I have made private vows to the evangelical counsels through a spiritual director, which is ongoing. This is not the consecrated life, but a dedicated life. Under Canon Law, consecrated life has specific definitions and private vows are not one of them. Initially I made the vows for one year for around 8 years and then for life. I have a distinct way of life that is based on The Gospel. If one wishes and with the agreement of the celebrant, private vows may be made at Mass.
I think it unwise to make private vows without consulting a spiritual director and on an ongoing basis for the life of the vows.
It is interesting that Pope Paul II in Vita Consecrata in giving thanks for the consecrated life in all its forms, does include :
We are all aware of the treasure which the gift of the consecrated life in the variety of its charisms and institutions represents for the ecclesial community. Together let us thank God *for the Religious Orders and Institutes devoted to contemplation or the works of the apostolate, for Societies of Apostolic Life, for Secular Institutes and* for other groups of consecrated persons, as well as for all those individuals who, in their inmost hearts, dedicate themselves to God by a special consecration.**
Nevertheless, to distinguish consecrated life as in Canon Law, private vows are, it seems (according to Canon Lawyers I have read), referred to as a dedicated life.