Filling a tank with a pump. Tank is straight-walled (constant capacitance). Flow is laminar (linear flow relation).    Energy quantities have been added.
Filling a tank with a pump. Tank is straight-walled (constant capacitance). Flow is laminar (linear flow relation).

Energy quantities have been added.
This model keeps track of the formal development of Timescale calculus available at  http://mds.marshall.edu/cgi/viewcontent.cgi?article=1036&context=etd&sei-redir=1&referer=http%3A%2F%2Fwww.google.com%2Furl%3Fsa%3Dt%26rct%3Dj%26q%3Dtime%2520scale%2520calculus%26source%3Dweb%26cd%3D8%26s
This model keeps track of the formal development of Timescale calculus available at http://mds.marshall.edu/cgi/viewcontent.cgi?article=1036&context=etd&sei-redir=1&referer=http%3A%2F%2Fwww.google.com%2Furl%3Fsa%3Dt%26rct%3Dj%26q%3Dtime%2520scale%2520calculus%26source%3Dweb%26cd%3D8%26sqi%3D2%26ved%3D0CFgQFjAH%26url%3Dhttp%253A%252F%252Fmds.marshall.edu%252Fcgi%252Fviewcontent.cgi%253Farticle%253D1036%2526context%253Detd%26ei%3Dd5peUOTkOan2igLrqICoDQ%26usg%3DAFQjCNH3g65pFJ4LV38xiG7FIfRexA9uiA .

The idea is to use infinitesimals to extend Geometric and Grassmann Algebra to better flush out the details of the interpretation of an unbound vector as a "massless point at the point at infinity". Essentially, the Grassmann and Geomeric Algebra is being generalized to admit multiplication of vectors by infinitesimals, not just real numbers. Doing so allows one to define a concept of a point approaching infinity without having to use limits. This is a work in progress, and so some of the ideas in the above description will likely change as more is descovered as the research unfolds.
Simulation of MTBF with controls   F(t) = 1 - e ^ -λt   Where    • F(t) is the probability of failure    • λ is the failure rate in 1/time unit (1/h, for example)   • t is the observed service life (h, for example)  The inverse curve is the trust time On the right the increase in failures brings its
Simulation of MTBF with controls

F(t) = 1 - e ^ -λt 
Where  
• F(t) is the probability of failure  
• λ is the failure rate in 1/time unit (1/h, for example) 
• t is the observed service life (h, for example)

The inverse curve is the trust time
On the right the increase in failures brings its inverse which is loss of trust and move into suspicion and lack of confidence.
This can be seen in strategic social applications with those who put economy before providing the priorities of the basic living infrastructures for all.

This applies to policies and strategic decisions as well as physical equipment.
A) Equipment wears out through friction and preventive maintenance can increase the useful lifetime, 
B) Policies/working practices/guidelines have to be updated to reflect changes in the external environment and eventually be replaced when for instance a population rises too large (constitutional changes are required to keep pace with evolution, e.g. the concepts of the ancient Greeks, 3000 years ago, who based their thoughts on a small population cannot be applied in 2013 except where populations can be contained into productive working communities with balanced profit and loss centers to ensure sustainability)

Early Life
If we follow the slope from the leftmost start to where it begins to flatten out this can be considered the first period. The first period is characterized by a decreasing failure rate. It is what occurs during the “early life” of a population of units. The weaker units fail leaving a population that is more rigorous.

Useful Life
The next period is the flat bottom portion of the graph. It is called the “useful life” period. Failures occur more in a random sequence during this time. It is difficult to predict which failure mode will occur, but the rate of failures is predictable. Notice the constant slope.  

Wearout
The third period begins at the point where the slope begins to increase and extends to the rightmost end of the graph. This is what happens when units become old and begin to fail at an increasing rate. It is called the “wearout” period. 
Simulation der Umlaufbahn der Erde um die Sonne
Simulation der Umlaufbahn der Erde um die Sonne
  b) 102,3 s, 2197,6 m   c) richtingscoefficiënt neemt toe, dus snelheid neemt toe, wat betekent dat omstandigheden veranderen. Dit is naast het dalen van rho en verandering van het gewicht, dus Fz  d) als er geen brandstof wordt verbruikt, werkt de motor niet
b) 102,3 s, 2197,6 m
c) richtingscoefficiënt neemt toe, dus snelheid neemt toe, wat betekent dat omstandigheden veranderen. Dit is naast het dalen van rho en verandering van het gewicht, dus Fz
d) als er geen brandstof wordt verbruikt, werkt de motor niet

A PID control loop for a simple linear system Some stochasticity in the throttle and sensor ​
A PID control loop for a simple linear system
Some stochasticity in the throttle and sensor ​
Simulation of MTBF with controls   F(t) = 1 - e ^ -λt   Where    • F(t) is the probability of failure    • λ is the failure rate in 1/time unit (1/h, for example)   • t is the observed service life (h, for example)  The inverse curve is the trust time On the right the increase in failures brings its
Simulation of MTBF with controls

F(t) = 1 - e ^ -λt 
Where  
• F(t) is the probability of failure  
• λ is the failure rate in 1/time unit (1/h, for example) 
• t is the observed service life (h, for example)

The inverse curve is the trust time
On the right the increase in failures brings its inverse which is loss of trust and move into suspicion and lack of confidence.
This can be seen in strategic social applications with those who put economy before providing the priorities of the basic living infrastructures for all.

This applies to policies and strategic decisions as well as physical equipment.
A) Equipment wears out through friction and preventive maintenance can increase the useful lifetime, 
B) Policies/working practices/guidelines have to be updated to reflect changes in the external environment and eventually be replaced when for instance a population rises too large (constitutional changes are required to keep pace with evolution, e.g. the concepts of the ancient Greeks, 3000 years ago, who based their thoughts on a small population cannot be applied in 2013 except where populations can be contained into productive working communities with balanced profit and loss centers to ensure sustainability)

Early Life
If we follow the slope from the leftmost start to where it begins to flatten out this can be considered the first period. The first period is characterized by a decreasing failure rate. It is what occurs during the “early life” of a population of units. The weaker units fail leaving a population that is more rigorous.

Useful Life
The next period is the flat bottom portion of the graph. It is called the “useful life” period. Failures occur more in a random sequence during this time. It is difficult to predict which failure mode will occur, but the rate of failures is predictable. Notice the constant slope.  

Wearout
The third period begins at the point where the slope begins to increase and extends to the rightmost end of the graph. This is what happens when units become old and begin to fail at an increasing rate. It is called the “wearout” period.