We propose a lockout avoidance algorithm for the k-exclusion problem on the asynchronous multi-writer/reader shared memory model. This algorithm is the extension of an accelerated version of the n-process algorithm to the k-exclusion problem. The running time by the algorithm for the trying region of any faultless process is bounded by (n - k)c + O(n(n - k)²)l if the number of stopping process failures is less than k, where n is the number of processes, l is an upper bound on the time between two successive atomic steps for any faultless process, and c is an upper bound on the time that any user spends in the criticalregion.