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

Me

an

Ta

ste

Sc

ore

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

Fra

ctio

n D

efec

tive

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

Sa

mp

le m

ean

Process 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

Sa

mp

le m

ean

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

Sa

mp

le m

ean 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 Control

One 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 57

2 53

3 51

4 58

5 36

6 63

7 55

8 51

9 39

10 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 o w er L im it = M ean - 3 (S td . D ev . )

= 3

nP nP P

nP nP P

( )

(. )( . )

( )

(. )( . )

1

5 0 3 1 0 0 5 5

5 0 1 5

6 5

1

5 0 3 1 0 0 5 5

5 0 1 5

3 5

Control Chart for # of HeadsControl Chart for # of Heads

Control Chart for Number of Heads

15

25

35

45

55

65

75

1 2 3 4 5 6 7 8 9 10

Day

# o

f h

ea

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 4

Tuesday 12 18 15 15

Wednesday 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