Chapter 1 Making Economic Decisionsweb.eng.fiu.edu/leet/TQM/chap31_2012.pdf · Title: Chapter 1 Making Economic Decisions Author: ENG Created Date: 5/20/2013 4:16:57 PM

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Chapter 31

Other DOE Considerations

31.1 Latin Square Designs and

Youden Square Designs

• A Latin square design is useful to investigate the effects of

different levels on a factor while having two different

blocking variables.

• Restrictions for use are that the number of rows, columns,

and treatments must be equal and there must be no

interactions.

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• For example, a Latin square design could be used to

investigate a response where the blocking variables are

machines and operators.

• If we consider operators A, B, C, and D, a 4x4 Latin square

design would then be

Run Machine

1 2 3 4

1 A B C D

2 B C D A

3 C D A B

4 D A B C



• A 3x3 Latin square design is sometimes called a Taguchi L9

orthogonal array.

• The analysis of a Latin square is available in Minitab (called

Taguchi designs).

• The Latin square design is not considered to be a factorial

design since it does not allow for interaction between

separate factors composing the design.

• Hunter (1989a) warns of dangers from misuse of Latin

square design.

• Youden square designs are similar to Latin square designs

with wide choice of the number of rows as design

alternatives.

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31.2 Evolutionary Operation (EVOP)

• Evolutionary operation (EVOP) is an analytical approach

targeted at securing data from a manufacturing process

where process conditions are varied in a planned factorial

structure from one lot to another without jeopardizing the

manufactured product.

• For previously described DOEs it is typically desirable to

include as many factors as possible in each design, which

keeps the factors studied-to-runs ratio as high as possible.

However, the circumstances when conducting an EVOP are

different.

• Box et al. (1978) provides the following suggestions when

conducting an EVOP:


• Because the signal/noise ratio must be kept low, a large

number of runs is usually necessary to reveal the effects of

changes.

• However, these are manufacturing runs that must be made

anyway and result in very little additional cost.

• In the manufacturing environment things need to be simple,

and usually it is practical to vary only two or three factors in

any given phase of the investigation.

• In these circumstances it makes sense to use replicated 22

or 23 factorial designs, often with an added center-point.

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• As results become available, averages and estimates of

effects are continually updated and displayed on an

information board as a visual factory activity in the area

under investigation.

• The information board must be located where the results are

visible to those responsible for running the process.

• In consultation with an EVOP committee, the process

supervisor uses the information board as a guide for better

process conditions.

31.3 Example 31.1: EVOP

• A study was conducted to decrease the cost per ton of a

product in a petrochemical plant (Jenkins l969; Box et al. I978).

• For one stage of the investigation two variables believed

important were:

• Reflux ratio of a distillation column

• Ratio of recycle flow to purge flow

• Changes to the magnitude of the input variables were expected

to cause transients, which would subside in about 6 hours.

Measurements for the study would be made during an

additional 18 hours of steady operation.

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7.25

7.5

7.75

8

6.5 6.7 6.9 7.1Recycle

/Pu

rge R

ati

o

Reflux Ratio

Phase I - 5 cycles

£ 92

£ 86

£ 92

£ 91

£ 95


• Recorded response was

the average cost per ton.

• The design was a 22

factorial with a center point.

Effects and their std. dev.

Reflux ratio 4.01.5

Recycle/purge ratio -5.01.5

Interaction 1.01.5



Reflux ratio 1.01.0

Recycle/purge ratio -3.01.0

Interaction 0.01.0

7.75

8

8.25

8.5

5.5 5.9 6.3 6.7Recycle

/Pu

rge R

ati

o

Reflux Ratio

Phase II - 5 cycles

£ 80

£ 83

£ 81

£ 84

£ 82

8

8.25

8.5

8.75

5.5 5.9 6.3 6.7Recycle

/Pu

rge R

ati

o

Reflux Ratio

Phase III - 4 cycles

£ 86

£ 84

£ 85

£ 83

£ 80


Reflux ratio -1.01.5

Recycle/purge ratio 2.01.5

Interaction 0.01.5

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• The cost for the described 4½-month program was £6,000,

which resulted in a per-ton cost reduction from £92 to £80. The

annualized saving was £100,000.

31.4 Fold-over Designs

• A technique called fold-over can be used to create a

resolution IV design from a resolution III design.

• To create a fold-over design, simply include with the original

resolution III design a second fractional factorial design with

all the signs reversed.

• This fold-over process can be useful in the situation where

the experimenter has performed a resolution III design

initially and now wishes to remove the confounding of the

main and 2-factor interaction effects.

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31.4 Fold-over Designs

1 2 3 4 5 6 7

V+ * * 3

V

IV * * * * 4

III * * * * 5 6 7

1 + - - + - + +

2 + + - - + - +

3 + + + - - + -

4 - + + + - - +

5 + - + + + - -

6 - + - + + + -

7 - - + - + + +

8 - - - - - - -

1 2 3 4 5 6 7

1 + - - + - +

2 + + - - + -

3 + + + - - +

4 - + + + - -

5 + - + + + -

6 - + - + + +

7 - - + - + +

8 - - - - - -

- + + - + -

- - + + - +

- - - + + -

+ - - - + +

- + - - - +

+ - + - - -

+ + - + - -

+ + + + + +

1 2 3 4 5 6 7 8 9 10 11

V+ * * * 4

V * * * *

IV * * * * * 6

III * * * * * * * * 9 10 11

1 + - - - + - - + + - +

2 + + - - - + - - + + -

3 + + + - - - + - - + +

4 + + + + - - - + - - +

5 - + + + + - - - + - -

6 + - + + + + - - - + -

7 - + - + + + + - - - +

8 + - + - + + + + - - -

9 + + - + - + + + + - -

10 - + + - + - + + + + -

11 - - + + - + - + + + +

12 + - - + + - + - + + +

13 - + - - + + - + - + +

14 - - + - - + + - + - +

15 - - - + - - + + - + -

16 - - - - - - - - - - -

1 2 3 4 5 6 7 8 9 10 11

31.5 DOE: Attribute Response

• In some situations, the appropriate response for a trial may

be an attribute data, e.g., number of failures in n trials.

• If the sample size is the same for each trial, the attribute

data can be analyzed, but a data transformation may be

needed.

• The accuracy of the analysis can become questionable

whenever the sample size is such that many trials have no

failures.

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31.6 DOE: Reliability Evaluations

• In some situations, it is beneficial when doing a reliability

evaluation to build and test devices/systems using a DOE

structure.

• This strategy can be beneficial when deciding on what

design changes should be implemented to fix a problem.

• This strategy can also be used to describe how systems are

built/configured when running a generic reliability test during

early stages of production.

• In this type of test, if all trials experience failures, a failure

rate or time of failure could be the response that is used for

the DOE analysis, with transformation considerations.

31.7 Factorial Designs with more than

2 Levels

• A multiple-experiment strategy that builds on two-level

fractional factorials can be a very useful approach for

gaining insight into what is needed to better understand and

improve a process.

• Usually nonlinear conditions can be addressed by not being

too bold when choosing factorial levels.

• If a description of a region is necessary, a response surface

design such as Box-Behnken or central composite design

(CCD) can be beneficial (see Chapter 33).

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2 Levels

• Tables M1 to M5 can be used to create designs for these test

considerations. To do this, combine the contrast columns of the

designs in Tables M1 to M5 for these test considerations (e.g., - -

= source W, - + = source X, + - = source Y, + + = source Z).

• However, an additional contrast column needs to be preserved in

the case of four levels, because there are 3 degrees of freedom

with 4 levels (4 levels - 1 = 3 degrees of freedom). The contrast

column to preserve is normally the contrast column that contains

the two-factor interaction effect of the two contrast columns

selected to represent the four levels.

• For example, if the A and B contrast columns were combined to

define the levels, the AB contrast column should not be assigned

a factor. These three contrast columns contain the four-level

main effect information.


2 Levels

• For test efficiency, most factor-level considerations above

the level of 2 should be reduced to the value of 2 during an

initial DOE experiment. Higher-level considerations that

cannot be eliminated from consideration can still be

evaluated in a test strategy that consists of multiple

experiments. When the factors that significantly affect a

response are reduced to a manageable number through

two-level experiments, response surface analysis

techniques can be used to find the factor levels that optimize

a response.

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31.8 Example 31.2:

Creating a 2-level DOE Strategy from a

Many-level Factorial Initial Proposal • Consider 2-level factorial experiments

where possible. However, it is

sometimes not very obvious how to

make the change from an experiment

design of many-level considerations.

• An experiment is proposed that

considers an output as a function of

the following factors, where the factor

A may be temperature at 4 levels and

B to F may consider the effects from

other process tolerances.

Factors # of

Levels

A 4

B 3

C 2

D 2

E 2

F 2

31.8 Example 31.2:

Creating a 2-level DOE Strategy from a

Many-level Factorial Initial Proposal • To use an experiment design that considers all possible

combinations of the factors, there would need to be 193

experiment trials.

• By changing all factors to 2-levels and reducing the amount

of interaction output information, a design alternative can be

determined using Tables M1 to M5. This experiment can

then be performed in 8, 16, 32 trials depending on the

desired resolution.

• A series of 2-level experiments is a more efficient test

strategy. After the significant parameters are identified, a

follow-up experiment is made at a resolution that better

assesses main effects and the 2-factor interactions.

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31.9 Example 31.3:

Resolution III DOE with Interaction

Consideration • An experimenter wants to assess the effects of 14 2-level

factors (A-N) on an output. Two of these factors are

temperature and humidity. Each test trial is very expensive,

hence, only a 16-trial resolution III screening experiment is

planned. However, the experimenter is concerned that

temperature and humidity may interact.

• From Table M3, it is noted that for a 14-factor experiment,

the 15th contrast column is not needed for any main effect

consideration. This column could be used to estimate

experimental error or the temperature-humidity interaction.

31.9 Example 31.3:

Resolution III DOE with Interaction

Consideration • To make the temperature-humidity interaction term appear in

this column, the factor assignments must be managed such

that they are consistent with this column.

• From Table N3, it is noted that there are several assignment

alternatives (i.e., AD, BH, GI, EJ, KL, FM, and CN). For

example, temperature could be assigned an A while

humidity is assigned a D.

• This method could be extended to address more than one

interaction consideration for both III and IV designs.

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31.10 Example 31.4:

Analysis of a Resolution III Experiment

with 2-Factor Interaction Assessment • A resolution III experiment was conducted to determine if a

product would give a desirable response under various

design tolerance extremes and operating conditions.

• The experiment had 64 trials with 52 2-level factors (A-Z, a-

z). From Table M5, the experiment design is as follows,

31.10 Example 31.4:


with 2-Factor Interaction Assessment Factors A B C D E F G H I J K L M N O P Q R S T U V W X Y Z a b c d e f g h i j k l m n o p q r s t u v w x y z Contrast 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

1 + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + 2 + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - 3 + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - 4 + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + 5 + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + 6 + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - 7 - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + 8 + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + 9 - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - +

10 + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - 11 - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + 12 + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + 13 + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - 14 - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + 15 - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - 16 + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - 17 + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + 18 - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - 19 + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - 20 + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + 21 + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + 22 - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + 23 + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - - 24 + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - - 25 - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + - 26 + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - + 27 - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + - 28 - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + + 29 + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + + 30 - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + + 31 - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - - + 32 + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - -

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31.10 Example 31.4:


with 2-Factor Interaction Assessment Factors A B C D E F G H I J K L M N O P Q R S T U V W X Y Z a b c d e f g h i j k l m n o p q r s t u v w x y z Contrast 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

33 + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + - 34 + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - + 35 - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + - 36 - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - + 37 - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - - 38 + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - - 39 - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + - 40 + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + + 41 + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - + 42 + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - - 43 + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - - 44 - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - - 45 - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + - 46 + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - + 47 - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - - 48 + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - - 49 - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - - 50 - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - - 51 - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + - 52 + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + + 53 + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + + 54 - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + + 55 - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + + 56 - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + + 57 - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - + 58 + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + - 59 - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - + 60 - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + - 61 - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - + 62 - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + - 63 - - - - - + - - - - + + - - - + - + - - + + + + - + - - - + + + - - + - - + - + + - + + + - + + - - + + 64 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

31.10 Example 31.4:


with 2-Factor Interaction Assessment • Consider that an analysis indicated that only contrast 6, 8,

and 18 were found statistically significant, which implies that

factors F, H, and R are statistically significant.

• However, from Table N3, it is noted that contrast column 6

(factor F) also contains the HR interaction, contrast column 8

(factor H) also contains the FR interaction, and contrast

column 18 (factor R) also contains the FH interaction. One

of the three 2-factor interactions might be making the third

contrast column statistically significant.

• To assess which of these scenarios is most likely from a

technical point of view, interaction plots can be made of the

possibilities assuming that each of them are true.

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31.11 Example 31.5:

DOE with Attribute Response

• A manufacturing surface mount assembles electrical

components onto a printed circuit board (PCB). Visual

assessment at several locations on the PCB of residual flux

and tin (Sn) residuals (lower value is most desirable). A

DOE was conducted with the following factors

Factors (−𝟏) Level (+𝟏) Level

A: Paste age (paste_age) Fresh Old

B: Humidity (humdty) Ambient High

C: Print-reflow time (pr_rfw_tm) Short Long

D: IR temperature (ir_temp) Low High

E: Cleaning temperature (cln_temp) Low High

F: Is component present (comp_prs) No Yes

31.11 Example 31.5:


• Inspectors were not blocked within the experiment though

they should have been.

• The results of the experiment with the trials are as follows,

Trial A B C D E F Insp Flux Sn

1 -1 -1 +1 -1 -1 -1 +1 0 3

2 +1 +1 +1 -1 -1 -1 +1 0 0

3 -1 +1 +1 -1 -1 +1 +1 0 0

4 +1 -1 +1 -1 -1 +1 +1 0 25

5 -1 +1 +1 +1 -1 -1 +1 7 25

6 +1 -1 +1 +1 -1 -1 +1 5 3

7 -1 -1 +1 +1 -1 +1 +1 11 78

8 +1 +1 +1 +1 -1 +1 +1 13 67

9 -1 +1 -1 -1 +1 -1 -1 0 0

10 +1 -1 -1 -1 +1 -1 -1 0 12

11 -1 +1 -1 -1 +1 +1 -1 0 150

12 +1 -1 -1 -1 +1 +1 -1 0 94

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31.11 Example 31.5:


Trial A B C D E F Insp Flux Sn

13 -1 -1 -1 +1 +1 -1 -1 0 424

14 +1 +1 -1 +1 +1 -1 -1 0 500

15 -1 -1 -1 +1 +1 +1 -1 0 1060

16 +1 +1 -1 +1 +1 +1 -1 0 280

17 +1 -1 +1 -1 +1 +1 +1 0 1176

18 -1 +1 +1 -1 +1 -1 +1 24 17

19 +1 -1 +1 -1 +1 -1 +1 5 14

20 -1 -1 +1 -1 +1 +1 +1 0 839

21 +1 +1 +1 +1 +1 +1 +1 0 376

22 -1 -1 +1 +1 +1 -1 +1 0 366

23 +1 +1 +1 +1 +1 -1 +1 0 690

24 -1 +1 +1 +1 +1 +1 +1 0 722

25 -1 +1 -1 -1 -1 -1 -1 0 50

26 -1 -1 -1 -1 -1 -1 -1 0 12

27 +1 +1 -1 +1 -1 -1 -1 0 50

28 -1 +1 -1 +1 -1 +1 -1 0 207

29 +1 -1 -1 +1 -1 +1 -1 0 172

30 +1 -1 -1 +1 -1 -1 -1 2 54

31 -1 -1 -1 -1 -1 +1 +1 0 0

32 +1 +1 -1 -1 -1 +1 +1 0 2

31.11 Example 31.5:


• Consider first an analysis of the flux response. There are many

0s, which makes a traditional DOE analysis impossible. However,

when the responses are ranked, there are 7 non-zero values.

The largest 6 values are with C= +1 and from the same inspector.

One might inquire whether a gage R&R study had been

conducted. These PCBs should also be reassessed.

Trial A B C D E F Insp Flux

18 -1 +1 +1 -1 +1 -1 +1 24

8 +1 +1 +1 +1 -1 +1 +1 13

7 -1 -1 +1 +1 -1 +1 +1 11

5 -1 +1 +1 +1 -1 -1 +1 7

6 +1 -1 +1 +1 -1 -1 +1 5

19 +1 -1 +1 -1 +1 -1 +1 5

30 +1 -1 -1 +1 -1 -1 -1 2

• If the results are

validated, one would

conclude that -1 level

for C is best.

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31.11 Example 31.5:


• Consider next an analysis of the tin (Sn) response. Because

the response is count data, a transformation should be

considered.

31.11 Example 31.5:

DOE with Attribute Response Factorial Fit: Sn versus A, B, C, D,

E, F, Insp

Estimated Effects and Coefficients

for Sn (coded units)

Term Effect Coef

Constant 507

A 227 114

B -292 -146

C 2393 1197

D 691 345

E 634 317

F 592 296

Insp -2543 -1271

A*B -433 -216

A*C 303 151

A*D 592 296

A*E 166 83

A*F 23 12

A*Insp -178 -89

B*C -406 -203

Term Effect Coef

Constant 507

B*D -268 -134

B*E -693 -347

B*F -491 -245

C*D 163 81

C*E 179 90

C*F -8 -4

D*E 1283 642

D*F -420 -210

E*F -438 -219

A*B*C -135 -67

A*B*D -988 -494

A*C*D 178 89

A*B*E -1011 -505

A*C*E 188 94

A*B*F 466 233

A*C*F 254 127

B*C*F -294 -147

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31.11 Example 31.5:


Analysis of Variance for Sn (coded units)

Source DF Seq SS Adj SS Adj MS F P

Main Effects 7 1775800 1485343 212192 * *

2-Way Interactions 16 1151550 1274442 79653 * *

3-Way Interactions 8 445497 445497 55687 * *

Residual Error 0 * * *

Total 31 3372848

31.12 Example 31.6:

A System DOE Stress to Fail Test

• During the development of a new computer, a limited amount of

test hardware is available to evaluate the overall design of the

product. 4 test systems are available along with 3 different

card/adapter types (designated as card A, card B, and adapter)

that are interchangeable between the systems.

• A “quick and dirty” fractional factorial test approach is desired

to evaluate the different combinations of the hardware along

with the temperature and humidity extremes.

• One obvious response for the experimental trial is whether the

combination of hardware “worked” or “did not work”. However,

more information was desired from the experiment than just a

binary response.

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31.12 Example 31.6:


• In the past, it was shown that the system design safety factor

could be quantified by noting the 5-V power supply output level,

both upward and downward, at which the system begins to

perform unsatisfactorily.

• A probability plot was then made of these voltage values to

estimate the number of systems from the population that would

not perform satisfactorily outside the 4.7-5.3 tolerance range of

the 5-V power supply.

• Determining a low-voltage failure value could easily be

accomplished for this test procedure because this type of

system failure was not catastrophic; i.e., the system would still

perform satisfactorily again if the voltage level were increased.

31.12 Example 31.6:


• However, the system voltage stressing would be suspended at

6.00 V because additional stressing might destroy more

components.

• The following table shows a 16-trial test matrix with measured

voltage levels.

• Note that the trial fractional factorial levels can be created from

Tables M1 to M5 where 4 levels of the factors are created by

combining contrast columns (e.g., --=1, -+=2, +-=3, and ++=4).

• It should be noted that the intent of this experiment was to do a

quick test at the boundaries of the conditions to assess the

range of response that might be expected when parts are

assembled in different patterns. No special care was taken

when picking the contrast columns, there will be confounding.

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31.12 Example 31.6:


Temp Humi System Card A Card B Adapter Elevated Lowered

95 50 1 4 1c 4 E1 5.92 E2 4.41

95 50 3b 3 3 2 sus 6.00 E3 4.60

95 50 4 1 2 1 sus 6.00 E2 4.50

95 50 2 2 4 3 sus 6.00 E2 4.41

55 20 1 4 1c 1 sus 6.00 E2 4.34

55 20 2 1 4 2 sus 6.00 E2 4.41

55 20 3ad 2 3 3 sus 6.00 E2 4.45

55 20 4 3 2 4 sus 6.00 E2 4.51

55 85 1 1 2 2 sus 6.00 E2 4.52

55 85 2 4 3 1 sus 6.00 E2 4.45

55 85 3b 2 4 4 sus 6.00 E3 4.62

55 85 4 3 1c 3 E1 5.88 E2 4.58

95 20 1 1 2 3 sus 6.00 E2 4.51

95 20 2 3 3 4 sus 6.00 E2 4.44

95 20 3ad 4 4 1 sus 6.00 E2 4.41

95 20 4 2 1c 2 E1 5.98 E2 4.41

b Lowering 5V

caused an E3

error.

c Lowering 5V

caused an E1

error. (3 out

of 4 times

when card

B=1.

3a new system

planar board

installed.

31.12 Example 31.6:


• It is noted that the system 3 planar board was changed during

the experiment. Changes of this type should be avoided;

however, if an unexpected event mandates a change, the

change should be documented.

• It is also noted that the trials containing system 3 with the

original planar resulted in a different error message when the

5V power supply was lowered to failure.

• It is also noted that the only “elevated voltage” failures occurred

(3 out of 4 times) when card B = 1. General conclusions from

observations of this type must be made with extreme caution

because aliasing and measurement errors can lead to

erroneous conclusions. Additional investigation is needed for

the purpose of confirmation or rejecting such theories.

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31.12 Example 31.6:


• The basic strategy behind this type of experiment is to assess

the amount of safety factor before failure.

• The DCRCA (DOE Collective Response Capability

Assessment) plot can give some idea of the safety factor in the

design. From this plot, a best-estimate projection is that about

99.9% of the systems will perform at the low-voltage tolerance

value at 4.7.

31.12 Example 31.6:


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31.12 Example 31.6:


• Consider next that a similar experiment is performed with a

new level of hardware.

• From the probability plot of the low-voltage stress values, one

of the points could be an outlier. This data should be

investigated for abnormalities.

• It appears that the later design have a larger safety factor.

• In manufacturing, it is feasible for the test strategy to be

repeated periodically. Data could be monitored on 𝑥 and 𝑅

control charts for degradation/improvement as a function of

time.

31.12 Example 31.6:


Temp Humi System Card A Card B Adapter Elevated Lowered

95 50 1 4 1 1 sus 6.00 E2 4.48

95 20 2 1 4 2 sus 6.00 E2 4.48

95 20 3 2 3 3 sus 6.00 E2 4.45

95 20 4 3 2 4 sus 6.00 E2 4.42

55 85 1 1 2 2 sus 6.00 E2 4.56

55 85 2 4 3 1 sus 6.00 E2 4.46

55 85 3 2 4 4 sus 6.00 E2 4.45

55 85 4 3 1 3 sus 6.00 E2 4.43

55 20 1 1 2 3 sus 6.00 E2 4.45

55 20 2 3 3 4 sus 6.00 E2 4.46

55 20 3 4 4 1 sus 6.00 E3 4.42

55 20 4 2 1 2 sus 6.00 E2 4.48

95 50 1 4 1 4 sus 6.00 E2 4.45

95 50 3 2 4 3 sus 6.00 E2 4.49

95 50 4 3 3 2 sus 6.00 E2 4.45

95 50 2 1 2 1 sus 6.00 E2 4.49

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31.12 Example 31.6:


31.12 Example 31.6:


Documents

Chapter 1 Making Economic Decisionsweb.eng.fiu.edu/leet/TQM/chap31_2012.pdf · Title: Chapter 1 Making Economic Decisions Author: ENG Created Date: 5/20/2013 4:16:57 PM