CSER 2015 March 18-19, 2015 1

On the Evolution of Solution Spaces Triggered by Emerging Technologies

ByAlejandro Salado and Roshanak Nilchiani

13th Annual Conference on Systems Engineering Research (CSER)

March 18, 2015

Stevens Institute of TechnologyHoboken, NJ

www.stevens.edu/sse/CSER2015org

CSER 2015 March 18-19, 2015 2

A year ago… Put your logo here on the master slide

CSER 2015 March 18-19, 2015 3

According to literature…

Adding a new requirement results in…

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A. Salado, R. Nilchiani, and D. Verma, “A formal theory of requirements engineering: stakeholder needs, system requirements, solution spaces, and requirements’ qualities,” unpublished.

Expand solution space

Open new regions of

solution space

Enable better solutions

More cost

Less solutions

CSER 2015 March 18-19, 2015 4

Two theorems… Put your logo here on the master slide

Theorem 13: A requirement cannot expand the solution space.

Proof: Using the inclusion of intersection theorem in set theory, then .QED.

Theorem 14: A system requirement reduces the solution space.Proof: Using Definition 15, system requirements do not overlap and are applicable to the system. Consequently, the inclusion of intersection theorem in set theory can be reworded as , i.e., since B does not overlap A and A does not

overlap B, or in other words and , then cannot be equal to A or B. Consequently, adding a system requirement reduces the compliant space.

QED.

A. Salado, R. Nilchiani, and D. Verma, “A formal theory of requirements engineering: stakeholder needs, system requirements, solution spaces, and requirements’ qualities,” unpublished.

CSER 2015 March 18-19, 2015 5

Question from the audience

What if… you add a requirement to use a technology that did not exist at the time of writing the initial set of requirements?

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Would the solution space not be expanded then?

NO

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What is a solution space? Put your logo here on the master slide

DSYSTEMS VALID SYSTEMS

COMPLIANT SYSTEMSDESIGNED/EXPLORED

SYSTEMS

CSER 2015 March 18-19, 2015 7

What is a solution space? Put your logo here on the master slide

DSYSTEMS VALID SPACE

COMPLIANT SPACEDESIGN SPACE

A. Salado and R. Nilchiani, “A mathematical justification for increasing the size of the solution space to improve the probabilities of designing compliant and affordable systems,” unpublished.

CSER 2015 March 18-19, 2015 8

Back to the original question Put your logo here on the master slide

TIME

What if… you add a requirement to use a technology that did not exist at the time of writing the initial set of requirements?

CSER 2015 March 18-19, 2015 9

What can happen? Put your logo here on the master slide

New technology New

stakeholder need

New requirement

13

2 4

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Case 1: T/-/- Put your logo here on the master slide

Theorem 1: An emerging technology that is able to support satisfaction of a given set of stakeholder needs, but that does not create new stakeholder needs for those stakeholders, increases the size of the valid space.

Proof: Using Definition 12 in [3], 𝑉𝑆𝑆𝑁𝑖ሺ𝑇1ሻ= ൛𝑍:𝑍 𝜖 𝐷𝑆𝑌𝑆𝑇𝐸𝑀𝑆𝑇1;𝑣𝑎𝑙ሺ𝑍,𝑆𝑁𝑖ሻ= 1ൟ= ൛𝑍:𝑍 𝜖 𝐷𝑆𝑌𝑆𝑇𝐸𝑀𝑆𝑇0;𝑣𝑎𝑙ሺ𝑍,𝑆𝑁𝑖ሻ= 1ൟ∪൛𝑍:𝑍 𝜖 ∆𝑆𝑌𝑆𝑇𝑇1𝑇0;𝑣𝑎𝑙ሺ𝑍,𝑆𝑁𝑖ሻ= 1ൟ= 𝑉𝑆𝑆𝑁𝑖ሺ𝑇0ሻ+൛𝑍:𝑍 𝜖 ∆𝑆𝑌𝑆𝑇𝑇1𝑇0;𝑣𝑎𝑙ሺ𝑍,𝑆𝑁𝑖ሻ= 1ൟ⊃ 𝑉𝑆𝑆𝑁𝑖ሺ𝑇0ሻ QED. Theorem 2: An emerging technology that is able to support satisfaction of a given set of stakeholder needs, but

that does not create new stakeholder needs for those stakeholders, increases the size of the compliant space if new system requirements are not added to the requirement set. Proof: Using Definition 12 in [3], 𝐶𝑆𝑅𝑖ሺ𝑇1ሻ= ൛𝑍:𝑍 𝜖 𝐷𝑆𝑌𝑆𝑇𝐸𝑀𝑆𝑇1;𝑣𝑒𝑟ሺ𝑍,𝑅𝑖ሻ= 1ൟ= ൛𝑍:𝑍 𝜖 𝐷𝑆𝑌𝑆𝑇𝐸𝑀𝑆𝑇0;𝑣𝑒𝑟ሺ𝑍,𝑅𝑖ሻ= 1ൟ∪൛𝑍:𝑍 𝜖 ∆𝑆𝑌𝑆𝑇𝑇1𝑇0;𝑣𝑒𝑟ሺ𝑍,𝑅𝑖ሻ= 1ൟ= 𝐶𝑆𝑆𝑁𝑖ሺ𝑇0ሻ+൛𝑍:𝑍 𝜖 ∆𝑆𝑌𝑆𝑇𝑇1𝑇0;𝑣𝑒𝑟ሺ𝑍,𝑅𝑖ሻ= 1ൟ⊃ 𝐶𝑆𝑅𝑖ሺ𝑇0ሻ QED

A FORMAL PROOF…

CSER 2015 March 18-19, 2015 11

A practical, simple example Put your logo here on the master slide

STAKEHOLDER NEEDS

SYSTEM REQUIREMENTS

TECHNOLOGIES

n1 - Read a book during night at home

n2 - Get a warm feeling.

r1 - Provide more than 1000 lux.

r2 - Provide warm temperature light.

T1 – Standard bulb.

T2 – Low consumption white bulb.

T3 – Low consumption yellow bulb.

CSER 2015 March 18-19, 2015 12

A practical, simple example Put your logo here on the master slide

Technology n1 n2 r1 r2

Standard bulb Y Y Y Y Y Y

Low consumption white bulb Y N Y N N N

Low consumption yellow bulb Y Y Y Y Y Y

2 2

n1 - Read a book during night at homen2 - Get a warm feeling.

r1 - Provide more than 1000 lux.r2 - Provide warm temperature light.

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Case 1: T/-/- Put your logo here on the master slide

Technology n1 n2 r1 r2

Standard bulb Y Y Y Y Y Y

Low consumption white bulb Y N Y N N N

Low consumption yellow bulb Y Y Y Y Y Y

Yellow LED Y Y Y Y Y Y

Green LED Y N Y N N N

Old (T0) 2 2

New (T1) 3 3

n1 - Read a book during night at homen2 - Get a warm feeling.

r1 - Provide more than 1000 lux.r2 - Provide warm temperature light.

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Case 2: T/-/r Put your logo here on the master slide

Technology n1 n2 r1 r2 r3

Standard bulb Y Y Y Y N Y N

Low consumption white bulb Y N Y N N N N

Low consumption yellow bulb Y Y Y Y N Y N

Yellow LED Y Y Y Y Y Y Y

Green LED Y N Y N Y N N

Old (T0) 2 2

New (T1) 3 1

n1 - Read a book during night at homen2 - Get a warm feeling.

r1 - Provide more than 1000 lux.r2 - Provide warm temperature light.

r3 - Use LED technology.

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Case 3: T/n/- Put your logo here on the master slide

Technology n1 n2 n3 r1 r2

Standard bulb Y Y N Y Y N Y

Low consumption white bulb Y N N Y N N N

Low consumption yellow bulb Y Y N Y Y N Y

Yellow LED Y Y N Y Y N Y

Green LED Y N N Y N N N

Color adaptive based on sensing Y Y Y Y N Y N

Old (T0) 3 3

New (T1) 1 3

n1 - Read a book during night at homen2 - Get a warm feeling.

n3 - Adapt the color temperature of the light according to the feelings of a reader.

r1 - Provide more than 1000 lux.r2 - Provide warm temperature light.

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Case 4: T/n/r Put your logo here on the master slide

Technology n1 n2 n3 r1 r2 r3

Standard bulb Y Y N Y - N N N

Low consumption white bulb Y N N Y - N N N

Low consumption yellow bulb Y Y N Y - N N N

Yellow LED Y Y N Y - N N N

Green LED Y N N Y - N N N

Color adaptive based on sensing Y Y Y Y - Y Y Y

Old (T0) 3 3

New (T1) 1 1

n1 - Read a book during night at homen2 - Get a warm feeling.

n3 - Adapt the color temperature of the light according to the feelings of a reader.

r1 - Provide more than 1000 lux.r2 - Provide warm temperature light. (deleted)

r3 - Adapt temperature to reader emotion.

CSER 2015 March 18-19, 2015 17

Wrapping up Put your logo here on the master slide

If a NEW technology does NOT change the stakeholder needs……then adding a requirement reduces the compliant space

FORMAL PROOF + PRACTICAL EXAMPLE

What about obsolescence?