On the Evolution of Solution Spaces Triggered by Emerging Technologies
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The document discusses the relationship between emerging technologies and solution spaces in systems engineering. It presents two theorems indicating that adding system requirements reduces the solution space, and introduces practical cases to illustrate how technologies can expand valid and compliant spaces without altering stakeholder needs. The research emphasizes the importance of understanding solution spaces to achieve compliant and cost-effective system designs.
![CSER 2015 March 18-19, 2015 10
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],
𝑉𝑆𝑆𝑁 𝑖
𝑇1 = 𝑍: 𝑍 𝜖 𝐷𝑆𝑌𝑆𝑇𝐸𝑀𝑆 𝑇1
; 𝑣𝑎𝑙 𝑍, 𝑆𝑁𝑖 = 1
= 𝑍: 𝑍 𝜖 𝐷𝑆𝑌𝑆𝑇𝐸𝑀𝑆 𝑇0
; 𝑣𝑎𝑙 𝑍, 𝑆𝑁𝑖 = 1 ∪ 𝑍: 𝑍 𝜖 ∆𝑆𝑌𝑆𝑇𝑇1 𝑇0
; 𝑣𝑎𝑙 𝑍, 𝑆𝑁𝑖 = 1
= 𝑉𝑆𝑆𝑁 𝑖
𝑇0 + 𝑍: 𝑍 𝜖 ∆𝑆𝑌𝑆𝑇𝑇1 𝑇0
; 𝑣𝑎𝑙 𝑍, 𝑆𝑁𝑖 = 1 ⊃ 𝑉𝑆𝑆𝑁 𝑖
𝑇0
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],
𝐶𝑆 𝑅 𝑖
𝑇1 = 𝑍: 𝑍 𝜖 𝐷𝑆𝑌𝑆𝑇𝐸𝑀𝑆 𝑇1
; 𝑣𝑒𝑟 𝑍, 𝑅𝑖 = 1
= 𝑍: 𝑍 𝜖 𝐷𝑆𝑌𝑆𝑇𝐸𝑀𝑆 𝑇0
; 𝑣𝑒𝑟 𝑍, 𝑅𝑖 = 1 ∪ 𝑍: 𝑍 𝜖 ∆𝑆𝑌𝑆𝑇𝑇1 𝑇0
; 𝑣𝑒𝑟 𝑍, 𝑅𝑖 = 1
= 𝐶𝑆𝑆𝑁 𝑖
𝑇0 + 𝑍: 𝑍 𝜖 ∆𝑆𝑌𝑆𝑇𝑇1 𝑇0
; 𝑣𝑒𝑟 𝑍, 𝑅𝑖 = 1 ⊃ 𝐶𝑆 𝑅 𝑖
𝑇0
QED
A FORMAL PROOF…](https://image.slidesharecdn.com/cser2015paper74presentation-151102132740-lva1-app6891/85/On-the-Evolution-of-Solution-Spaces-Triggered-by-Emerging-Technologies-10-320.jpg)
On the Evolution of Solution Spaces Triggered by Emerging Technologies
- 1. CSER 2015 March 18-19, 2015 1 On the Evolution of Solution Spaces Triggered by Emerging Technologies By Alejandro Salado and Roshanak Nilchiani 13th Annual Conference on Systems Engineering Research (CSER) March 18, 2015 Stevens Institute of Technology Hoboken, NJ www.stevens.edu/sse/CSER2015org
- 2. CSER 2015 March 18-19, 2015 2 A year ago… Put your logo here on the master slide
- 3. CSER 2015 March 18-19, 2015 3 According to literature… Adding a new requirement results in… Put your logo here on the master slide 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
- 4. 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 𝐴 ∩ 𝐵 ⊆ 𝐴 ∧ 𝐵, then 𝐶𝑆𝑆𝐸𝑇 ⊆ 𝐶𝑆𝑆𝐸𝑇 . 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 𝐴 ∩ 𝐵 ⊂ 𝐴 ∧ 𝐵, i.e., since B does not overlap A and A does not overlap B, or in other words 𝐴 ⊄ 𝐵 and 𝐵 ⊄ 𝐴, then 𝐴 ∩ 𝐵 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.
- 5. 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? Put your logo here on the master slide Would the solution space not be expanded then? NO
- 6. CSER 2015 March 18-19, 2015 6 What is a solution space? Put your logo here on the master slide DSYSTEMS VALID SYSTEMS COMPLIANT SYSTEMSDESIGNED/EXPLORED SYSTEMS
- 7. 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.
- 8. 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?
- 9. 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 1 3 2 4
- 10. CSER 2015 March 18-19, 2015 10 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], 𝑉𝑆𝑆𝑁 𝑖 𝑇1 = 𝑍: 𝑍 𝜖 𝐷𝑆𝑌𝑆𝑇𝐸𝑀𝑆 𝑇1 ; 𝑣𝑎𝑙 𝑍, 𝑆𝑁𝑖 = 1 = 𝑍: 𝑍 𝜖 𝐷𝑆𝑌𝑆𝑇𝐸𝑀𝑆 𝑇0 ; 𝑣𝑎𝑙 𝑍, 𝑆𝑁𝑖 = 1 ∪ 𝑍: 𝑍 𝜖 ∆𝑆𝑌𝑆𝑇𝑇1 𝑇0 ; 𝑣𝑎𝑙 𝑍, 𝑆𝑁𝑖 = 1 = 𝑉𝑆𝑆𝑁 𝑖 𝑇0 + 𝑍: 𝑍 𝜖 ∆𝑆𝑌𝑆𝑇𝑇1 𝑇0 ; 𝑣𝑎𝑙 𝑍, 𝑆𝑁𝑖 = 1 ⊃ 𝑉𝑆𝑆𝑁 𝑖 𝑇0 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], 𝐶𝑆 𝑅 𝑖 𝑇1 = 𝑍: 𝑍 𝜖 𝐷𝑆𝑌𝑆𝑇𝐸𝑀𝑆 𝑇1 ; 𝑣𝑒𝑟 𝑍, 𝑅𝑖 = 1 = 𝑍: 𝑍 𝜖 𝐷𝑆𝑌𝑆𝑇𝐸𝑀𝑆 𝑇0 ; 𝑣𝑒𝑟 𝑍, 𝑅𝑖 = 1 ∪ 𝑍: 𝑍 𝜖 ∆𝑆𝑌𝑆𝑇𝑇1 𝑇0 ; 𝑣𝑒𝑟 𝑍, 𝑅𝑖 = 1 = 𝐶𝑆𝑆𝑁 𝑖 𝑇0 + 𝑍: 𝑍 𝜖 ∆𝑆𝑌𝑆𝑇𝑇1 𝑇0 ; 𝑣𝑒𝑟 𝑍, 𝑅𝑖 = 1 ⊃ 𝐶𝑆 𝑅 𝑖 𝑇0 QED A FORMAL PROOF…
- 11. 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.
- 12. CSER 2015 March 18-19, 2015 12 A practical, simple example Put your logo here on the master slide Technology n1 n2 r1 r2 #𝑉𝑆𝑆𝑁 𝑖 #𝐶𝑆 𝑅 𝑖 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 home n2 - Get a warm feeling. r1 - Provide more than 1000 lux. r2 - Provide warm temperature light.
- 13. CSER 2015 March 18-19, 2015 13 Case 1: T/-/- Put your logo here on the master slide Technology n1 n2 r1 r2 #𝑉𝑆𝑆𝑁 𝑖 #𝐶𝑆 𝑅 𝑖 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 home n2 - Get a warm feeling. r1 - Provide more than 1000 lux. r2 - Provide warm temperature light.
- 14. CSER 2015 March 18-19, 2015 14 Case 2: T/-/r Put your logo here on the master slide Technology n1 n2 r1 r2 r3 #𝑉𝑆𝑆𝑁 𝑖 #𝐶𝑆 𝑅 𝑖 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 home n2 - Get a warm feeling. r1 - Provide more than 1000 lux. r2 - Provide warm temperature light. r3 - Use LED technology.
- 15. CSER 2015 March 18-19, 2015 15 Case 3: T/n/- Put your logo here on the master slide Technology n1 n2 n3 r1 r2 #𝑉𝑆𝑆𝑁 𝑖 #𝐶𝑆 𝑅 𝑖 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 home n2 - 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.
- 16. CSER 2015 March 18-19, 2015 16 Case 4: T/n/r Put your logo here on the master slide Technology n1 n2 n3 r1 r2 r3 #𝑉𝑆𝑆𝑁 𝑖 #𝐶𝑆 𝑅 𝑖 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 home n2 - 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.
- 17. 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?