Value streams performance estimation and the PESEP framework

Copyrights © 2011-2017 Pragmatic Cohesion Consulting LLC, All Rights Reserved

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Article

Value Streams Performance Estimation and the PESEP™ Framework

By Atiogbe Didier KOFFI

Abstract

This article presents a model that describes the relative influences that Mission Statements, Business Objectives, Business Capabilities, and Business Processes exert on each other when the Enterprise decides to adopt and implement new Mission Statements. The model stipulates that these relative influences aim at reducing Enterprise Pursuits uncertainty in a coherent manner across Enterprise Endeavor Scopes. The paper describes how the model relates to Value Streams and how it offers an overarching context for their accurate definitions. The quantitative version of the model estimates an enterprise probability of fully delivering a Value Stream value based on efficiency and effectiveness levels applied to its implementation. The paper also describes how the famous Golden Ratio relates to a Value Stream Performance.

Keywords

Business architecture, value streams, business capabilities, performance, alignment, maturity, enterprise risk management, enterprise pursuits, enterprise endeavor scopes.

INTRODUCTION

A very common source of uncertainty within any enterprise has to do with knowing whether or not it is doing the right things for the enterprise as well as doing things right within the enterprise [Drucker 2004].

This article presents a model named the Pragmatic Endeavor Scopes of Enterprise Pursuits (PESEP™) framework that describes the relative influences that enterprise Mission Statements, Business Objectives, Business Capabilities and Business Processes exert on each other when the enterprise decides to adopt and implement new Mission Statements. The model stipulates that these relative influences aim at reducing Enterprise Pursuits uncertainty in a coherent manner.

Value Streams [The Open Group 2017] have gained significant attention and recognition from the Business Architecture Community due to their pragmatic way of modeling value from the perspective of customers and stakeholders. The paper describes how the PESEP™ framework relates to Value Streams and how it offers an overarching context for their accurate definitions.

The paper describes a quantitative formulation of the PESEP™ framework and how it estimates an enterprise probability of fully delivering a Value Stream value based on the efficiency and effectiveness levels applied to its implementation. The paper also describes how the famous Golden Ratio relates to a Value Stream Performance.

ENTERPRISE PURSUITS

Doing the right things for the enterprise entails determining its desired direction in terms of Mission Statements [Talbot M 2003], and Business Objectives [Granger C 1964]. Doing things right within the enterprise is about enabling and sustaining the proper Business Capabilities [The Open Group 2016] and Business Processes [Harvard Business School Press 2010] that realize the desired enterprise direction. Mission Statements, Business Objectives, Business Capabilities, and Business Processes are important enterprise concepts that this article refers to as Enterprise Pursuits.

Figure 1 summarizes the influence that Enterprise Pursuits have on each other. The qualitative interpretation of Mission Statements [Talbot M 2003] leads to the identification of Business Objectives and their critical success factors [Howell M. 2010]. Business Objectives critical success factors influence targeted Business Capabilities and their assessment metrics relative priorities or weights [Schnapper and Rollins 2006]. Business Capabilities assessment metrics goals in turn influence Business Processes and their key performance indicators [Raynus 2011].

Key performance indicators provide information about the achievement of Business Capabilities targeted Metrics. Business Capabilities achieved Metrics measure the attainment of Business Objectives’ critical


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success factors. The numbers of critical success factors that are met indicate how well an enterprise fulfills its Mission.

Figure 1: Enterprise Pursuits Influencing Constraints

ENTERPRISE ENDEAVOR SCOPES

Doing the right things and doing things right for an Enterprise can be achieved at the following distinct Endeavor Scopes: Strategic, Tactical, Operational, and

Clerical [Kurstedt 2001]. Figure 2 shows that generally speaking, at the Strategic scope the enterprise decides what problems to solve and what opportunities to seize in order to achieve given Outcomes. At the Tactical scope the enterprise decides what resources to employ and control to generate particular Outputs. Operational scope is concerned with defining the Methods needed to follow selected transformation paths of inputs into outputs. At the Clerical Scope the enterprise Executes Steps required to run its operation.

Figure 2: Enterprise Endeavors Influencing Constraints

An important characteristic of PESEP™ is that it groups Enterprise Pursuits according to Endeavor scopes. Each Endeavor scope provides a common context for its Pursuits by focusing them on managing either: Outcomes, Outputs, Methods, or Execution Steps. Each one of the four Enterprise Pursuits types can therefore occur within each Enterprise Endeavor scope.

As a result the following can be said about Mission Statements:

Strategic Mission Statements manage Outcomes that constrain Tactical Mission Statements

Tactical Mission Statements manage Outputs that constrain Operational Mission Statements

Operational Mission Statements manage input to output transformation Methods that constrain Clerical Mission Statements

Next, we will use Table 1 to illustrate the influences that Strategic Scope Enterprise Pursuits have on each other.


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Table 1: Strategic Endeavor Scope Example

Strategic Scope:

Manage Outcomes and Opportunities

Doing the Right Things Doing Things Right

Strategic Mission

Statement

Strategic Business Objectives

Strategic Business Capabilities

Strategic Business Processes

“Give people the power to share and make the world more open and connected” -Facebook

Empower people all around the world to connect and share information

-Channels Partners Management

-Channels Policy Management

-Market Segment Management

Advertise connection channels

-Account Administration

-Information Management

-Security Privacy and Data Protection

Maintain list of connected people


Offer information sharing opportunities


Enabled selected sharing method



-Infrastructure Management

Share and display information between connected people



-Infrastructure Management

Maintain shared information

Table 1 shows a Strategic Mission Statement focused on outcomes: empower people to share and bring about a more open and connected world. The enterprise could mandate the following critical success factors to constrain the Strategic Business Objective “Empower people all around the world to connect and share information”:

Connect 1 Billion people over the next 5 years

Connect people over all continents over the next 5 years

Connect people whenever they desire

Allow people to share as much information as they desire

Expend the service and product portfolio by 50% over the next 2 fiscal years

Users have access to 80% of Services and Products offered for free

The identified critical success factors influence the selection of the following Business Capabilities best suited for fulfilling the Strategic Objective:

Channels Partners Management

Channels Policy Management

Market Segment Management

Account Administration

Security Privacy and Data Protection

Information Management

Infrastructure Management

Table 1 shows examples of Business Processes relevant to achieving the Strategic Business Objective and that are enabled by the targeted Business Capabilities:

Advertise connection channels

Maintain list of connected people

Offer information sharing opportunities

Enabled selected sharing method

Share and display information between connected people

Maintain shared information Examples of Tactical Mission Statements that focus on resources used or controlled to deliver outputs are:

“Stay connected with friends and family” which generates “Sustained Connections” as output

“Discover what’s going on in the world” which generates “Discovered Information” as output

“Share and express what matters to people” which generates “Shared Relevant Information” as output

Examples of Operational Mission Statements that focus on Methods or Paths that deliver transformation of inputs into outputs are:

“Use Agile methods to develop product and services”

“Use Lean principles to run the business operation”

PESEP™ QUALITATIVE FRAMEWORK

The PESEP™ framework geometry is that of a two-dimensional 4x4 matrix that has four rows for Endeavor Scopes and four columns for Enterprise Pursuit types. Figure 3 illustrates how each cell in the matrix contains


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business concepts in line with a particular enterprise Pursuit type and a particular Enterprise Endeavor scope.

To implement all PESEP™ framework cells, an enterprise starts with defining its Strategic Mission Statement and proceeds down the first column to sequentially specify its corresponding Tactical, Operational, and Clerical Mission Statements [Schearer 2006]. With a clear definition of Mission Statements at all four Endeavor Scopes, the enterprise can tackle the PESEP™ framework’s second column and define Strategic, Tactical, Operational, and Clerical Business Objectives that are align with their corresponding Mission Statements. The enterprise continues this process in a similar fashion covering all remaining framework columns from left to right. Figure 3 conveys the sequence of actions with orange arrows going from each Mission Statement cell to the one located right below it and blue arrows going from each cell to the one located at its right.

Figure 3: PESEP™ Framework

Value Stream Relations to the PESEP™ Framework

A Value Stream is a sequence of Value Stages arranged along a transformation path of inputs into outputs that delivers value to stakeholders [The Open Group 2017]. Each Value Stream Stage is enabled by Business Capabilities that could belong to the following three stratification levels: Strategic, Core, and Supporting. Figure 4 presents an example of Value Streams taken from the Open Group Value Streams Guide.

Figure 4: Value Stream Example from the Open Group Guide to Value Streams

The following attributes describe a value Stream [The Open Group 2017]:

Name such as “Recruit Employee”

Description such as “The activities involved in identifying and hiring suitably qualified employees”

Stakeholder such as “A Hiring Manager looking to fill a specific position”

Value such as “A new employee with good fit for the job, hired rapidly, and working productively”

A Value Stream Stage has the following set of attributes:

Name such as “Define Position”

Description such as “The act of determining the need for staffing, identifying skills and qualifications, and documenting them”

Participating Stakeholders such as “ Hiring Manager, HR Recruitment Lead”

Entrance Criteria such as “Staffing changes identified”

Exit Criteria such as “Recruitment needs identified”

Value Items such as “Time and expense saved on search for candidates”

The PESEP™ framework can be used to identify and classify Value Streams according to the framework’s top three rows. Value Streams that deliver Outcome values correspond to the PESEP™ Strategic Endeavor. Value Streams that deliver Output values relate to Tactical Endeavors. Value Streams that address Transformation Methods of inputs into outputs correspond to Operational Endeavors. Since the “Recruit Employee” Value Stream delivers a value that is an Output i.e. a new Employee, it corresponds to a Tactical Mission Statement and belongs to the Tactical Endeavor scope as illustrated in Table 2.

The PESEP™ framework brings additional value to Value Streams by providing an overarching business context to them. Using the example in table 2, the Value Stream value statement maps to a Tactical Business Objective: “A new employee with good fit for the job, hired rapidly, and working productively”. According to the PESEP™ framework that Tactical objective must


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translate into Critical Success Factors (CSFs) that describe the conditions required for the Tactical Objective to be met. Here are examples of such CSFs:

Company’s need for the job position must fully reflect the company’s policies

Employee is fit for the job when she has at least 90% of the job required skills and qualifications

Employee hiring process should not exceed one month from receiving their application to starting the job

Employee is working productively when she is fully integrated to the work environment

These CSFs are also used to constrain targeted Business Capabilities and their assessment metrics relative priorities or weights.

PESEP™ Tactical Business Processes correspond to Value Stream Stages. Each Value Stream Stage has Value Items that are similar to a Key Performance Indicators (KPIs). For example, “Define Position” has the following Value Item: “Time and expense saved on search for candidates”

Table 2: Example of Value Stream Mapping to Tactical Endeavor Scope

Tactical Scope:

Manage Outputs and Controls

Doing the Right Things

Doing Things Right

Tactical Mission Statements

Tactical Business Objectives

Tactical Business Capabilities

Tactical Business Processes

Recruit Employee

A new employee with good fit for the job, hired rapidly, and working productively

-Program Management: Program /Resource matching -HR Management: Competency Management

-Policy Management: Policy Dissemination

1.Define Position

-HR Management: Employee Supply and Demand Management, Position Advertising -Finance Management: Labor Funding

2.Communicate Position

PESEP™ KPIs provide information about the achievement of Metrics applicable to Business Capabilities that enable the Value Stream Stage. “Define Position” is enabled by the following three Business Capabilities: Resource Matching, Competency Management, and Policy Dissemination. The KPIs can drive the following question: What Assessment Metrics can be applied to Resource Matching , Competency Management, and Policy Dissemination Capabilities to save time and expense on search for candidates?

The answer to the question could be: Relevance Metrics for Resource Matching, Accuracy Metrics for Competencies Management and Conformance Metrics for Policy Dissemination. These Metrics direct Capability Assessment activities.

Resource Matching is part of the Program Management Capability. Competency Management is part of the HR Management Capability. Policy Dissemination is part of the Policy Management Capability. The Tactical Objective CSFs are used to constrain targeted Business Capabilities and their assessment metrics relative priorities or weights:

“Company’s need for the job position must fully reflect the company’s policies” constrains Policy Management Capability and Conformance Metrics

“Employee is fit for the job when she has at least 90% of the job required skills and qualifications” constrains HR Management Capability and Accuracy Metrics

“Employee hiring process should not exceed one month from receiving their application to starting the job” constrains Program Management Capability and Relevance Metrics

“Employee is working productively when she is fully integrated to the work environment” constrains Policy Management Capability and Conformance Metrics

“Communicate Position” has the following Value Item: “High likelihood of finding qualified candidates”. This KPI drives the following question: What Assessment Metrics can be applied to Employee Supply and Demand Management, Position Advertising, and Labor Funding to ensure a high likelihood of finding qualified candidates?

The answer to the question could be: Balance Metrics for Employee Supply and Demand Management, Conversion Metrics for Position Advertising and Budget Metrics for Labor Funding.

Employee Supply and Demand Management and Position Advertising are part of the HR Management


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Capability. Labor Funding is part of Finance Management Capability.

The Operational Objectives’ CSFs generate the following constrains:

“Employee is fit for the job when she has at least 90% of the job required skills and qualifications” constrains HR Management Capability and Balance Metrics

“Employee hiring process should not exceed one month from receiving their application to starting the job” constrains HR Management Capability and Balance Metrics and Conversion Metrics

“Employee hiring process should not exceed one month from receiving their application to starting the job” constrains Finance Management Capability and Budget Metrics

HR Management Capability has one occurrence of Accuracy Metrics for Competencies Management, one occurrence of Conversion Metrics for Position Advertising, and two occurrences of Balance Metrics for Supply and Demand Management. These occurrences can be converted into the following relative weights: 25% for Accuracy, 25% for Conversion, and 50% for Balance.

The full mapping of Value Stream Stages to their enabling Business Capabilities reveals that HR Management Capability appears 5 times out of 13 occurrences of Business Capabilities at a similar level. HR Management Capability is therefore given a weight of 5/13 ~ 38%.

Figure 5 summarizes the Enterprise Pursuits influences previously described.

Figure 5: Enterprise Pursuit Influences Example

PESEP™ QUANTITATIVE MODEL

Each PESEP™ framework Pursuit type imposes constraints upon itself through the nature of the business concept it represents. For example in table 1, the Strategic Mission Statement must be stated in ways that convey a Mission Statement focused on Outcomes and/or Opportunities.

Each PESEP™ framework Pursuit type also imposes constraints upon the Pursuit type located to its right on the same row:

Mission Statement imposes qualitative Interpretation constraints upon Business Objective

Business Objective imposes critical success factors constraints upon Business Capabilities

Business Capabilities impose assessment metric goals constraints upon Business Processes

Enterprise Pursuits Uncertainty

Each Pursuit type with the exception of Mission Statements provides feedback to the Pursuit type located to its left by indicating how well its constraints are met. For each Pursuit type, we define an Alignment Uncertainty (AU) ratio as the ratio of Missed Constraints


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to Imposed Constraints [Juran and Gryna 1993]; AU ratio = (Missed Constraints) / (Imposed Constraints).

Using table 1 as example, the Strategic Objective “Empower people all around the world to connect and share information” has six critical success factors. Let’s say that only "Allow people to share as much information as they desire” and “Expend the service and product portfolio by 50% over the next 2 fiscal years” are missed by the selected Business Capabilities then “Empower people all around the world to connect and share information” has an AU ratio of 2/6= 33%.

When AU has a value strictly greater than zero, it implies that the enterprise has unmet constraints that need further attention in order to be fulfilled.

Quantitative Model Formulation

Let’s use the following Enterprise Pursuit abbreviations to help formulate the PESEP™ quantitative model for a given Endeavor Scope:

M stands for Mission Statement

O stands for Business Objective

C stands for Business Capabilities

P stands for Business Processes

AU ratio represents the relative amount of unmet constraints that a Pursuit type has with respect to the Pursuit immediately to its left. Table 3 illustrates these concepts across a given Endeavor scope for a given Mission Statement with the following three possible AU ratios:

AU1 is the percentage of unmet constraints imposed by Mission Statement qualitative interpretations upon Business Objective.

AU2 is the percentage of unmet constraints imposed by Business Objectives critical success factors upon Business Capabilities.

AU3 is the percentage of unmet constraints imposed by Business Capabilities metric goals upon Business Processes.

Each row in table 3 shows the constraint strengths imposed upon the corresponding Pursuit type.

Normalizing the rows of Table 3 results in Table 4.

Table 3: Enterprise Pursuits Constraints

M O C P

M 1 1 0 0

O AU1 1 1 0

C 0 AU2 1 1

P 0 0 AU3 1

Table 4: Normalized Enterprise Pursuits Constraints

M O C P

M 1

2

1

2

0 0

O AU1

2 + AU1

1

2 + AU1

1

2 + AU1

0

C 0 AU2

2 + AU2

1

2 + AU2

1

2 + AU2

P 0 0 AU3

1 + AU3

1

1 + AU3

PUTTING THE MODEL INTO PRACTICE

N-Step Transition Matrix

The content of table 4 is analog to a two dimensional matrix that we call MP. Each row in MP shows the distribution of constraints applied to the corresponding Enterprise Pursuit type. Markov’s Chains N-Step transition matrix can be used to describe how MP’s constraint distributions evolve from one Pursuit type to another over consecutive implementation and corrective iterations starting with the definition of a Mission Statement [Koffi 2010].

To illustrate the use of our model, let’s assume that all AU ratios have the same value AU0. When AU0=0; all constraints imposed upon an Enterprise Pursuit type by its left side Pursuit type are fulfilled without a need for corrective iterations. Figure 6 presents the evolution of constraints distributions in that case.


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Figure 6: Pursuits Constraint Distributions for AU0=0

When AU0=0, the first iteration ends with constraints split between Mission Statement (50%) and Business Objectives (50%); no constraints are yet placed on Business Capabilities and Business Processes. At the end of step 2, constraints are distributed as follow: 25% for Mission, 50% for Business Objectives, and 25% for Business Capabilities; no constraints are yet placed on Business Processes. Iteration cycles continue in this manner with each cycle changing the constraints distributions. In the long run, constraints placed on Business Processes reach their steady state distribution (Pf). When AU0=0 and when all constraints imposed upon the targeted Enterprise Pursuits are met Pf approaches 100%. At that point the following has occurred:

All targeted Business Capability metric improvement goals are met

All selected Business Objective critical success factors are met.

And all qualitative interpretations of Mission Statements are met.

Pf is the probability that the Mission Statement is fulfilled in the long run.

PESEP™ Quantitative Model, Value Streams, and the Golden Ratio

Since AU0 represents the ratio of constraints missed by a Pursuit type, 1-AU0 represents the ratio of constraints met by a Pursuit type. For Mission Statement and Business Objectives, 1-AU0 is analogous to enterprise Effectiveness which indicates how well an enterprise does the right things. For Business Capabilities and Business Processes, 1-AU0 is similar to enterprise Efficiency which conveys how well an enterprise does things right to fulfill a given Mission Statement.

Figure 7 shows a graph of Pf when 1-AU0 varies from 0 to 1.

According to figure 7, when the enterprise increases its Effectiveness and Efficiency metrics (1-AU0), Pf increases at an accelerated rate. When Pf equals 50%, the enterprise has an equal probability of fulfilling or not fulfilling a Mission Statement in the long run. Point S on Pf’s curve shows that Pf equals 50% when the enterprise Effectiveness and Efficiency metrics is very close to 0.618 which is also known as the reciprocal of

the famous Golden Ratio . The Golden Ratio has many

mathematical properties that have fascinated scientists and artists for centuries [Posamentier and Lehmann

2012]. Within the PESEP™ framework, 1/ is an

important threshold above which the enterprise becomes more likely to succeed than to fail at fulfilling a Mission Statement.

We have described how Value Streams map to the

PESEP™ framework, therefore 1/ is an important

threshold for Value Streams Performance. 1/=61.8% is

a lower bound to the level of effectiveness and efficiency with which Value Streams must be implemented in order to have a chance equal to or higher than 50% of delivering their value.

Point E on Pf’s curve shows that if 1-AU0 =1/2 then Pf

also equals 1/2 =0.309. When 1-AU0 is less than 1/2 then the probability of delivering a Value Stream value is higher than the effectiveness and efficiency levels with which the Value Stream is implemented. If the effectiveness and efficiency level with which the Value

Stream is implemented is between 1/2 and 1 then the probability of delivering the Value Stream value is always lower than that level.

Figure 7: Probability of Delivering Value Streams Value


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CONCLUSION

The paper introduced the PESEP™ framework qualitative and quantitative models. The PESEP™ model can help an enterprise determine whether or not it is doing the right things in terms of following a desired direction. It can also help an enterprise assert how well it is doing things right when it comes to enabling and sustaining the Business Capabilities and Business Processes that realize the desired enterprise direction.

The PESEP™ qualitative model organizes important business concepts such as Mission Statements, Business Objectives, Business Capabilities, and Business Processes into four Enterprise Pursuit types. The model stipulates that these Pursuit types can all occur at any one of the following four Enterprise Endeavor scopes: Strategic, Tactical, Operational, and Clerical. The PESEP™ qualitative model is therefore a two dimensional 4x4 matrix where each matrix cell represents a specific Enterprise Pursuit occurring at a given Enterprise Endeavor scope.

The paper presented how the four Pursuit types place performance expectation constraints upon each other. These constraints are the basis for the formulation of the PESEP™ quantitative model which describes how effectiveness and efficiency levels with which Pursuits meet their respective constraints can estimate the probability that a Mission Statement is fulfilled.

The paper described how to map Value Streams to the PESEP™ qualitative model. That mapping allows the PESEP™ quantitative model to estimate the probability that a Value Stream fully delivers its value based on the effectiveness and efficiency levels with which it is implemented.

The paper revealed that the PESEP™ quantitative model has interesting properties that involved the

famous Golden Ratio . Within the PESEP™

framework, 1/2 and 1/ are important threshold values for the effectiveness and efficiency levels with which Enterprise Pursuits constraints are met. When Value Streams are mapped to the PESEP™ framework, these threshold values have insightful impacts on the probability that Value Streams fully deliver their values.

ABOUT THE AUTHOR

Mr. Atiogbe Didier Koffi is a Business Architect and Business Systems Analyst with 20+ years of professional experience in the IT Industry. He is the founder of Pragmatic Cohesion Consulting LLC. His career has covered government and private sectors with services to the Department of Defense, the Department of Labor, leading biomedical research and development

organizations, leading pay-media companies, and Fortune 100 healthcare and retail organizations. His published work is listed in the ACM Enterprise Architecture Tech Pack. Mr. Koffi holds a Master of Science degree in Systems Engineering from Virginia Tech. He is an active member of the Association of Enterprise Architects (AEA), the Association for Computing Machinery (ACM), and the International Council on Systems Engineering (INCOSE). You can contact [email protected] for comments or questions.

REFERENCES

Drucker P., The effective executive – The definitive guide to getting the right things done, HarperCollins Publishers, New York, NY (2006)

Granger C.H., The hierarchy of objectives, Harvard Business Review, May issue (1964)

Harvard Business School Press, Improving business processes, Harvard Business Review Press, Boston, MA (2010)

Howell M.T., Critical success factors simplified, Taylord and Francis Group, LLC, New York, NY (2010)

Juran J. and Gryna F. (1993), Quality planning and analysis, McGraw Hill Inc.

Koffi A.D., A model for characterizing the influence of the Zachman framework’s enterprise architecture perspectives. Journal of Enterprise Architecture, volume 6, number 2, pp30-47 (2010)

Kurstedt H. A., Management systems theory, applications, and design. Virginia Tech ISE pp560-563 (2000)

Posamentier A.S. and Lehmann I., The glorious golden ratio, Prometheus Books, Amherst, NY (2012)

Raynus J., Improving business process performance – Gain agility, create value, and achieve success, Taylord & Francis Group, LLC, Boca Raton, FL (2011)

Schearer C., Everyday excellence – Creating better workplace through attitude, action, and appreciation, Quality Press, Milwaukee, WI (2006)

Schnapper M., Rollins S., Value-based metrics for improving results- An enterprise project management toolkit, J. Ross Publising, inc. ,Fort Lauderdale, FL (2006)

Talbot M., Make your mission statement work – Identify your organization’s values and live them every day, How To Books Ltd, Oxford, UK (2003)

The Open Group, Value Streams –Open Group guide, Berkshire, UK (2017)

The Open Group, Business Capabilities –Open Group guide, Berkshire, UK (2016)

mailto:[email protected]


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APPENDIX A: PROOF THAT WHEN 1-AU0 = 1/ , PF IS VERY CLOSE TO 50%

MP =

(

1/2 1/2 0 0

𝐴𝑈1/(2 + 𝐴𝑈1) 1/(2 + 𝐴𝑈1) 1/(2 + 𝐴𝑈1) 0

0 𝐴𝑈2/(2 + 𝐴𝑈2) 1/(2 + 𝐴𝑈2) 1/(2 + 𝐴𝑈2)

0 0 𝐴𝑈3/(1 + 𝐴𝑈3) 1/(1 + 𝐴𝑈3))

Let’s assume that all AU ratios have the same value α =AU0. MP then becomes:

MP =

(

1/2 1/2 0 0

𝛼/(2 + 𝛼) 1/(2 + 𝛼) 1/(2 + 𝛼) 0

0 𝛼/(2 + 𝛼) 1/(2 + 𝛼) 1/(2 + 𝛼)

0 0 𝛼/(1 + 𝛼) 1/(1 + 𝛼))

Let’s define A = 2+ 𝛼 .

Therefore 𝛼 = A-2 and 1+ 𝛼 = A-1. MP then becomes:

MP =

(

1/2 1/2 0 0

(𝐴 − 2)/𝐴 1/𝐴 1/𝐴 0

0 (𝐴 − 2)/𝐴 1/𝐴 1/𝐴

0 0 (𝐴 − 2)/(𝐴 − 1) 1/(𝐴 − 1))

MP steady state constraint distributions correspond to the following variables:

Π1 for Mission

Π2 for Objectives

Π3 for Capabilities

Π4 for Processes

The following set of equations describes the relationships between the steady state constraint distributions:

(1) Π1 = Π1

2+(𝐴−2)Π2

𝐴

(2) Π2 = Π1

2+Π2

A+(𝐴−2)Π3

𝐴

(3) 1 =Π1 + Π2 + Π3 + Π4

(4) Π4 = Π3

A+

Π4

𝐴−1

(4) implies that Π3 = 𝐴(𝐴−2)Π4

A−1

(2) implies that (I) Π2 = 𝐴

(A−1)(Π1

2+(𝐴−2)Π3

𝐴)

(1) implies that Π1 = 2(𝐴−2)Π2

𝐴

Substituting Π1 inside (I) gives:

Π2 = (𝐴 − 2)Π3

Π2 = 𝐴(𝐴−2)2

A−1Π4

Therefore: Π1 = 2(𝐴−2)3

A−1Π4

(3) implies that 1 = Π4 +𝐴(𝐴−2)

A−1Π4 +

𝐴(𝐴−2)2

A−1Π4 +

2(𝐴−2)3

A−1Π4

Therefore: 1

Π4= 1 +

𝐴(𝐴−2)

A−1+𝐴(𝐴−2)2

A−1+2(𝐴−2)3

A−1

When Pf = Π4= ½, the previous equation becomes:

1 =𝐴(𝐴−2)

A−1+𝐴(𝐴−2)2

A−1+2(𝐴−2)3

A−1

Since A = 2+ 𝛼 , substituting in the previous equation gives:

(E) 𝟑𝛂𝟑 + 𝟑𝛂𝟐 + 𝛂 = 𝟏

When α = 1-1/ where is the golden ratio 𝜑 =1+√5

2,

the left side of (E) equals 0.9868 which is very close to

1, therefore α = 1-1/ is a close approximate solution to (E). Since 1-α represents the efficiency or effectiveness with which the PESEP framework constraints are met, 1-

α = 1/ is a close approximation of the efficiency and effectiveness value for which Pf = 50%

Solving (E) 3𝛼3 + 3𝛼2 + 𝛼 = 1 has only one non-imaginary solution:

𝟏 − 𝛂 =𝟒 − √𝟏𝟎

𝟑

𝟑~𝟎. 𝟔𝟏𝟓~

𝟏

𝐏𝐟 =𝛂+𝟏

𝛂+𝟏+𝛂(𝛂+𝟏)(𝛂+𝟐)+𝟐𝛂𝟑

If 1-α = 0 then Pf = 1/5. If 1-α = 1 then Pf = 1

Technology

Value streams performance estimation and the PESEP framework