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 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.  This means: One million microbes is the basis for the calculations, which is why prior cleaning is necessary. Too many microbes on the items, more than one million, would require a greater processing time or temperature..

Each negative 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). This is a "Log of 6" ( a log of 6 equals 1 million microbes). 

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

Repeating our process again, we empty 90% of what is left over in the glass. This is a "log of 4" (10,000-10% microbes left over from the first step, minus 90% leaves 1,000 microbes

10⁶ 1,000,000 microbes
10⁵ 1,000,000 minus 90% = 100,000
10⁴ 100,000 minus 90% = 10,000
10³ 10,000 minus 90% = 1,000
10² 1,000 minus 90% = 100
10¹ 100 minus 90% = 10
10⁰ 10 minus 90% = 1
10^-1 1 minus 90% of 1? - can't have 10% of one microbe
       but we can think of it as 1 microbe among 10 items. = -1

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 it as a probability: In other words
If we had one item we would have one microbe on that item. 
If we had 10 items we can say we might have one microbe among ten items (a 90% reuction),

.  This level is 10 ^-1, Ten to the minus one meaning one microbe per 10 items. A log of reduction to 10^-2 therefore means one microbe per 100 items, etc. A log of 10^-6 means
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 10^-6.

The level of disinfection-sterilization varies according to the appropriate use of the item.

Topically applied "sterile" products, a log of 10^-3 is considered suitable.

Implantables require a SAL of 10^-6 Log.

Normal saturated steam processing produces one log of reduction (90% "kill") every 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 and an additional 5 minutes is considered precautionary for "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 or leave the sterilizer run longer than 20 minutes without known and good reason. In tattoo and piercing non-hospital environment. You can certainly give your clients the greatest confidence that the products you are using are sterile.

The importance of cleaning is to reduce the original microbial load so that you can be sure of this SAL of 10^-6.  If you started 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)

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  that you send for testing. 
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."  Tests may show adverse indicators if the test is held at either a much higher temperature or much longer dwell times.
Higher temperatre and longer dwell may be evaluated as a failed test.

Flash Sterilizatio: fast, higher temperature, is not designed for routine sterilization.