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Sterility assurance means that repeated biological testing consistently produces negative results.

The level of disinfection-sterilization varies according to the appropriate use of the item being disinfected or sterilized
A Log- 3 is considered suitable for topically applied "sterile" products. 
Implantables require a SAL of Log-6.  The level that your sterilizer must produce to be called "sterile,"  is Log-6 or a one microbe per million items probability.
Normal saturated steam processing produces one  log of reduction (90% "kill") in each 1 to 2 minutes at 15 Lbs. psi. and 250F.  
"Sterility" under the conditions of saturated steam can be reached in about 12 to 15 minutes at this time-temp-pressure.
From this you can see the importance of cleaning to reduce the original microbial load so that you can be sure of this SAL of -6.  If you started instead with 10 billion microbes ( a quantity of 1010) you can see that to reach a probability of 1 in a million items (10-6) will require a longer cycle time or higher temperatures. (Sterilization Technology)

The longer the time the lower the probability of survival. The higher the temp-pressure the shorter the time to reach a specific level.

It is the nature of water (suffciient in quantity) that in an enclosed container subjected to heat it will reach 15 Lbs psi at 250F.  If you know the temperature the pressure is  known with or without a meter.  If you know only the pressure the temperature is also known.

Overkill is a term referring to the additional time a sterilizer operates beyond the time necessary to reach the kill level of sterilization.  

The common bio-reference is the bacterial spore G. Stearothermophilus which is used most often for biological monitoring of steam sterilization, which is usually in your BI  that you use for biological testing.  

Normally two Biological Indicators (BIs) that bear the same lot control number are used. One is processed in the sterilizer and the other is not.  The non-sterilized BI is called the control. Both are then cultured in an incubator.  

If your sterilizer is working properly the processed BI that you sterilized will not grow (usually indicated by not changing color) and the unprocessed control BI will grow (usually indicated by a change in color).
Normal sterilization of the BI is usually achieved in 6 minutes with the rest of the time considered "overkill."  A holding time of 15 to 20 minutes at temperature and pressure is considered adequate  "overkill."  It would be un-reasonable to require or use a longer time period without sterility-related justifiable cause.

Sterility assurance means that repeated biological testing consistently produces negative results.