RMQSI Answers ForumCategory: Reliability ModelsPOF with scheduled maintenance
evelyn lui asked 12 years ago

hi,

I would like to check how to calculate POF of the following :

1) servo life 100hrs, mission 1 hr, discard time 80hrs
2) servo life 100hrs, mission 1 hr

Is the probability of failure the same for item (1) and (2) ? how can i factor in the concept of scheduled maintenance in the calculation of POF during the life of the item ?

thanks
evelyn

3 Answers
smorris answered 12 years ago

If these things wear out at the 100 hour point, then you calculate the probability of failure differently than if they are just subject to random, “freak” failures over time. If they wear out, say at 100 hours, with a standard deviation of 20 hours, then you use a “Z-table” to calculate the area under the normal distribution curve to the right of the mission time. For the normal distribution, the mean and standard deviation completely define the shape of the curve, and thus the area under the curve at different points to the right or left of the mean. For example, because the normal distribution is symmetrical about the mean, if the mean life is 100 hours and the mission time is also 100 hours, then there is a 50% probability of success (the area under the normal curve to the right of 100 hours) and there is a 50% chance of failure (the area under the normal curve to the left of the 100 hour point). You do not say what the standard deviation of the life estimate is, but if it is relatively small, say 20 hours, then for a mission of length of 1 hour, the reliability (area under the normal curve to the right of the 1 hour point) is basically most all of the area, or about 1.0. Since the probability of failure is 1-reliability, the probability of failure is about zero. If the servo is renewed to “as good as new” for the second one hour mission, then the reliability is the same as the first mission. However, if it is not “as good as new” for the second mission, then you would calculate the reliability as the area to the right of the 2 hour point. The probability of failure would be the area under the normal curve to the left of the 2 hour point.

Here is a link to a book on Goolgle that goes into more detail:
http://books.google.com/books?id=0Xu4NSnt7ygC&pg=PA241&lpg=PA241&dq=calculating+reliability+using+a+z-table&source=bl&ots=hnzrkNTHFA&sig=pdWAxa_zjFbfuuXO2KLps7ZZRwI&hl=en&ei=LYWfSez8Gde4tweKvKD-DA&sa=X&oi=book_result&resnum=1&ct=result#PPA241,M1

Also, search Google for “Z-Table” to find tables and/or on-line calculators for performing these calculations.

evelyn lui answered 12 years ago

thanks very much !

Please advise me how can i get the standard deviation of the life estimate of the servo.

rgds
evelyn

smorris answered 12 years ago

Procedures for calculating standard deviation can be found in most all probability and statistics text books. Wikipedia also has a detailed explanation and example calculations, which can be found at http://en.wikipedia.org/wiki/Standard_deviation