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{{For|the Roman town of Cusum|Petrovaradin}}
{{Infobox control chart
| name =                      CUSUM chart
| proposer =                  E. S. Page
<!-----Process observations----->
| subgroupsize =              n = 1
| measurementtype =          Cumulative sum of a quality characteristic
| qualitycharacteristictype = [[Variable and attribute (research)|Variables data]]
| distribution =              [[Normal distribution]]
<!---------Performance---------->
| sizeofshift =              ≤ 1.5σ
| arl =
<!---Process variation chart--->
| varchart =
| varcenter =
| varupperlimit =
| varlowerlimit =
| varstatistic =
<!------Process mean chart------>
| meanchart =
| meancenter =                The target value, T, of the quality characteristic
| meanupperlimit =            <math>C_i^+ = max \lbrack 0, x_i - \left ( T + K \right ) + C_{i - 1}^+\rbrack</math>
| meanlowerlimit =            <math>C_i^- = max \lbrack 0, \left ( T - K \right ) - x_i + C_{i - 1}^-\rbrack</math>
| meanstatistic =            <math>C_i = \sum_{j=1}^i \bar x_j - T</math>
}}
 
In [[statistical process control|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]].<ref name=grigg>{{cite journal
|title=The Use of Risk-Adjusted CUSUM and RSPRT Charts for Monitoring in Medical Contexts
|author=Grigg ''et al.''
|journal=Statistical Methods in Medical Research
|volume=12
|pages=147–170
|year=2003
|doi=10.1177/096228020301200205
|pmid=12665208
|last2=Farewell
|first2=VT
|last3=Spiegelhalter
|first3=DJ
|issue=2
}}</ref>
CUSUM was announced in [[Biometrika]], in 1954, a few years after the publication of [[Abraham Wald|Wald]]'s [[SPRT]] algorithm.<ref name=page>{{cite journal
|first=E. S.
|last=Page
|title=Continuous Inspection Scheme
|journal=Biometrika
|volume=41
|issue=1/2
|date=June 1954
|pages=100–115
|jstor=2333009}}</ref>
 
Page referred to a "quality number" <math>\theta</math>, 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 <math>\theta</math>.<ref>{{cite journal
|first=G.A.
|last=Barnard
|authorlink=George Alfred Barnard
|title=Control charts and stochastic processes
|journal=[[Journal of the Royal Statistical Society]]
|volume=B (Methodological)
|issue=21, number 2
|year=1959
|pages=239–71
|jstor=2983801
}}</ref>
 
==Method==
As its name implies, CUSUM involves the calculation of a '''cu'''mulative '''sum''' (which is what makes it "sequential"). Samples from a process <math>x_n</math> are assigned weights <math>\omega_n</math>, and summed as follows:
 
:<math>S_0=0</math>
:<math>S_{n+1}=\max(0, S_n+x_n-\omega_n)</math>
 
When the value of ''S'' exceeds a certain threshold value, a change in value has been found. The above formula only detects changes in the positive direction. When negative changes need to be found as well, the min operation should be used instead of the max operation, and this time a change has been found when the value of ''S'' is ''below'' the (negative) value of the threshold value.
 
Page did not explicitly say that <math>\omega</math> represents the [[likelihood function]], but this is common usage.
 
Note that this differs from SPRT by always using zero function as the lower "holding barrier" rather than a lower "holding barrier".<ref name=grigg/> Also, CUSUM does not require the use of the likelihood function.
 
As a means of assessing CUSUM's performance, Page defined the ''average run length'' (A.R.L.) [[Metric (mathematics)|metric]]; "the expected number of articles sampled before action is taken." He further wrote:<ref name=page/>
 
<blockquote>
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 error]]s ([[Neyman-Pearson lemma|Neyman & Pearson]], 1936<ref>{{cite journal
|title=[[Sufficient statistic]]s and [[statistical power|uniformly most powerful tests]] of statistical hypotheses
|journal=[[Statistical Research Memoirs]]
|volume=I
|pages=113–137
}}</ref>).  On  the other  hand,  for  constant  poor  quality  the A.R.L.  measures  the delay and thus  the amount of scrap produced before the rectifying action is taken,  i.e., [[Type II error]]s.
</blockquote>
 
construct cusum chart for the following 30 observations these observations were drawn at random
from a normal distribution
1)with mean(μ)=10 and σ=1.
2)when mean and variance are unknown.
 
sample i Xi
1 9.45
2 7.99
3 9.29
4 11.66
5 12.16
6 10.18
7 8.04
8 11.46
9 9.2
10 10.34
11 9.03
12 11.43
13 10.51
14 9.4
15 10.08
16 9.37
17 10.62
18 10.31
19 8.52
20 10.84
21 10.9
22 9.33
23 12.29
24 11.5
25 10.6
26 11.08
27 10.38
28 11.62
29 11.31
30 10.52
 
==References==
{{reflist}}
 
==Further reading==
* {{cite book
|url=http://www.irisa.fr/sisthem/kniga/
|title=Detection of Abrupt Changes: Theory and Application
|author=Michèle Basseville and Igor V. Nikiforov
|publisher=[[Prentice-Hall]], [[Englewood Cliffs]], N.J.
|isbn=0-13-126780-9
|date=April 1993}}
 
==External links==
*[http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc323.htm "Engineering Statistics Handbook - Cusum Control Charts" ]
 
{{DEFAULTSORT:Cusum}}
[[Category:Statistical charts and diagrams]]
[[Category:Quality control tools]]
[[Category:Sequential methods]]

Revision as of 03:19, 1 February 2014

28 year-old Painting Investments Worker Truman from Regina, usually spends time with pastimes for instance interior design, property developers in new launch ec Singapore and writing. Last month just traveled to City of the Renaissance. Template:Infobox control chart

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.[1] CUSUM was announced in Biometrika, in 1954, a few years after the publication of Wald's SPRT algorithm.[2]

Page referred to a "quality number" θ, 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 θ.[3]

Method

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

S0=0
Sn+1=max⁡(0,Sn+xn−ωn)

When the value of S exceeds a certain threshold value, a change in value has been found. The above formula only detects changes in the positive direction. When negative changes need to be found as well, the min operation should be used instead of the max operation, and this time a change has been found when the value of S is below the (negative) value of the threshold value.

Page did not explicitly say that ω represents the likelihood function, but this is common usage.

Note that this differs from SPRT by always using zero function as the lower "holding barrier" rather than a lower "holding barrier".[1] Also, CUSUM does not require the use of the likelihood function.

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." He further wrote:[2]

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[4]). On the other hand, for constant poor quality the A.R.L. measures the delay and thus the amount of scrap produced before the rectifying action is taken, i.e., Type II errors.

construct cusum chart for the following 30 observations these observations were drawn at random from a normal distribution 1)with mean(μ)=10 and σ=1. 2)when mean and variance are unknown.

sample i Xi 1 9.45 2 7.99 3 9.29 4 11.66 5 12.16 6 10.18 7 8.04 8 11.46 9 9.2 10 10.34 11 9.03 12 11.43 13 10.51 14 9.4 15 10.08 16 9.37 17 10.62 18 10.31 19 8.52 20 10.84 21 10.9 22 9.33 23 12.29 24 11.5 25 10.6 26 11.08 27 10.38 28 11.62 29 11.31 30 10.52

References

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    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

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    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

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  2. ↑ 2.0 2.1 One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

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    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

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  3. ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

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  4. ↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
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