Statistical Process ControlStatistical Process Controlof Project Performanceof Project Performance

1. Define the work.

2. Schedule the work.

3. Allocate the Budgets100

50

80

20

50

10

20

Funding Reserve

Sch

edu

le Reserve

BCWS

Time

Co

st

Walt LipkeSoftware DivisionTinker AFB, OK

SCEA 2002June 11-14Scottsdale, AZ

2

ObjectiveObjective

To discuss the application ofTo discuss the application ofSPC Control Charts to the SPC Control Charts to the

EVM indicators,SPI and CPIEVM indicators,SPI and CPI

EVM

CPI

SPI

ControlCharts

SPC

3

OverviewOverview

• Introduction• SPC applied to Software Development?• Review EVM & SPC• SPC with EVM – Does What?• Problems / Cause• Solution Criteria• Proposed Solutions• Testing / Results• Summary

4

IntroductionIntroduction• Software Division

– SEI CMM Level 2 (1993) – First in Air Force– SEI CMM Level 4 (1996) – First in Federal Service– ISO 9001 / TickIT (1998)– IEEE / SEI Software Process Achievement Award (1999)

• EVM Facilitated the Achievements

5

Why SPC?Why SPC?

• SEI CMM Level 4 – Then & Now

• “Statistically Manage the Sub-process”

• CMM Evaluators “Show me the SPC Control Charts”

• Quality Control vs Performance Management

6

SPC ReviewSPC Review

• Several Methods Control Charts

• Control Charts Several Types

• Individuals and Moving Range

Average23 2 3

Process Behavior

AnomalousBehavior

AnomalousBehavior

7

Control ChartControl Chart

1 2 3 4 5 6 20 21 22 23 24 25

3σ

3σ

xObservedValues

Anomalous(“signal”)

Observations – in sequence

8

EVM ReviewEVM Review

Time

BCWS

ACWP

BCWP

$

Total Allocated Budget

Budget at Completion

Management Reserve

BCWS

BCWPSPI

ACWP

BCWPCPI

ProjectCompletion

Date

NegotiatedCompletion

Date

9

SPC with EVM – Does What?SPC with EVM – Does What?

• Performance Prediction– Probability of Success– EAC & ECD – range

• Project Planning– Historical Data– Risk MR Strategy

• Process Improvement– Plan Execution– Decreasing Variation

10

Planning/Performance/ImprovementPlanning/Performance/Improvement

Time

$$

3σ

3σ-

3σ

3σ-

Cost Distribution

Schedule Distribution

Performance Window (PW)

Negotiated Performance (> 50% PW)

Planned Performance (= 50% PW)

TotalAllocatedBudget

Budgetat

Completion

PlannedProject

Completion

NegotiatedProject

Completion

11

ProblemsProblems

SPI Control Chart SPI-1 Control Chart

- 1 . 5

- 0 . 5

0 . 5

1 . 5

2 . 5

3 . 5

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0

2.9813 σ

-0.6723 σ

0.609σ

1.154SPI

S P I

M o n t h s

0

0 . 6

1 . 2

1 . 8

2 . 4

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0

1.9143 σ

0.0893 σ 0.304σ

1.001SPI -1 S P I - 1

M o n t h s

12

ProblemsProblems

SPI (signal removed) SPI-1 (no signal)

0

1

2

3

4

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0

1.8593 σ

0.1793 σ

0.277σ

1.029SPI

S P I

M o n t h s

0

0 . 6

1 . 2

1 . 8

2 . 4

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0

1.9143 σ

0.0893 σ 0.304σ

1.001SPI -1 S P I - 1

M o n t h s

13

ProblemsProblems

Legend:Solid Line ( ) - actualDashed line ( ) - expected

Legend:Solid Line ( ) - actualDashed line ( ) - expected

7.448

0.365 σ

1.013 x

2

Count

CPI

3σ1.8σ 0.6σ 0.6σ1.8σ3σ

5.958

0.404 σ

1.119 x

2

Count

CPI-1

3σ1.8σ 0.6σ 0.6σ1.8σ3σ

14

0

0 . 6

1 . 2

1 . 8

2 . 4

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0

1.9143 σ

0.0893 σ

0.304σ 1.001SPI -1

S P I - 1

M o n t h s

0.960SPI cum-1

- 1 . 5

- 0 . 5

0 . 5

1 . 5

2 . 5

3 . 5

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0

2.9813 σ

-0.6723 σ

0.609σ

1.154SPI

S P I

M o n t h s

1.042SPI cum

More ProblemsMore Problems

1.0 Signal

SPI SPI cum

1.0 Signal No

SPI SPI cum-1-1

Observations

15

Problem ExampleProblem Example

-2

-1

0

1

2

3

4

5

3σ

3σ

SPI

aSPI

bSPI

-2

-1

0

1

2

3

4

5

3σ

3σ

-1SPI

a-1SPI

b-1SPI

SP

I

SP

I-1

16

Problem SummaryProblem Summary

• <PI> > PIcum & <PI-1> > PI-1cum

• <PI>-1 <PI-1> • Signals (nearly always) > 1.0• PI signals PI-1 signals• PI sigma PI-1 sigma• Histograms Normal Distribution

• Without Resolution SPC Application

17

Problem – Cause?Problem – Cause?

......

...............

0

0

PI or PI-1

Skewed Distribution

Normal Distribution

•Average•Signals•Sigma

18

Solution CriteriaSolution Criteria

(1) <PI>-1 = <PI-1>

(2) PI Signals = PI-1 Signals

(3) PI Sigma = PI-1 Sigma

(4) Histograms Normal Distribution

19

Problem SolutionProblem Solution

0.0

0.2

1.0

5.0

-3.0

* Invert Data < 1.0 - Inverted Data behave as if 1.0

* Distinguish Inverted Data

* Use Inverted Data and Unchanged Data for SPC analysis

SPIa SPIb-1

SPIb

~SPIb-1

20

Data Transform RulesData Transform RulesData Transform RulesData Transform Rules

• If PI 1.0, then ~PI = PI

• If PI < 1.0, then ~PI = 2 - PI-1

• If ~PI 1.0, then PIu = <~PI>

• If ~PI < 1.0, then PIu = (2- ~PI)-1

Perform SPC analysis with Transformed Data

21

Problem Solution -ExampleProblem Solution -Example

-2

-1

0

1

2

3

4

5

2.6SPI

aSPI

bSPI

-3

-2

-1

0

1

2

3

4

5

1.0SPIu

bSPI~

aSPI~

SP

I

~S

PI

22

0

0 . 5

1

1 . 5

2

2 . 5

3

3 . 5

4

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0

1.9783 σ

0.0163 σ

0.327σ

0.997SPI~u

~ S P I

M o n t h s

- 2

- 1 . 5

- 1

- 0 . 5

0

0 . 5

1

1 . 5

2

2 . 5

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0

1.9843 σ

0.0223 σ

0.327σ

1.003SPI~u

-1

~ S P I - 1

M o n t h s

Proposed Solution EvaluationProposed Solution Evaluation

• Demonstrates meeting criteria 1, 2, and 3• Mathematically meets criteria 1, 2, and 3• Proof enough?

23

Co

un

t

5.9582

0.214)P( 2 4.6432

Co

un

t

0.341)P( 2

Data Transform –Data Transform –Histogram TestHistogram Test

3σ1.8σ 0.6σ 0.6σ1.8σ3σ3σ1.8σ 0.6σ 0.6σ1.8σ3σ3σ1.8σ 0.6σ 0.6σ1.8σ3σ3σ1.8σ 0.6σ 0.6σ1.8σ3σ

CPI-1 Histogram ~CPI-1 Histogram

areas. histogram the of one is i where,

count /expected)count expectedcount (observed ii

2ii

2

24

Proposed Solution - #2Proposed Solution - #2

0

1

2

3

4

5

2.6SPI

aSPI

bSPI

-2

-1

0

1

2

1.0SPI lnu

bSPI ln

aSPI ln

SP

I

ln S

PI

0.2

0SPI ln

(1.609)

(-1.609)

• Resolves PI vs PI-1

• Resolves PI < 1.0• Transformation Simplicity• Satisfy Criteria?

Logarithm Property:x ln xx-1 -ln x

ln 1 = 0

25

- 1

- 0 . 5

0

0 . 5

1

1 . 5

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0

0.266σ 0.994SPI ln u

l n ( S P I )

M o n t h s

- 1 . 5

- 1

- 0 . 5

0

0 . 5

1

1 . 5

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0

0.266σ 1.006SPI ln u-1

l n ( S P I - 1 )

M o n t h s

Natural Log – Criteria TestNatural Log – Criteria Test

ln SPI ln SPI-1

26

Natural Log – Histogram TestNatural Log – Histogram Test

0.551)P(

3.0662

2

Co

un

t

Legend: Solid Line ( ) - actual Dashed line ( ) - expected

3σ 1.8σ 0.6σ 0.6σ 1.8σ 3σ

ln CPI-1 Histogram

27

Testing SummaryTesting Summary

Test Raw Transformation Logarithm

1. PI-1 = PI-1 No Yes Yes

2. PI Signals = PI-1 Signals No Yes Yes

3.PI Sigma = PI-1 Sigma

No Yes Yes

4. Histograms ~ Normal DistributionVery

UnlikelyUnlikely Likely

28

Sensitivity AnalysisSensitivity Analysis

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

SPIs

(0.284,0.025)

SPI(0.625,0.112)

SPIsu

(0.327,0.007)

SPIu

(0.651,0.082)

lnSPIsu

(0.266,0.01)

lnSPIu

(0.384,0.018)

P

I-

PI c

um

Note: 1. Subscript s indicates the signal is removed from the calculations.2. Subscript u indicates the average value is untransformed from

the average value determined from the SPC analysis

29

SummarySummary

• SPC application to Software Development

• SPC applied to CPI & SPI– Project Execution– Project Planning– Process Improvement

• Problems– Data Representation– SPC Results

30

SummarySummary

• Solutions– Data Transform– Natural logarithm

• Criteria– Results independent from data representation– Results derived from Normal Distribution

• Testing/Results– Data Transform – Good– Natural Logarithm - Better

31

Final RemarksFinal Remarks

• Equivalent to CPI and SPI– CV% = 1 – CPI-1

– SV% = SPI –1

• Distribution is skewed

• Data transformation is needed

Managing to CV% and SV%

32

Final RemarksFinal Remarks

• SPC – Better Management Decisions

• Weekly EV – More Management Decisions

• Weekly EV w/o SPC – Process Tampering

• Try SPC – It’s Not Difficult

Weekly EV vs Monthly SPC