Analytical Hierarchy Process (AHP)

(1)

DFSS: Measure 44

SIX SIGMA ADVANTAGE,Inc … for Software Development

DFSS: Measure 44

Analytical Hierarchy Process (AHP)

• Simple Excel AHP Tool

(2)

DFSS: Measure 8

Analytical Hierarchy Process (AHP)

The problem:

Prioritization, judgments and decisions

bog down (a lot) as complexity and

number of choices goes up

The AHP solution:

1. Create an efficient set of pair-wise comparisons

2. Synthesize the comparisons to rational priorities

3. (optional) Check the internal consistency

in the synthesis

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V D A M D MM AA DD VV D

D _{AHP was initially developed by Thomas Saaty}

(3)

DFSS: Measure 9

Basic AHP Prioritization

AHP Example1.xls

A B Cproducts power prodvec Priorities

Facto rs

Same Factors

Simple AHP Illustration

A 1 1 1 1.00 1.00 3.0 3.0 33% A

B 1.00 1 1 1.00 1.00 3.0 3.0 33% B

C 1.00 1.00 1 1.00 1.00 3.0 3.0 33% C

Sums 3.0 100%

#Factors 3 Consistency Index 0.0

Constant for 3 factors 0.58 Inconsistency Ratio 0.0

1

5 Considerably More 10 Much More / No Question 1/5Considerably Less

1/10 Absolutely Less / No Question if Fac2 is stronger,

use the reciprocal to indicate the relationship in the top half of the grid

Equal Facto rs V D A M D MM AA DD VV D D

How does

(the row item)

_{(the column item)?}

Compare with

In terms of preference, likelihood, risk, etc

One way to represent all the pair-wise comparisons among a set of factors is in a matrix. In this simple example, three factors (A, B, C) are assessed. There are 3

comparisons (AB, AC, BC) that need to be made. That requires only ‘half’ the matrix, on one side of the diagonal. The other half of the matrix is computed as the reciprocals of the one that directly receives user data.

A scale using 1 to represent “the same” rates the comparison of the row item to a

corresponding ‘column’ item at the

intersection being evaluated. In this example all comparisons are shown as 1, meaning A=B=C. This illustrates that the priorities are all equal and that there is no inconsistency in the set of comparison (i.e. it can be self-consistent that all three things would be equal).

(4)

DFSS: Measure 10

Checking for Consistency

A

B

C

= C

???

Inconsistency!

Shows up in Inconsistency Ratio

Rule of thumb: IR > about 0.1 can cause concern

A B Cproducts power prodvec Priorities

…with Fac2

Simple AHP Illustration

Comp aring Fac1 A 1 7 2 14.00 2.41 7.7 3.2 65% A B 0.14 1 1 0.14 0.52 1.7 3.2 14% B C 0.50 1.00 1 0.50 0.79 2.5 3.2 21% C Sums 3.2 100%

#Factors 3 Consistency Index 0.1

Constant for 3 factors 0.58 Inconsistency Ratio 0.2

1 Equal

5 Considerably More 10 Much More / No Question 1/5Considerably Less

1/10 Absolutely Less / No Question

In [importance, preference, likelihood, etc] Fac1 (row) to Fac2 (column) is.

if Fac2 is stronger, use the reciprocal to indicate the relationship in the top half of the grid

Comp aring Fac1 V D A M D MM AA DD VV D D

This case illustrates inconsistency.

A is evaluated to be a lot more important than B (the 7 in the upper left white cell in the matrix). A is assessed to be only a little more important than C (the 2). Note the visual representation of the comparison to the right – A is a lot higher than B and only a little higher than C. The final evaluation cell indicates that B is equal to C (the 1). This is inconsistent … there’s no way that all these relationships can coexist. Sometimes AHP users show these kinds of inconsistencies in their thinking when they work through a set of comparisons.

(5)

DFSS: Measure 45

Simple Excel AHP Tool

Gathers user input in spreadsheet

Computes linear priorities

Reports in Pareto Chart

Executive Input: Stratetic Priorities (CTQ's) Prioritization

Request: The team needs the top strategic business priorities (Project CTQ's) validated and prioritized

These weighted and prioritized CTQ's will be the road map for making trade-off decisions in developing the product. How can you provide this input?

AHP Tool

Step 1 Review the list of CTQ's for completeness (if you add any, noted equations need to be updated) Step 2 Fill out the AHP by methodically comparing each CTQ to the other ones

Step 3 Use the scoring method (more, same, less important) as defined on the AHP tab Step 4 Gray cells are calculated and the score is automatically calculated

Step 5

Pros Cons

Most accurate way Must take a minute to understand AHP Calculated scores AHP sometimes is laborous

Example: Instructions

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DFSS: Measure 46

Excel AHP Tool

Scale Simple AHP

1 - equally important Instructions

5 - More Important Fill the CTQ's in the rows. They are automatically copied into the column headers

10 - Much more important Fill in bottom half of the matrix and the top calculates itself as the inverse

1/5 - Less Important These criteria and scores are pulled into the Decision Matrix weighting column

1/10 - Much less important Note: Grey boxes are calculated fields, do not edit

D Rank

Strategic Business Priorities

Tim eto mar ket ( Tech nolo gy #1) Tim eto mar ket ( Tech nolo gy #2) Clin ically inte grat ed Mee tsbe tacu stom erda tes Exce eds the com petit ion Prof itabl e Effic ient inst all Effic ient supp ort c apab ility Perfo rman ce(a vgsc reen to scre en& field tofie ld< 1sec ) Scal able (to10 ,000 user s) Cust omiza ble Ligh twei ght o nin (one mea s with C

9 Time to market (Technology #1) 10 0.2 1 5 5 1 1 0.2 0.2 5 1

16 Time to market (Technology #2) 0.1 0.1 0.1 0.1 5 0.1 0.1 0.1 0.1 1 0.2

4 Clinically integrated 5 10 5 5 5 1 1 1 1 5 1

8 Meets beta customer dates 1 10 0.2 5 5 1 1 1 1 5 5

13 Exceeds the competition 0.2 10 0.2 0.2 5 0.2 0.2 0.2 0.2 1 1

17 Profitable 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 1 1

7 Efficient install 1 10 1 1 5 5 5 0.2 0.2 5 5

10 Efficient support capability 1 10 1 1 5 5 0.2 0.2 0.2 5 5

2

Performance (avg screen to screen & field to

field < 1sec) 5 10 1 1 5 5 5 5 1 5 10

3 Scalable (to 10,000 users) 5 10 1 1 5 5 5 5 1 5 10

18 Customizable 0.2 1 0.2 0.2 1 1 0.2 0.2 0.2 0.2 1

12

Lightweight on infrastructure (one measure

could be: works with Citrix) 1 5 1 0.2 1 1 0.2 0.2 0.1 0.1 1 Fill-in

Is [row] more important than [column]? (>1)

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DFSS: Measure 47

Excel AHP Tool

Sort by this column ascending to make the bar graph sorted

Weight Factor

14 7.3 Architected for next big thing

11 8.1 Customizable

6 8.3 Profitable

2 9.7 Time to market (Technology #2)

13 12.1 ASP architected

16 21.5 Performance improvement for Market Segment #2 customers

5 22.9 Exceeds the competition

12 23.3 Lightweight on infrastructure (one measure could be: works with Citrix) 15 31.4 Performance improvement for Market Segment #1 customers

8 46.1 Efficient support capability 1 47.8 Time to market (Technology #1)

4 53.4 Meets beta customer dates

7 58.9 Efficient install

17 75.4 Open architecture

18 75.4 Community connectivity

3 76 Clinically integrated

10 85.1 Scalable (to 10,000 users)

9 95.1 Performance (avg screen to screen & field to field < 1sec)

19 151 Product Defect Containment

20 21 22

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DFSS: Measure 48

Excel AHP Tool

Executive Priorities - AHP results

0 20 40 60 80 100 120 140 160 Architected for next big thing

Customizable Profitable Time to market (Technology #2) ASP architected Performance improvement for Market Segment #2 customers Exceeds the competition Lightweight on infrastructure (one measure could be: works with Citrix) Performance improvement for Market Segment #1 customers Efficient support capability Time to market (Technology #1) Meets beta customer dates Efficient install Open architecture Community connectivity Clinically integrated Scalable (to 10,000 users) Performance (avg screen to screen & field to field < 1sec) Product Defect Containment

AHP Weight Notes:

If results are not sorted go to the "Results (Sort Please)" Tab and sort as instructed. If you add factors update the range that is graphed

(9)

DFSS: Measure 49

Prioritizing Requirements

w/

Expert Choice

TM

AHP

Start Expert Choice

- Select ‘Create new model

(Direct modeling method)

Describe the Goal

V D A M D MM AA DD VV D D

Expert Choice software facilitates the data gathering and analysis for AHP. We have permission to distribute their demo and tutorials, and we provide here a short orientation to their tool. Beyond that, we have no particular connection to the product. To learn more, or to get help while

evaluating the demo software contact: James Devlin

VP Professional Services 703-243-5595

Tech Support 800-447-0506 www.expertchoice.com

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DFSS: Measure 50

AHP Modeling Steps

Right click – select

‘Insert Child of Current Node’

Type:

VOC <Enter>

VOB < Enter >

< Enter >

_{Important…. an extra < Enter >}

closes out the node insertion

Should look

like this

One builds a hierarchy by defining

nodes under the goal, then adding

child and sibling nodes to build out

the detail.

User interface note:

When typing in a series of nodes at

the same level

-hitting <enter> initiates a new

node

-you must terminate the process by

hitting <enter> twice.

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DFSS: Measure 51

AHP Modeling Steps

EC1.ahp

Open

A simple hierarchy

has been entered

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DFSS: Measure 52

AHP Modeling Steps

Synthesize

(after assessments made)

Model View

Pairwise

Assessments

1. Select ‘Improving business results’

2. **Select ‘ABC’ above (*)**

*

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DFSS: Measure 53

AHP Modeling Steps

Compare the relative importance with respect to VOC\Improving business results

Compare the choices with

respect to the node’s goal

(Improving business results)

The array displays results.

Click in empty white cells to

make specific judgments

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DFSS: Measure 54

AHP Modeling Steps

Note

- Nodes with assessments to be done are marked

- Completed nodes are solid

- Assessments relate to the currently selected node

Done

Not yet

assessed

Exercise: Complete all the assessments in the hierarchy

- VOC as an advocate for a customer you can represent

- VOB from your point of view

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DFSS: Measure 55

AHP Modeling Steps

When the assessments are

complete, the indicators will

change to boxes with green

shading bars

Select the node:

‘VOC’

Select ‘Synthesize’

> With respect to current node

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DFSS: Measure 56

AHP Modeling Steps

Compare the choices

with respect to the current node (VOC)

(17)

DFSS: Measure 57

AHP Modeling Steps

Synthesize all the choices

Look also at Sensitivity Graphs to

investigate how each factor weighed

into the synthesis

(18)

DFSS: Measure 58

Going Further

AHP typically extends the use of this prioritization of criteria

connected with the goal in two ways:

1. Synthesis of inputs from a group

Each participant’s

evaluation of the

pair-wise

comparisons is

stored and used in a

group synthesis.

Inconsistencies

among the

participants become

part of the

assessment

(19)

DFSS: Measure 59