Componendo and dividendo: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit

en>Cydebot

en>Bgwhite
m Reverted edits by 115.240.34.65 (talk) to last version by 117.221.120.215
en>Cydebot
m Robot - Speedily moving category Fractions to Category:Fractions (mathematics) per CFDS.
 
Line 1: Line 1:
{{For|the Roman town of Cusum|Petrovaradin}}
According to Daniel Drell of the U.S. DOE Human Genome Program, energy several factors to key into individual DNA virtually any individual. Drell uses the example of identifying a suspect with a crime scene to illustrate his period.<br><br>LaBron James was named since the NBA Rookie from 12 months within 2003-04 as well as named the actual NBA best player last year, 10 as well as 2012 air jordan shoes . Lebron James net worth originates from his handler's the National basketball association. He's won each All-NBA choice and All-Star every single day every session because june 2006. He's been included perhaps a member from the USA nationwide basketball group who successful a bronze medal as 2004 Olympics along having a gold medal in the 2008 Olympics.<br><br>Nike jordan sneakers were born being an affair in between Nike Company and Michael Jordan- the famous basket ball player. Yes, this affair took location in 1980's and soon, it resulted in form of Nike nike air jordans sneakers. Nike is one such company provides a repute of its very due to the class of the company's products specially the sportswear. Its shoes were already in market and used turn out to be supported from your sports circle as skillfully. But, in 1980's, Nike went in a contract with Michael Jordan, who had previously been the  basketball player all around the globe at period. They got him to endorse their type. Hence, the contract was signed and Nike Jordans shoes were only available in to industry industry.<br><br>There is an additional kind of trainers that are hot within the sports slippers. It is Nike Air force ones, also named Air force Forms. It is famous for leather cross trainers available as both high tops and low tops. Such a hybrid shoes is looked upon by Nike Air force ones because the "best of both worlds" by combining them into one. There are two regarding opinions, some have loved the air jordan Fusion concept from Jordan Brand, others have hated such a design. Issue how what opinion you hold, the combination is still to be looked into as the "best of both worlds" in the sports international.<br><br>Nike Air Force Shoes "Infrared" of your of the statements Few expected this year, although none belonging to the sellers of brand Jordan would release these sneakers. But provide you with more be that could get quantity of his pix. make this multi-dot shoes, especially eye-catching. Get the first stop after 13 to 21 August at the latest, James travels in Washington along with his home - Akron, Ohio, died August 24 in Beijing, August 28, 1926 in Shenyang Shanghai August 1 to a few September is here in Paris, France, April-May 2009 london, uk.<br><br>The last highlight may be the wonderful a sense passing and shooting produced from the SF III running footwear. And you also can feel like touching the ball quite simply. This should be an goal of the Superlfy III Soccer cleats.<br><br>When you beloved this short article in addition to you want to obtain more info concerning [http://www.plongeeo.com/chaussure-air-jordan-pas-cher/ chaussure air jordan pas cher] generously check out our own page.
{{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]]

Latest revision as of 03:35, 11 November 2014

According to Daniel Drell of the U.S. DOE Human Genome Program, energy several factors to key into individual DNA virtually any individual. Drell uses the example of identifying a suspect with a crime scene to illustrate his period.

LaBron James was named since the NBA Rookie from 12 months within 2003-04 as well as named the actual NBA best player last year, 10 as well as 2012 air jordan shoes . Lebron James net worth originates from his handler's the National basketball association. He's won each All-NBA choice and All-Star every single day every session because june 2006. He's been included perhaps a member from the USA nationwide basketball group who successful a bronze medal as 2004 Olympics along having a gold medal in the 2008 Olympics.

Nike jordan sneakers were born being an affair in between Nike Company and Michael Jordan- the famous basket ball player. Yes, this affair took location in 1980's and soon, it resulted in form of Nike nike air jordans sneakers. Nike is one such company provides a repute of its very due to the class of the company's products specially the sportswear. Its shoes were already in market and used turn out to be supported from your sports circle as skillfully. But, in 1980's, Nike went in a contract with Michael Jordan, who had previously been the basketball player all around the globe at period. They got him to endorse their type. Hence, the contract was signed and Nike Jordans shoes were only available in to industry industry.

There is an additional kind of trainers that are hot within the sports slippers. It is Nike Air force ones, also named Air force Forms. It is famous for leather cross trainers available as both high tops and low tops. Such a hybrid shoes is looked upon by Nike Air force ones because the "best of both worlds" by combining them into one. There are two regarding opinions, some have loved the air jordan Fusion concept from Jordan Brand, others have hated such a design. Issue how what opinion you hold, the combination is still to be looked into as the "best of both worlds" in the sports international.

Nike Air Force Shoes "Infrared" of your of the statements Few expected this year, although none belonging to the sellers of brand Jordan would release these sneakers. But provide you with more be that could get quantity of his pix. make this multi-dot shoes, especially eye-catching. Get the first stop after 13 to 21 August at the latest, James travels in Washington along with his home - Akron, Ohio, died August 24 in Beijing, August 28, 1926 in Shenyang Shanghai August 1 to a few September is here in Paris, France, April-May 2009 london, uk.

The last highlight may be the wonderful a sense passing and shooting produced from the SF III running footwear. And you also can feel like touching the ball quite simply. This should be an goal of the Superlfy III Soccer cleats.

When you beloved this short article in addition to you want to obtain more info concerning chaussure air jordan pas cher generously check out our own page.

Retrieved from "https://en.formulasearchengine.com/w/index.php?title=Componendo_and_dividendo&oldid=259596"