  In this paper, we explore the theme of orbifold stratified spaces and
establish a general criterion for them to be smooth orbifolds. This criterion
utilizes the notion of linear stratification on the gluing bundles for the
orbifold stratified spaces. We introduce a concept of good gluing structure to
ensure a smooth structure on the stratified space. As an application, we
provide an orbifold structure on the coarse moduli space $\bar{M}_{g, n}$ of
stable genus $g$ curves with $n$-marked points.
  Using the gluing theory for $\bar{M}_{g, n} $ associated to horocycle
structures, there is a natural orbifold gluing atlas on $\bar{M}_{g, n} $. We
show this gluing atlas can be refined to provide a good orbifold gluing
structure and hence a smooth orbifold structure on $\bar{M}_{g,n}$. This
general gluing principle will be very useful in the study of the gluing theory
for the compactified moduli spaces of stable pseudo-holomorphic curves in a
symplectic manifold.
