Sterility is a probability, not an absolute.
Though "Sterilization" is meant to convey an absolute (the destruction or inactivation of all microorganisms - either something is sterile or it is not)

     A. It cannot be known with whether all microorganisms have been killed.
          1. We may not be aware of the existence of some.
          2. We may not actually be culturing for all microorganisms.

     B. We cannot prove the existence of a negative absolute.

Therefore the approach is to employ a "process" definition. 

Sterilization is the process by which living organisms are removed or killed to the extent that they are no longer detectable in standard culture media in which they had previously proliferated.   (Block, 4th Edition, Dis. Ster. Pres.)

Both the process and the methods used to test are equally important. In actuality it is a probability and not an absolute.

Sterility measurement is expressed as a probability.
Sterility is considered achieved when it reaches what is called a "log of minus 6 of reduction" rather than as an absolute and is called the "Sterility Assurance Level" (SAL) which can be quantitatively (in numbers) expressed.  Let's see what this means.
Each log represents a 90% reduction of microbes.
Imagine a glass full of water. Assume for a moment the water represents the microbes and it equals one million microbes (estimated to be on your product). We would call this "level  6", or a "Log of 6" (this is what a log of 6 will mean for our example: equals 1 million, the starting point). 

If we empty 90% of the water it leaves 10% of the water.  Our original one million (1,000,000 microbes - our water) minus 90% is 100,000 microbes left, and since we are reducing we go down the logs, as it were, and now have a "log of 5" (or, now only 100,000 microbes-90% have been killed or inactivated). 

We proceed to empty 90% of what is left over in the glass and we get a "log of 4" (100,000 microbes left over,  minus 90% (90,000 microbes), equals now 10,000 microbes left) and so forth.

If we do this a total of 6 times we have a "log of 0", which would be one microbe left.  If we now continue and want to empty 90% of what's left (our 1 microbe) of course we can't empty 90% of just one microbe.

But we can think of probability like this: 
If we had one item we were sterilizing we would at this level have one microbe on that item.  Suppose though there were ten items we were sterilizing and we did our log reductions up to this point. Since there is 1 microbe left, we can say we have one microbe among the ten items after the 6 logs of reduction.  This level would be (minus one)  Log of -1,  meaning one microbe per 10 items. A log of reduction to -2 therefore means would mean the same thing as having one microbe per 100 items, etc. A log of -6 means that only one microbe might survive on a million items presuming that the original microbial load was one million microbes or less. This is what is called a  Sterility Assurance Level (SAL) 10^-6 =  One microbe per million items. That's it.
This is the level that your sterilizer must produce to be acceptable as "sterile,"  a log of (minus) -6.
A log of - 3 is considered suitable for topically applied "sterile" products.  Implantables require a SAL of -6 Log.  The level of disinfection-sterilization varies according to the appropriate use of the item.
Normal saturated steam processing produces one  log of reduction (90% "kill") in about 1 to 2 minutes at 15 Lbs. psi. and 250°F.
"Sterility" under the conditions of saturated steam can be reached in about 12 to 15 minutes.
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 per minute time or higher temperatures. (Sterilization Technology)

To be Assured of your sterility, thorough cleaning is required.
Items should be cleaned, dried and placed into sterilization pouches. Though air is a source of microbes to possibly contaminate items after washing and before bagging, even hospital air has been measured to only an estimated load of 128 microbes per cubic meter, so air is not of great concern unless you live in areas that have a heavy soil particle air count.  Soils are the predominant source of spores.

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 reference is the bacterial spore G. Stearolthermphilus which is used for biological monitoring of the sterilization process, which is usually in your spore test strips that you send to the lab for testing.  Test kits normally contain two strips or one ampoule. One is processed by you in the sterilizer and the other is not. Both are sent back to lab where they are cultured. Hopefully the processed strip that you sterilized will not grow and the unprocessed strip that you did not sterilize will grow. 
Normal sterilization of the BI can usually be 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 extend this time without known and good reason. In our non-hospital environment you can certainly give your clients the greatest confidence that they will not be in danger.