Hardy–Littlewood inequality

Operational Availability is a management concept that evaluates the following.

• Diagnostic down time
• Criticality
• Fault isolation down time
• Logistics delay down time
• Corrective maintenance down time

Any failed item that is not corrected will induce operational failure. $A_o$ is used to evaluate that risk. Operational failure is unacceptable in any situation where the following can occur.

• Capitol equipment loss
• Injury or loss of life
• Sustained failure to accomplish mission

History

Aircraft systems, ship systems, missile systems, and space systems have a large number of failure modes that must be addressed with limited resources.

Formal reliability modeling during development is required to prioritize resource allocation before operation begins. Estimated failure rates and logistics delay are used to identify the number of forward positioned spare parts required to avoid excessive down time. This is also used to justify the expense associated with redundancy.

Formal availability measurement is used during operation to prioritize management decisions involving upgrade resource allocation, manpower allocation, and spare parts planning.

Principle

Operational availability is used to evaluate the following performance characteristic.

$A_o=0.9\approx 877hoursdowntimeperyear$

$A_o=0.99\approx 87hoursdowntimeperyear$

$A_o=0.999\approx 8hoursdowntimeperyear$

$A_o=0.9999\approx 52minutesdowntimeperyear$

$A_o=0.99999\approx 5minutesdowntimeperyear$

The following data is collected for maintenance actions while in operation to prioritize corrective funding.

• Diagnostic down time is required to identify the amount of time spent perform maintenance when fault reporting does not support condition-based maintenance.
• Criticality identifies level of risk associated with loss of mission, injury or loss of life, and capitol equipment.
• Fault isolation down time is required to identify the amount of time spent locating a failure.
• Logistics delay down time is required to identify the amount of time required to obtain replacement parts or software.
• Corrective maintenance down time is required to identify the amount of time required to install and reconfigure replacement parts and software.

This data is applied to the reliability block diagram to evaluate individual availability reduction contributions using the following formulas.

$A_o^D=\left(\frac{TotalTime}{TotalTime+DiagnosticDownTime}\right)$

$A_o^{FI}=\left(\frac{TotalTime}{TotalTime+FaultIsolationDownTime}\right)$

$A_o^L=\left(\frac{TotalTime}{TotalTime+LogisticsDownTime}\right)$

$A_o^C=\left(\frac{TotalTime}{TotalTime+CorrectiveDownTime}\right)$

Redundant items do not contribute to availability reduction unless all of the redundant components fail simultaneously.

Operational Availability is the overall availability considering each of these contributions.

$A_o=A_o^D\times A_o^{FI}\times A_o^L\times A_o^C$

See also

• Active redundancy
• Operational availability
• Reliability block diagram

References

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