Step-1: Generate m independent observations $W_1,W_2,\dots ,W_m$ which each follow the standard uniform distribution. Step-2: Set $Z_i=W_i^{\frac{1}{i+R_m+\dots +R_{m-i+1}}}$, for $i=1,\dots ,m$. Step-3: Set $Y_i=1-Z_m\dots Z_{m-i+1}$, for $i=1,\dots ,m$. Then, $Y_1,\dots ,Y_m$ are the desired progressive Type-II censored sample which comes from the standard uniform distribution. Step-4: At last we set $X_i=F^{-1}\left(Y_i\right)$, for $i=1,\dots ,m$, where $F^{-1}\left(Y_i\right)$ stands for the inverse culmulative density function of any distribution considered. $X_1,X_2,\dots ,X_m$ are the desired progressive Type-II censored sample out of the distribution $F\left(\right)$. In this article, $F\left(\right)$ is the Kumaraswamy distribution. Step-4.1: When $T<X_k<X_m$, the generalized progressive hybrid censored sample are $(X_1,X_2$, …, $X_k)$ (i.e., Case I); Step-4.2: When $X_k<T<X_m$, J can be determinde which makes $X_J<T<X_{J+1}$, and the generalized progressive hybrid censored sample is $(X_1,X_2$, …, $X_J)$ (i.e., Case II); Step-4.3: When $X_k<X_m<T$, the generalized progressive hybrid censored sample is $(X_1,X_2$, …, $X_m)$ (i.e., Case III).