Abstract
AbstractThe conventional CUSUM chart is usually designed for a known shift size against which the protection is required. In practice, the shift sizes are rarely known, but they may vary within a given interval. Given a range of the shift size, the weighted adaptive CUSUM (WAC) chart provides better protection than the CUSUM chart. In this paper, we propose two types of the WAC chart for monitoring different kinds of shifts in the variance of a normal process, named WAC‐I and WAC‐II charts, based on the CUSUM and Crosier CUSUM charts, respectively. Monte Carlo simulations are used to compute the run length characteristics of the proposed one‐sided and two‐sided charts. The proposed charts are compared with existing adaptive and non‐adaptive charts in terms of the average run length. It is found that the proposed charts perform uniformly and substantially better than the existing charts. A real dataset is considered to support the theory.
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