Journal of Quality Technology · 2000 · 252 citations · 10 references
Forecasting MethodologyEngineeringSpatiotemporal OrganizationNetwork AnalysisBusiness AnalyticsVolume PredictionLocalizationOperations ResearchProbabilistic ForecastingSpatial NetworkData ScienceUncertainty QuantificationManagementConventional CusumStatisticsQuantitative ManagementPredictive AnalyticsComputer ScienceForecastingCusum ProceduresCusum ChartsProduction ForecastingFast MaBusiness ForecastingSpatio-temporal ModelConventional Cumulative Sum
The conventional CUSUM with k = 0.5 is the default statistic when future shifts are unknown. This paper designs CUSUM procedures to efficiently signal a range of future expected but unknown location shifts, advocating two approaches. The authors employ two strategies: a three‑statistic conventional CUSUM with varied resetting boundaries, and an adaptive CUSUM that adjusts to one‑step‑ahead deviations, comparing performance via average run length and illustrating with several applications. The resulting procedures exhibit multi‑level memory and signal a broader range of location shifts more efficiently than the conventional CUSUM with k = 0.5.
The conventional cumulative sum (CUSUM) with k = 0.5 is often used as the default CUSUM statistic when future shifts are unknown. In this paper, CUSUM procedures are designed to be efficient at signalling a range of future expected but unknown location shifts. Two approaches are advocated. The first uses three simultaneous conventional CUSUM statistics with different resetting boundaries. This results in a procedure that has, on average, several levels of memory, and thus signals a broader range of location shifts more efficiently than the conventional CUSUM with k = 0.5. The second uses an adaptive CUSUM statistic that continually adjusts its form to be efficient for signalling a one-step-ahead forecast in deviation from its target value. Average run length (ARL) is used to compare the relative performance of procedures. Several applications are used to illustrate procedures.
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E. S. Page · Biometrika · 1954 · 4.5K citations
Reliability Engineering, Engineering, Quality Inspection +11
Procedures for Reacting to a Change in Distribution
G. Lorden · The Annals of Mathematical Statistics · 1971 · 1.3K citations · Full text