This is where cheques are useful. Make the payment to the customer by cheque and mark the back with "in full and final settlement regarding all and any claims connected to the installation of . . . . on . . . ". You can then get the cashed cheque returned to you by your bank.
Responsibility...
I don't know what trade you are in or the product in question but do you not have contacts or a colleague you could pay to carry out the repair for you?
That's only true for the first six months following purchase. After that it's up to the consumer to show the fault isn't due to fair wear and tear or is due to a manufacturing fault.
If a customer gets stroppy and decides to go for it they can hire an "expert" to testify at which point costs...
Unless the customer has employed legal representation then the costs will be minimal. The problem you have is that you won't know until the case came to court. Personally I'd wait until the customer sent you a "letter before action" at which point you have a decision to make.
If the customer can show that the fault is not due to misuse or what could be considered fair wear an tear then if you supplied and filled the item within the last six years you are liable for the full cost of any repair.
I've been caught out in the past trying to fight such a claim and lost...