This article develops a nonparametric cumulative sum (CUSUM) for sequential monitoring of independent and identically distributed observations when the underlying in-control density is arbitrary and unknown but can be estimated from historical in-control data. The approach utilizes a smooth bootstrap algorithm along with an adaptive nonparametric kernel density estimator to make the CUSUM work for reasonably sized sets of in-control data. The authors discuss how the CUSUM fits into a two-stage SPC algorithm.
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