# CUSUM

Cumulative sum charts
In statistical quality control, the CUSUM (or cumulative sum control chart) is a sequential analysis technique developed by E.wikipedia
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### Control chart

control chartsAttribute chartCUSUM
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.
Other types of control charts have been developed, such as the EWMA chart, the CUSUM chart and the real-time contrasts chart, which detect smaller changes more efficiently by making use of information from observations collected prior to the most recent data point.

### Change detection

Change point detectionchange-point detection
It is typically used for monitoring change detection.
A key technique for minimax change detection is the CUSUM procedure.

### Step detection

When the CUSUM method is applied to changes in mean, it can be used for step detection of a time series.
Such algorithms include the classical CUSUM method applied to changes in mean.

### Sequential probability ratio test

SPRT
CUSUM was announced in Biometrika, in 1954, a few years after the publication of Wald's SPRT algorithm.

### Time series

time series analysistime-seriestime-series analysis
When the CUSUM method is applied to changes in mean, it can be used for step detection of a time series.

### Statistical process control

statistical quality controlstatistical controlSPC
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.

### Sequential analysis

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.

### University of Cambridge

Cambridge UniversityCambridgeUniversity
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.

### Biometrika

Biometrika Trust
CUSUM was announced in Biometrika, in 1954, a few years after the publication of Wald's SPRT algorithm.

### Abraham Wald

WaldWald, Abraham
CUSUM was announced in Biometrika, in 1954, a few years after the publication of Wald's SPRT algorithm.

### Probability distribution

distributioncontinuous probability distributiondiscrete probability distribution
Page referred to a "quality number" \theta, by which he meant a parameter of the probability distribution; for example, the mean.

### Mean

mean valueaveragepopulation mean
Page referred to a "quality number" \theta, by which he meant a parameter of the probability distribution; for example, the mean.

### George Alfred Barnard

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

### Likelihood function

likelihoodlikelihood ratiolog-likelihood
Page did not explicitly say that \omega represents the likelihood function, but this is common usage.

### Metric (mathematics)

metricdistance functionmetrics
As a means of assessing CUSUM's performance, Page defined the average run length (A.R.L.) metric; "the expected number of articles sampled before action is taken."

### Neyman–Pearson lemma

Neyman-Pearson lemmaabstractNeyman & Pearson
When the quality of the output is satisfactory the A.R.L. is a measure of the expense incurred by the scheme when it gives false alarms, i.e., Type I errors (Neyman & Pearson, 1936 ).

### Type I and type II errors

Type I errorfalse-positivefalse positive
When the quality of the output is satisfactory the A.R.L. is a measure of the expense incurred by the scheme when it gives false alarms, i.e., Type I errors (Neyman & Pearson, 1936 ).

### Variable and attribute (research)

variablesvariablevariables data

### Normal distribution

normally distributedGaussian distributionnormal

### List of statistics articles

List of statistical topicsList of statistics topicsIndex of statistics articles

### Structural break

Sup-LR testStructural break testSup-LM test
In general, the CUSUM (cumulative sum) and CUSUM-sq (CUSUM squared) tests can be used to test the constancy of the coefficients in a model.

### Real-time outbreak and disease surveillance

RODS (Real-Time Outbreak Disease Surveillance)

### Energy monitoring and targeting

The CUSUM can then be plotted against time on a new graph, which then yields more information for the energy efficiency specialist.

### Serbia in the Roman era

Roman periodRoman SerbiaByzantine Serbia