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73). λ = 1/MTTF (3-3) For the data set of Table 3-2, it can be seen that nineteen (19) failures are listed. Given that the data started with twenty-six (26) units operating, seven units are still operating successfully at the end of the year. The MTTF for those seven units operating successfully at one year is not known. If it is conservatively assumed that all seven will operate for at least one more hour, then an MTTF of 8761 could be used for those seven units. Given those numbers, the average value for time to failure (MTTF) equals 6479 hours.

Some take this data and do an incorrect calculation. The operational hours are estimated by saying that 26 units run for one year – 26 × 8760 = 227,760 hours. book Page 38 Thursday, March 31, 2005 10:39 PM 38 Equipment Failure The problem with this method is that it implicitly assumes that all units fail at the very end of the time period. This is terribly optimistic and results in an incorrect low estimate of the failure rate. One could assume that all failures occur in the first hour of the time period.

EXAMPLE 4-6 Problem: The plant maintenance team has made the following estimates: Average time to detect that a failure has occurred in the basic process control system = 18 hours. Average time to obtain spare parts = 24 hours. Average time to make the repair and test the system = 8 hours. What is the Mean Time To Restore? What is the restore rate? Solution: Assuming these are sequential operations, the MTTR is the sum of the estimated times. MTTR equals 50 hours. 02 restores per hour. Mean Time Between Failures (MTBF)—MTBF is defined as the average time period of a failure/repair cycle.

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New Methods for Quantum Mechanical Reaction Dynamics [thesis]

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