monitor & control processes in the integration management 1 mec-6

Monitor & Control Processesin the

Integration Management

1

MEC-6

Agenda

2

Monitor & Control Project Work Perform Integrated Change Control

Monitor & Control Project Work - Inputs & Outputs

3

Monitor & Control Project Work

1. PMP 2. WPI3. OPA

1. WPR2. Change Requests3. PMP Updates4. PD Updates5. OPA Updates

4. Schedule Forecast5. Cost Forecast6. Validated Changes7. EEF

Monitor & Control Project Work Inputs – 1/5

4

Input Details

Project Management Plan

• Communications management plan• Cost baseline• Cost management plan• Human resource management plan• Process improvement plan• Procurement management plan• Scope baseline• Quality management plan• Requirements management plan• Risk management plan• Schedule baseline• Schedule management plan• Scope management plan• Stakeholder management plan


5

Input Details

Schedule Forecast (from Control Schedule)

• Derived from progress against the schedule baseline and expressed in terms of schedule variance (SV) and schedule performance index (SPI)

• Forecasted Project Completion Date derived from Planned Project Duration and SPI

• The forecast may be used to determine if the project is still within defined tolerance ranges and identify any necessary change requests.

Cost Forecast (from Control Cost)

• Derived from progress against the cost baseline and computed estimates to complete (ETC), expressed in terms of cost variance (CV) and cost performance index (CPI)

• Estimate at completion (EAC) can be compared to the Budget at completion (BAC) to see if the project is still within tolerance ranges or if a change request is required

• Forecast also ascertained through ETC and TCPI


6

Input Details

Validated Changes

• Approved changes that result from the Perform Integrated Change Control process require Validation to ensure that the change was appropriately implemented

• A validated change provides the necessary data to confirm that the change was appropriately executed

WPI • WPI is the WPD collected from various controlling processes, analyzed in context, and integrated based on relationships across areas. Thus WPD data is transformed into WPI

• WPD in itself cannot be used in the decision-making process as it has only out-of-context meaning. Work performance information, however, is correlated and contextualized, and provides a sound foundation for project decisions

• WPI is circulated through communication processes• Examples: Status of deliverables, implementation status for

change requests, and forecasted estimates to complete


7

Input Details

EEF • Governmental or industry standards (e.g., regulatory agency regulations, codes of conduct, product standards, quality standards, and workmanship standards)

• Organization work authorization systems• Stakeholder risk tolerances• Project Management Information System (e.g., an automated tool

suite, such as a scheduling software tool, a configuration management system, an information collection and distribution system, or web interfaces to other online automated systems).


8

Input Details

OPA • Organisational communication requirements• Financial controls procedures (e.g., time reporting, required

expenditure and disbursement reviews, accounting codes, and standard contract provisions)

• Issue and defect management procedures defining issue and defect controls, issue and defect identification, and resolution and action item tracking

• Change control procedures, including those for scope, schedule, cost, and quality variances

• Risk control procedures including risk categories, probability definition and impact, and probability and impact matrix

• Process measurement database used to make available measurement data on processes and products

• Lessons learned database

Monitor & Control Project Work Outputs … 1/3

9

Output Details

Change Requests

• Variances from comparing planned results to actual results• Change Requests expand, adjust, or reduce Project Scope, Product

Scope, or Quality Requirements and Schedule or Cost Baselines• Change Requests may necessitate the collection and documentation

of new requirements• Change Requests can impact the project management plan, project

documents, or product deliverables• Changes that meet the project’s change control criteria should go

through the integrated change control process established for the project

• Changes may include:- Corrective action—An intentional activity that realigns the

performance of the project work with the Proj Management Plan- Preventive action—An intentional activity that ensures the future

performance of the project work is aligned with the Project Management Plan

- Defect Repair—an intentional activity to modify a nonconforming product or product component

Monitor & Control Project Work Outputs … 2/3

10

WPR • WPR are the physical or electronic representation of WPI compiled in project documents, intended to generate decisions, actions, or awareness

• Project information may be communicated verbally from person to person. However, in order to record, store, and sometimes distribute WPI, a physical or electronic representation in the form of project documents is required

• WPR are a subset of project documents, which are intended to create awareness and generate decisions or actions

• Specific work performance metrics may be defined at the start of the project and included in the normal WPR provided to key stakeholders

• Examples: status reports, memos, justifications, information notes, recommendations, and updates

PMP/PD Updates

Monitor & Control Proj Work – Tools & Techniques … 1/2

11

Tools & Techs Details

Expert Judgement

To interpret the information provided by the monitor and control processes, or to resolve any situation emerging from the M&C process, expert judgement from professionals in the industry may be sought

Project Management Information System

Provides access to automated tools, such as scheduling, cost, and resourcing tools, performance indicators, databases, project records, and financials used during the Monitor and Control Project Work process.

Meetings • May include project team members, stakeholders, and others involved in or affected by the project

• Types: User groups, Review Meetings, Focal Groups etc

Monitor & Control Proj Work – Tools & Techniques … 2/2

12

Tools & Techs Details

Analytical Techniques

To forecast potential outcomes based on possiblevariations of project or environmental variables and their relationships with other variables:• Regression analysis• Grouping methods• Causal analysis• Root cause analysis• Forecasting methods (e.g., time series, scenario building,

simulation, etc.)• Failure mode and effect analysis (FMEA)• Fault tree analysis (FTA)• Reserve analysis• Trend analysis• Earned value management (EVM)• Variance analysis

M&C PW – Tools & Techniques - Grouping

13

• Grouping methods• Causal analysis• Root cause analysis• Failure Mode & Effect Analysis (FMEA)• Fault Tree Analysis (FTA)

• Regression Analysis• Forecasting methods• Trend analysis• Earned Value Management• Variance Analysis

• Reserve analysis

Root Cause Analysis

Trend Analysis, Smoothing, Forecasting

Risk Analysis

Grouping Methods

14

Grouping methods are techniques for classifying observations into meaningful categories

Example Defects on a deliverable, say a generator. Grouping by:

By basic engineering: Mechanical, Electrical, Chemical (battery) etc

By Deliverable area: Engine, Generator, Controls, Battery etc

By Load Conditions: Over, Heavy, Medium, Low, Under

Route Cause Analysis (RCA) & Causal Analysis

15

A specific technique used to identify a problem, discover the underlying causes that lead to it, and develop preventive action

The root cause, once removed from the problem fault sequence, prevents the final undesirable event from recurring

Methods:- Cause-and-effect diagrams/fishbone diagrams/Ishikawa

diagrams- The 5 Ws (Whys)- FMEA- FTA- Pareto etc

RCA – Cause & Effect Diagram• Project: Improving the Quality of a University's MBA3.5 (3.5 yrs) Programme• 1st Objective: Root cause the reason for low quality of MBA(3.5 yrs) graduates

16

Weak Inter-Personal Skills

Low Quality Product in MBA (3.5 yrs)

Educational Background

Personality

Extent of Business Education

Other Reasons

Weak FA/FSc

Weak BA/BSc/BCom

BA/BSc/BCom from Low-Key Institutes

BA/BSc in Low-Key subjects

Weak English

3.5 yrs vis-à-vis 5.5/6.5 others

Late StartRelatively

Early Finish

Roadmap unextenable

Time & Cost Fixed

Years since FA/FSc/A-Lvl0 1 2 3 4 5 6 7 8 9

BBA4/Masters MBA 2.5 BBA 4 MBA 1.5

BA/BSc/BCom MBA 3.5

RCA – Cause & Effect Diagram leading to Pareto Analysis

17

Root Causes Count

1 Weak FA/FSc 90

2 Weak BA/BSc/BCom 18

3 BA/BSc/BCom from low-key institutes 7

4 BA/BSc/BCom in low-key subjects 15

5 Weak Inter-Personal Skills 97

6 Weak English 95

7 MBA3.5 roadmap unextendable 12

8 3.5 yrs vis-à-vis 5.5/6.5 others 88

9 Late start 12

10 Relatively early finish 15

11 Time & Cost fixed 10

Count %age Cum %age

5 97 21.1% 21.1%

6 95 20.7% 41.8%

1 90 19.6% 61.4%

8 88 19.2% 80.6%

2 18 3.9% 84.5%

4 15 3.3% 87.8%

10 15 3.3% 91.1%

7 12 2.6% 93.7%

9 12 2.6% 96.3%

11 10 2.2% 98.5%

3 7 1.5% 100.0%

The possible root causes ascertained from the Cause & Effect diagram could next could be short-listed through further RCA. Say a sample of 100 MBA(3.5yrs) students was surveyed which returned the following data which could then be subjected to Pareto analysis to identify those root-causes which would be responsible for 80% of the problem.

Raw Survey Data Pareto Tabulation

RCA – Cause & Effect Diagram leading to Pareto Analysis

18

0

20

40

60

80

100

120

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

RCA – the 5 Whys• Problem: Excavator, an important source on the project, not starting

1st Why Why is the excavator not starting?Flat battery

2nd Why Why Flat battery? Alternator not working

3rd Why Why Alternator not working? Drive belt from the engine broken

4th Why Why Drive belt broken? Poor maintenance

19

Part Not Available5th Why Why Part Not Available?

Old excavator

Failure Mode & Effect Analysis (FMEA)

20

Each potential failure Mode in every component of a product is analyzed to determine its effect on the reliability of that component and, by itself or in combination with other possible failure modes, on the reliability and function of the deliverable, product or system

Primarily a Design/Planning Tool; also used for Monitoring & Control where it provides a basis for identifying Root Failure Causes and developing effective Corrective Actions

FMEA - Application

21

Monitoring & Control: Track changes to process-incorporated to avoid potential failures

FMEA22

• Project: New Fuel-Efficient, Composite Material Commercial Plane (Boeing 787 Dreamliner)

• Deliverable: Lithium Ion Batteries

Product/Deliverable: Lithium Ion BatterySystem: ElectricalSub-System: Back-Up PowerPart No: xxxx-xxxx-xxxx

FMEA Team: ABC (Chief Designer) DEF (Head of Elect Dept) GHI (Battery Specialist) IJK (Configuration Manager)

Page No: 7 of 104FMEA No. 1234Date: 7 Nov 2010

Function Potential Failure Mode

Potential Effect(s) of Failure

Severity (S)

Potential Causes of Failure

Occurrence (O)

Current Controls/ Tests

Detection (D)

Recommend-ed Actions

RPN

Provide back-up power to aircraft instrumentation

Overheating/Meltdown

- Toxic Fumes in cabin

- Explosion in battery compt

- Fire

10 Short-circuiting in Fuel Cells

2 (Test No) 10 Redesign 200

Recharging Malfunction

3 (Test No) 10 Check Elect Charging Sys

300

Unbalanced Chemical Reaction

2 (Test No) 10 Redesign 200

Battery Compt AC failure

3 (Test No) 1 Check AC system

30

FMEA

23

• Project: New Fuel-Efficient, Composite Material Commercial Plane (Boeing 787 Dreamliner)

• Deliverable: Lithium Ion Batteries• Problem: Over-heating & melt-down

- Battery Compartment

Fault Tree Analysis (FTA)

24

A top-down, Deductive failure analysis in which an undesired state of a system is analysed using Boolean logic to combine a series of lower-level events

Helps monitor and control Project Processes and Deliverables Scope

Functions as a diagnostic tool to identify and correct causes of Process failing or a Deliverable not meeting the Scope either in specifications or performance parameters

Fault Tree Analysis• Project: New Commercial Plane• Deliverable: Evacuation Chute• Problem: Failure of Auto-Deployment

25

Fault Tree Analysis• Project: New Commercial Plane• Deliverable: Evacuation Chute• Problem: Failure of Auto-Deployment

26

Auto- Deployment

Failure

Mech Failure

Power Failure

Missing Part

Gen Fault

Faulty Wiring

Faulty Signal

Signal Failure

Part Failure

Lub Failure

Missing Signal

Tx Fault Faulty Wiring

Rx Fault

Servo Failure

Part Failure

1 2

3

4 5 6 7 8 9

Quantitative Forecasting

27

Quantitative Forecasting

Causal Forecasting

Time Series Forecasting

Auto Regression

Moving Average

Exponential Smoothing

Trend Models

Moving Average … 1/3

• Moving Average (Rolling Average or Running Average) is a calculation to analyse data points by creating a series of averages of different subsets of the full data set

• Variations include: Simple, Weighted, Centred, Exponential etc

• Moving Average is used to overcome irregular, random, seasonal or cyclic variations

• Overcoming variations is called "smoothing“

• Moving Average is a smoothing process

• Smoothing by Moving Average is done by taking average of three (or more) recent observations, then dropping the first observation and advancing to the next one, and continuing the process till getting to the period/unit for which forecast is required

28


• Each new data point is included in the average as it becomes available, and the oldest data point is discarded

• The number of observations averaged is referred to as the “k” number; the constant number k is specified at the outset

• The smaller the number k, the more weight is given to recent periods; the greater the number k, the less weight is given to recent periods

• A large k is desirable when there are wide, infrequent fluctuations in the series.

• A small k is most desirable when there are sudden shifts in the level of series

• For quarterly data, a four-quarter moving average, MA(4), eliminates or averages out seasonal effects

29


• For monthly data, a 12-month moving average, MA(12), eliminate or averages out seasonal effect

• Equal weights are assigned to each observation used in the average

30

Forecasting Variations

31

Trend Long-term movement in dataIrregular variations Caused by unusual circumstancesRandom variations Caused by chance

Trend

Irregularvariation

Cycle Wave-like variations lasting more than one year

Cycle

Seasonal Variations

Seasonality Short-term Regular variations in data

Simple Moving Average (SMA) – Understanding the Basic Concepts

32

Simple and Moving Averages can be used to forecast and smoothen data.

Example: On a multi-housing project, the time of completion of the first 10 houses (H1 to H10) is indicated in the tables, headed Case A and Case B. What can be the forecasted duration of House # 11 (H11) in each case?

House #

Duration to Complete

1 2602 2453 2554 2465 2546 2437 2538 2429 254

10 24811 ?

Case AHouse

#Duration to Complete

1 2502 2803 2304 2205 2606 2507 2608 2309 220

10 24011 ?

Case B

SMA – Understanding the Basic Concepts

33

H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11220

225

230

235

240

245

250

255

260

265260

245

255

246

254

243

253

242

254

248

Forecasted Duration of H11Mean 250.0 Fixed AverageMean (minus 1st) 248.9 (the 1st House it took longer)Mean (last 3) 248.0 Moving Average at k = 3Mean (last 4) 249.3 Moving Average at k = 4Mean (last 5) 248.0 Moving Average at k = 5

House #


1 2602 2453 2554 2465 2546 2437 2538 2429 254

10 24811 ?

Case A

SMA – Understanding the Basic Concepts

34

House #


1 2612 2573 2604 2535 2566 2457 2478 2409 242

10 23911 ?

Case B

H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11220

225

230

235

240

245

250

255

260

265261

257

260

253256

245

247

240

242239

f(x) = − 2.61818181818182 x + 264.4

Forecasted Duration of H11

Mean 250.0 Fixed AverageMean (minus 1st three) 246.0 (first three houses took longer)Mean (last 3) 240.3 Moving Average at k = 3Mean (last 4) 242.0 Moving Average at k = 4Mean (last 5) 242.6 Moving Average at k = 5Using Trend Line 235.6 (trend line considers all data)

SMA – How to work out

35

House #


(a)

1 2602 2453 2554 2465 2546 2437 2538 2429 254

10 24811

Case ASMA(k=3)

(b)

253.3

248.7

251.7

247.7

250.0

246.0

249.7

248.0

SMA(k=4)

(c)

251.5

250.0

249.5

249.0

248.0

248.0

249.3

Error Squared (k=3)

Error Squared (k=4)

(a-b)2 (a-c)2

53.8

28.4 6.3

75.1 49.0

28.4 12.3

64.0 49.0

64.0 36.0

2.8 0.0

6.7 5.0

-(a-b)2/n -(a-c)2/nMean Square Error

SMA – Graphical Representation

36H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11

235

240

245

250

255

260

265

260

245

255

246

254

243

253

242

254

248 248

249.25

Actual Durations SMA (k=3) SMA (k=4)

H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11220225230235240245250255260265260

245

255

246

254

243

253

242

254

248Case A

Weighted Moving Average (WMA)

• WMA is used when it is required to give different weightage to different data. For example it may be required to give more weightage to recent data

• Example: In the original multi-housing project example (Case A), it is required to forecast the duration of the 11th house by giving 1/2 weightage to the most recent house duration, 1/3 to the middle duration and 1/6 to the earliest.

37

8 2409 245

10 25311 Forecast = 240/6 + 245x1/3 + 253x1/2 = 248.2

Centred Moving Average (CMA)

• CMA is used for a number of situations particularly when there is a seasonal component, or when there is a requirement to use the past data

• CMA can be computed, using data equally spaced on either side of the point in the series where the mean is calculated

• When k is even, “smoothing of smoothing” is done

38

House #


SMA(k=3)

CMA(k=3)

CMA Error Squared (k=3)

(a) (b) (c) (a-c)2

1 2602 245 253.3 69.43 255 248.7 40.14 246 253.3 251.7 32.15 254 248.7 247.7 40.16 243 251.7 250.0 49.07 253 247.7 246.0 49.08 242 250.0 249.7 58.89 254 246.0 248.0 36.0

10 248 249.711 248.0

Mean Square Error (MSE) 6.6

-(a-c)2/n

CMA

39

k odd (3) Data as per Case A

CMA

40H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11

235

240

245

250

255

260

265

260

245

255

246

254

243

253

242

254

248 248

248.0

Actual Durations SMA (k=3) CMA (k=3)

Data as per Case A

CMA

41

House #

Dur to Complete

SMA (k=4) CMA (k=4) CMA Error Sq (k=4)

(a) (c) (c) (a-c)2

1 2602 245

2.5 250.03 255 249.9 26.3

3.5 249.84 246 249.9 15.0

4.5 250.05 254 251.5 250.1 15.0

5.5 250.36 243 250.0 250.4 54.4

6.5 250.57 253 249.5 248.6 19.1

7.5 246.88 242 249.0 247.8 33.1

8.5 248.89 254 248.0

10 248 248.011 249.3

Mean Square Error (MSE) 5.2-(a-c)2/n

Data as per Case Ak even (4)

CMA

42H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11

235

240

245

250

255

260

265

260

245

255

246

254

243

253

242

254

248249.25

247.75

Actual Durations SMA (k=4) CMA (k=4)

Data as per Case A

Exponential Moving Average (EMA)

• EMA forecasts the value of next event based on:a. Actual Value of the previous itemb. Forecasted Value of the previous itemc. Weight assigned

• EMA weigh past observations using exponentially decreasing weights as the observations get older; recent observations are given relatively more weight than the older observations

• The amount of weight applied to the past observations, or the degree of smoothing required, is determined by the “smoothing constant”

• EMA is in contrast to the SMA. In SMA, the same weights (=1/n) are assigned to the observations. In EMA, there are one or more smoothing parameters to be determined (or estimated) and these choices determine the weights assigned to the observations

43

EMA

• The exponential smoothing equation is:Fn+1 = - yn + (1- -)Fn

where Fn+1 = Forecast for the next unit (to be estimated)a = Smoothing constant, such 0 < - ≤ 1yn = Actual value of the most recent unit

Fn = Forecasted value of the most recent unit• Expanding the Equation:

Fn+1 = - yn + (1- -)Fn

= - (1- -)0yn + (1- -)

= -(1- -)0yn + -(1- -)yn-1 + (1- -)2Fn-1

= -(1- -)0yn + -(1- -)1yn-1 + (1- -)2Fn-1

= -(1- -)0yn + -(1- -)1yn-1 + -(1- -)2

= -(1- -)0yn + -(1- -)1yn-1 + -(1- -)2yn-2+ (1- -)3Fn-2

= -(1- -)0yn + -(1- -)1yn-1 + -(1- -)2yn-2+ -(1- -)3yn-3 ……… -(1- -)n-1F1

= -[(1- -)0yn + (1- -)1yn-1 + (1- -)2yn-2+ (1- -)3yn-3 ……… (1- -)n-1y1]

(F1 is taken as y1)

44

[- yn-1 + (1- -)Fn-1]

[- yn-2 + (1- -)Fn-2]

EMA

45

Fn+1 = - Yn + (1- -)Fn

- Yn (1- -)0+ (1- -) 1Fn

(1- -) 1[-Yn-1 +(1- -)Fn-1]

-(1- -) 1Yn-1 +(1- -)2Fn-1

-(1- -) 1Yn-1 +(1- -)2Fn-1 -(1- -) 1Yn-1

+(1- -)2Fn-1

EMA

• However, in application, EMA is a simple affair. All what is required to be done is:– Select a suitable smoothing constant (-)– Take the most recent observation (yn) and multiply it with the smoothing

constant

– Take what was the forecasted (Fn) value of the most recent observation/ event and multiply it with the complementary of the smoothing constant i.e (1- -)

– Add the two products; the sum is the forecasted value for the next unit

• If the forecasted value (Fn) of the recent most event is not available, then:– Start analysing the data from the start, or from where the last (Fn) is

available, by calculating Fn using the EMA equation

– Continue calculating Fn by applying the EMA equation until the forecasted value of the target event is available

46

EMA47

# Actual Observation

(yn)

Forecasted Observation

(Fn, ,-=0.8)

1 260

2 245 260.0

3 255 248.0

246 253.6

254 247.5

243 252.7

253 244.9

n-2 242 251.4

n-1 254 243.9

n 248 252.0

n+1

# Actual Observation

(yn)

Forecasted Observation

(Fn,-=0.8)

1 260

2 245

3 255

246

254

243

253

n-2 242

n-1 254

n 248

n+1

- 260

260.0

248.0

253.6

247.5

252.7

244.9

251.4

243.9

252.0

248.8248.8

EMA

• Large - (- - 1) would mean:– Maximum consideration to actual/historical data, little consideration to

previously forecasted data– Little smoothing of the data

• Small - (- - 0) would mean:– Little consideration to actual/historical data, maximum consideration to

previously forecasted data– Maximum smoothing of the data

48

EMA – Example (original Case A)

• Consider the data for the original Case A• yn & Fn for various values of - are tabulated:

49

H # Duration to Complete (yn)

1 260 2 2453 2554 2465 2546 2437 2538 2429 254

10 24811

Forecasted Duration (Fn)

- = 1 - = 0.8 - = 0.6 - = 0.5 - = 0.4 - = 0.2 - = 0.1 - = 0.0

260.0 260.0 260.0 260.0 260.0 260.0 260.0 260.0

260.0 260.0 260.0 260.0 260.0 260.0 260.0 260.0

245.0 248.0 251.0 252.5 254.0 257.0 258.5 260.0

255.0 253.6 253.4 253.8 254.4 256.6 258.2 260.0

246.0 247.5 249.0 249.9 251.0 254.5 256.9 260.0

254.0 252.7 252.0 251.9 252.2 254.4 256.6 260.0

243.0 244.9 246.6 247.5 248.5 252.1 255.3 260.0

253.0 251.4 250.4 250.2 250.3 252.3 255.0 260.0

242.0 243.9 245.4 246.1 247.0 250.2 253.7 260.0

254.0 252.0 250.5 250.1 249.8 251.0 253.8 260.0

248.0 248.8 249.0 249.0 249.1 250.4 253.2 260.0

-

EMA – Example (original Case A)50

H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11238

240

242

244

246

248

250

252

254

256

258

260

262

248248.0248.8249.1250.4

253.2

260.0

Yn Fn @ α=1.0 Fn @ α=0.8Fn @ α=0.6 Fn @ α=0.5 Fn @ α=0.4Fn @ α=0.2 Fn @ α=0.1 Fn @ α=0.0

EMA – Example (original Case B)

• Consider the data for the original Case B• yn & Fn for various values of - are tabulated:

51

H # Duration to Complete (yn)

1 2612 2573 2604 2535 2566 2457 2478 2409 242

10 23911

Forecasted Duration (Fn)

- = 1 - = 0.8 - = 0.6 - = 0.5 - = 0.4 - = 0.2 - = 0.1 - = 0.0

261.0 261.0 261.0 261.0 261.0 261.0 261.0 261.0

261.0 261.0 261.0 261.0 261.0 261.0 261.0 261.0

257.0 257.8 258.6 259.0 259.4 260.2 260.6 261.0

260.0 259.6 259.4 259.5 259.6 260.2 260.5 261.0

253.0 254.3 255.6 256.3 257.0 258.7 259.8 261.0

256.0 255.7 255.8 256.1 256.6 258.2 259.4 261.0

245.0 247.1 249.3 250.6 252.0 255.5 258.0 261.0

247.0 247.0 247.9 248.8 250.0 253.8 256.9 261.0

240.0 241.4 243.2 244.4 246.0 251.1 255.2 261.0

242.0 241.9 242.5 243.2 244.4 249.3 253.9 261.0

239.0 239.6 240.4 241.1 242.2 247.2 252.4 261.0

-

EMA – Example (original Case B)52

H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11238

240

242

244

246

248

250

252

254

256

258

260

262

239 239.0239.6240.4241.1242.2

247.2

252.4

261.0

Yn Fn @ α=1.0

Fn @ α=0.8 Fn @ α=0.6

Fn @ α=0.5 Fn @ α=0.4

Fn @ α=0.2 Fn @ α=0.1

Fn @ α=0.0

EMA – Example (original Case A)53

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T1360

62

64

66

68

70

72

74

76

78

80

Yn Fn @ α=1.0Fn @ α=0.8 Fn @ α=0.6Fn @ α=0.5 Fn @ α=0.4Fn @ α=0.2 Fn @ α=0.1

Correlation & Regression

Correlation is a statistical method used to determine whether a linear relationship between variables existsRegression is a statistical method used to describe the nature of the relationship between variables, that is, positive or negative, linear or nonlinear

• Together, Correlation & Regression address these questions statistically:1. Are two or more variables linearly related?2. If so, what is the strength of the relationship?3. What type of relationship exists?4. What kind of predictions can be made from the relationship?

54

Equation of a Straight Line

y = a + bx

where

x = value of independent variable, on the x-axis

y = value of dependent variable, on the y-axis

a = intercept on the y-axis; fixed cost, quantity etc

b = slope of the line; ratio of differential in y-values to corresponding differential in x-values

55

-2 -1 0 1 2 3 4 5

-2

-1

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

f(x) = 2 x + 3

Intercept on Y-axis (= 3 = a)

y-di

ffere

ntial

(=8)

x-differential (=4)

Slope = = = y-diff 8x-diff 4 2 = b

Correlation & Regression - Example

• The amount of cement consumed on a multi-housing project is a function of the covered area of the house

• Independent Variable (x) - Covered Area (deca square meters)Dependent Variable (y) - Cement consumed (deca bags)

• Data as follows:

• Work out the Regression Line and the Correlation Coefficient (R)

56

x

10

12

6

15

8

5

y

30

32

25

46

29

19

Correlation & Regression - Example57

x

10

12

6

15

8

5

y

30

32

25

46

29

19

xy

300

384

150

690

232

95

x2

100

144

36

225

64

25

y2

900

1,024

625

2,116

841

361 - 56 181 1,851 594 5,867

= 6x1,851 – 56x181 = 0.95 -(6x594-562) (6x5,5867-1812)

R

= 181x594 – 56x 1,851 = 9.01 6x56-594

= 6x1,851 – 56x181 = 2.27 6x594-562

y = 2.27x + 9.014

Correlation & Regression - Example

58

4 5 6 7 8 9 10 11 12 13 14 15 16 17 1815

20

25

30

35

40

45

50

Covered Area (sq meter x 10 )

Cem

ent B

ags

(x10

)

y = 2.27x + 9.014R = 0.95

Correlation & Regression

59

Finding the Regression Line Equation & the “R”

60

R

How to Work out “R” & Regression Equation

• Manually (like we did)

• Scientific Calculator

• Trend line on Chart

• Excel Sheet, manually with formula

• Excel Sheet, using SLOPE and INTERCEPT commands

• Excel Sheet, using Data Analysis Feature

• Softwares, eg Minitab

61

monitor & control processes in the integration management 1 mec-6

Documents