Abstract
Cimulative Sum (CUSUM) schemes for attributes can be formulated through a Markov chain, and the most important characteristic, ARL, is obtained by solving an inverse matrix whose size is as large as number of possible values the CUSUM takes. The calculation becomes practically impossible when the CUSUM is intended for very small process mean since the corresponding k should be taken a small fraction value and it causes a very large sized computation of an inverse matrix. This study presents an alternative solution without any matrix manipulation based on the authers' result for the sequential probability ratio test. The solution can give an explicit expression of ARL, and its algorithm is also devised. A design table for small valued k to 0.001 is given corresponding to the exisiting table of k larger than 0.25.
