What it means
ためしがない expresses the speaker’s strong judgment that something has never happened, or that someone has never performed an action, up to the relevant point in time. It usually follows the plain past form of a verb and emphasizes the complete absence of even one such instance, making it stronger than a neutral statement of infrequency.
Usage note
ためしがない normally follows a verb in the plain past form, as in Vたためしがない. The polite counterpart is formed by changing only the final ending to ためしがありません; it should not be confused with ためにならない, which means that something is useless or harmful.
How to use it
Verb (た-form)ためしがありません
彼は約束を守ったためしがありません。
He has never kept a promise.
Verb (た-form)ためしがない
彼は約束を守ったためしがない。
He has never kept a promise.