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 LifeIf 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 LifeThe 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.
WearoutThe 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.
![Simple model to illustrate oyster growth based on primary production of Phytoplankton as a state variable, forced by light and nutrients, running for a yearly period. Phytoplankton growth based on on Steele's and Michaelis-Menten equations), where: Primary Production=(([Pmax]*[I]/[Iopt]*exp(1-[I]](https://insightmakercloud-files.storage.googleapis.com/bb2c988c-c937-4a62-8260-24725a965796/images/cover.jpg?X-Goog-Algorithm=GOOG4-RSA-SHA256&X-Goog-Credential=insightmakercloud-file-access%40insightmakercloud.iam.gserviceaccount.com%2F20251221%2Fauto%2Fstorage%2Fgoog4_request&X-Goog-Date=20251221T104849Z&X-Goog-Expires=3600&X-Goog-SignedHeaders=host&X-Goog-Signature=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)
