I have a challenging situation to determine what a 1% improvement would mean from a value perspective and I need help from an EE Pro who is very mathematically oriented.

Here is the Scenario: We have a piece of complex equipment that is used in remote locations. We have a 95% reliability/availability rating on this Asset. What we are considering is what would be the incremental value in going to a 96% or a 97% reliability level? For purposes of solving this, consider each field asset costs $1M and requires $30K / yr. for maintenance. The intangible value of being "more competitive" in our market is certainly an intangible and hard to measure. But for actual value recognition (and add any assumptions you would like that can explain how to approach this mathematical problem), what formula should be used or explanation of considerations should be put forth.

Your help and assistance is appreciated. Thank you in advance,

B.

https://en.wikipedia.org/wiki/Bathtub_curve

2. What model are these percentages based on?

The bathtub effect noted earlier assumes an expected lifespan where the failure rate increases significantly, and whose failure rate is constant between the early high failure rate and end of lifetime.

For the case where we assume that the failure rate is constant (and hence the availability rate is constant), then IIRC, we are dealing with a Poisson distribution. "Can be used to evaluate the probability of an isolated event occurring a specific number of times in a given time interval, e.g. # of faults, # of lightning strokes time interval"

http://www.engr.usask.ca/classes/EE/445/notes/notes67d.pdf

Here is a chart based on annualized availability rates:

https://technet.microsoft.com/en-us/library/aa996704(v=exchg.65).aspx

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The link gives a formula for computing downtime assuming 24 x 7 and 8 x 7 hour usage.Assuming 24 x 7 usage, Let Pa = Availability Probability; T = Total Time in use in a year; D = downtime in a year

Pa = (T - D)/T = 1 - D/T

Solving for D:

D = (1 - Pa) * T

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