CUSUM

In statistical quality control, the CUSUM (or cumulative sum control chart) is a sequential analysis technique developed by E. S. Page of the University of Cambridge. It is typically used for monitoring change detection. CUSUM was announced in Biometrika, in 1954, a few years after the publication of Wald's SPRT algorithm.

Page referred to a "quality number" , by which he meant a parameter of the probability distribution; for example, the mean. He devised CUSUM as a method to determine changes in it, and proposed a criterion for deciding when to take corrective action. When the CUSUM method is applied to changes in mean, it can be used for step detection of a time series.

A few years later, George Alfred Barnard developed a visualization method, the V-mask chart, to detect both increases and decreases in .

Method

As its name implies, CUSUM involves the calculation of a cumulative sum (which is what makes it "sequential"). Samples from a process are assigned weights , and summed as follows:

Petrovaradin

Petrovaradin (Serbian Cyrillic: Петроварадин, pronounced [petroʋarǎdiːn]) is a town and municipality in Serbia, part of the agglomeration of City of Novi Sad. Population of the Petrovaradin town numbered 14,298 and whole municipality 33,865 people in 2011. Lying across the river Danube from the main part of Novi Sad, it is built near the Petrovaradin Fortress, known as the "Gibraltar of the Danube".

Name

Petrovaradin was founded by Celts, but its original name is not known. During Roman administration it was known as Cusum. After the Romans conquered the region from the Celtic tribe of Scordisci, they built the Cusum fortress where present Petrovaradin Fortress now stands. In addition, the town received its name from the Byzantines, who called it Petrikon or Petrikov (Πετρικον) and who presumably named it after Saint Peter.

In documents from 1237, the town was first mentioned under the name Petrovaradin (Pétervárad), which was named after Hungarian lord Peter, son of Töre. Petrovaradin was known under the name Pétervárad during Hungarian administration, Varadin or Petervaradin during Ottoman administration, and Peterwardein during Habsburg administration.