How do we know that breakdowns of the crematory ovens in Auschwitz-Birkenau would not have significantly impaired the cremation of the bodies of nearly 900,000 Jews?
Holocaust deniers claim:
The crematory ovens in Auschwitz-Birkenau broke down so often that the number of bodies that could be cremated was significantly reduced.
The facts are:
The crematory ovens in Auschwitz-Birkenau were in constant operation, which did cause breakdowns requiring repairs. These repairs were easily fixed and did not impair the mass murder. Likewise, when the number of bodies overwhelmed the capacity of the ovens, open-air burning pits were used.
Italian Holocaust denier Carlo Mattogno asserts that the cremation of 675,000 bodies would “have required at least four complete substitutions of the fire-resistant walls of all the chambers.” This would have required 256 tons of fire-resistant wall material and 7,200 hours of labor time. There is no indication in the Auschwitz building records that such extensive projects were ever undertaken. Thus, Mattogno concludes, “The cremation of 675,000 corpses is technologically impossible, and consequently no mass extermination was perpetrated at Auschwitz-Birkenau.” 
Primary-source document about the maintenance of the ovens:
On June 28, 1943, Karl Bischoff, head of the Central Building Administration in Auschwitz-Birkenau, sent a letter to Hans Kammler, an important Nazi German engineer, in Berlin. The letter states that the ovens at Auschwitz-Birkenau should ideally operate on a continuous basis. In reality, breakdowns did occur.
Overuse and misuse caused the bricks in the muffles and inside the chimneys to crack or break, requiring maintenance or mending. However, most repairs could be made quickly. Filip Müller, a member of one of the Sonderkommandos who stoked the ovens, recalled that a special fireclay paste was used to patch the cracks.
Perpetrator eyewitness testimony about other options for cremation:
When the number of bodies to be cremated exceeded the capacity of the ovens, open-air burning pits were used. Pery Broad, a member of the Gestapo in Auschwitz-Birkenau, recalled: “The four crematoria were exploited to the utmost. Because of the over-use, the ovens were constantly in need of repair…There was no help for it—the pyres had to be used again to dispose of the thousands of bodies lying in big heaps behind the crematoria…There were no breaks.”
By Chmee2 or Mikee (Own work) [GFDL (http://www.gnu.org/copyleft/fdl.html), CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons
Thus, when the number of bodies to be cremated overwhelmed the capacity of the ovens capable of being used—such as in mid-1944, when 8,000 to 10,000 Hungarian Jews were murdered per day—open-air burning pits were used to cremate thousands of bodies at a time.
The crematory ovens in Auschwitz-Birkenau did require repair and maintenance, although not to the extent that Mattogno claims. Furthermore, there were other methods for disposing of the bodies, such as open-air burning pits. These pits could also cremate thousands of bodies at once. Eyewitness testimony confirms the continuous assembly line of murder at Auschwitz-Birkenau.
 Carlo Mattogno, Auschwitz: The End of a Legend: A Critique of J.C. Pressac (Institute for Historical Review, 1994), p. 30.
 Filip Müller, Eyewitness Auschwitz: Three Years in the Gas Chambers (Ivan R. Dee, 1979), p. 124 and John C. Zimmerman, “Body Disposal at Auschwitz: The End of Holocaust Denial” (“Cremation Capacity”) at http://www.phdn.org/archives/holocaust-history.org/auschwitz/body-disposal/.
 KL Auschwitz Seen by the SS (Auschwitz-Birkenau State Museum, 1995), p. 137.