# CUSUM

**Cumulative sum charts**

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

28 Related Articles

### 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

**sequentialsequential testingadaptive**

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**

### 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.