Calibration and short runs
Up to now, we have not said much about the estimation of the in-control parameters, except to point out that large samples are necessary to estimate them adequately. To get some feeling for this, we try to quantify the impact of uncertainty in the parameter estimates in the case of a normal CUSUM. Suppose that the process stream is N (μ, σ2). To calibrate the CUSUM, we take a sample ofsize m and compute its mean X and standard deviation s, and substitute X for μ and s for σ. This means that our figure for the true mean is in error by the amount μ — X, and the figure for the true standard deviation is in error by the ratio σ /s.
KeywordsDoyle Cali Havoc
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