on the evolution of solution spaces triggered by emerging technologies
TRANSCRIPT
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
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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of requirements engineering: stakeholder needs, system requirements, solution spaces, and requirements’ qualities,” unpublished.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of requirements engineering: stakeholder needs, system requirements, solution spaces, and requirements’ qualities,” unpublished.
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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?
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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…
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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.
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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?