An ordered set partition of {1, 2, . . . , n} is a partition with an ordering on the parts. Let OP n,k be the set of ordered set partitions of [n] with k blocks. Godbole, Goyt, Herdan and Pudwell defined OP n,k (σ) to be the set of ordered set partitions in OP n,k avoiding a permutation pattern σ and obtained the formula for |OP n,k (σ)| when the pattern σ is of length 2. Later, Chen, Dai and Zhou found a formula algebraically for |OP n,k (σ)| when the pattern σ is of length 3.In this paper, we define a new pattern avoidance for the set OP n,k , called WOP n,k (σ), which includes the questions proposed by Godbole, Goyt, Herdan and Pudwell. We obtain formulas for |WOP n,k (σ)| combinatorially for any σ of length 3. We also define 3 kinds of descent statistics on ordered set partitions and study the distribution of the descent statistics on WOP n,k (σ) for σ of length 3.