
tossing a head or tail You’re willing to bet $1,000 that I don’t have a
fair coin, but you want more data. I agree to
toss the coin 100 times, count the number of heads, and repeat this experiment once a day over the
next 10 days.
The ResultsThe ResultsDay # of heads
1 572 533 514 585 366 637 558 51 9 3910 44
How Will You Bet?How Will You Bet? Based on these results, do you think I have a
fair coin or a biased coin?
Control Chart for # of HeadsControl Chart for # of Heads Let P = probability of tossing a head = 0.50 Let n = number of tosses = 100 How many heads would you expect on each
toss? What is the standard deviation of the number
of heads tossed?
Control Chart for # of HeadsControl Chart for # of Heads
M ean nP
Std D ev nP P
1 0 0 0 5 0 5 0
1 1 0 0 5 5
5
( . )
. . ( ) (. )( . )
U p p er L im it = M ean + 3 (S td . D ev . )
= + 3
L ow er L im it = M ean - 3 (S td . D ev . )
= 3
nP nP P
nP nP P
( )
(. )( . )
( )
(. )( . )
1
50 3 100 5 5
50 1 5
65
1
50 3 1 00 5 5
50 15
35
Control Chart for # of HeadsControl Chart for # of Heads
Control Chart for Number of Heads
15253545556575
1 2 3 4 5 6 7 8 9 10
Day
# of
hea
ds # of Heads
LCL
UCL
Control ChartsControl Charts Based on the control chart, what can you
conclude? How would you bet?
Coin is fair? Coin is not fair?
Production ExampleProduction Example Make up a production example that is
analogous to coin tossing experiment by answering the following questions: What do the 100 tosses per day represent?
What do the two outcomes, head and tail, represent?
Production ExampleProduction Example What is the meaning of P = 0.5?
How can zero defects be achieved?
Principle of Rational SubgroupingPrinciple of Rational Subgrouping Principle states that we want to select samples to minimize variation within the samples but maximize the variation between.
If something unusual is going on, we want it to occur between samples, not within.
If it occurs within samples, we may miss it.
Violation of Rational SubgroupingViolation of Rational Subgrouping
Day
Sample(Diameter)
1 2 3 Mean
Monday 3 5 4 4Tuesday 12 18 15 15Wednesday 1 10 1 4
Control Charts ErrorsControl Charts Errors
Actual Condition of Process
Conclusion Based on Control Chart
Process In Control
Process Not In Control
In Control Correct Type I Error
Out of Control
Type II Error Correct
Type I ErrorType I Error
Sample number
UCL
LCL1 2 3 4
Type I Error-Thinking shift occurred when it didn’t—false alarm
P(Type 1 Error)=2(.00135)=.0027
Mean
Type II ErrorType II Error
Sample number
UCL
LCL1 2 3 4
Type II Error-Shift occurred but we failed to detect it
Mean
NewMean