Data Analytics Modeling

Information & data analysis from courses I’m taking

Poisson Distribution Excel File: Poisson Distribution example template 1

CUSUM related Info: (please view table horizontally for a full view)

Variable

Pronounced / Read As / Summary Definition

Description Detail

Source

Equivalence

In this Doc

μ

“Mu”

Let’s call Mu the expected value of the observations x.  μ=mean of x, if no change

Dr. Sokol Lecture 6.2 (M)

 

 

μ = µ0

µ0

“Mu0”/”MuZero”

Tabular Cusum Choose a target value µ0

NCSU slides link

CUSUM Wikipedia link

μ = µ0

T

“T Target Value”

Center line, the target value, T, of the quality characteristic

CUSUM Wikipedia link

μ = µ0=T

K

 

a reference value K

Used if a change of process needs to be detected quickly, it’s the allowable “slack” in the process. In the CUSUM point formula, it specifies the size of the shift you want to detect. 

NCSU slides link

CUSUM Wikipedia link

 

K = k*sigma

Ci Ci+, Ci

Ci is CUSUM or result of “the calculation of a cumulative sum”. In R the qcc package provides a function cusum() to make a chart showing Ci+, Ciand control limits at ±H,  

NCSU slides link

CUSUM Wikipedia link

Ci = St

i

“i” index

i, j, and k (sometimes l or h) are often used to denote varying integers or indices in an indexed family

Wikipedia variable link

t = i

 

St

“metric S sub t”

The basic idea is to calculate a metric S sub t and declare that we’ve observed a change when and if that metric goes above a threshold capital T.

Dr. Sokol Lecture 6.2 (M)

 

Ci = St

t

“time t”

Suppose we have some data, x sub t where x sub t is the observed value at time t.

Dr. Sokol Lecture 6.2 (M)

 

t = i

H

H = 5σ

“Control Limit”

 

Also, a decision interval H = 5σ is often used. The process is declared out of control if either Ci+ or Ciexceeds a

decision interval H.

NCSU slides link

 

 

H = T

(T threshold)

 

T

“threshold capital T”

Control Limit

“if that metric goes above a threshold capital T.”

 

Note:  Also referred to as “Limits” (for my one-sided control chart) and “Upper”

Dr. Sokol Lecture 6.2 (M)

 

H = T

(T threshold)

Note: T threshold is different than

T Target variable

 

xi

“x sub i”

Samples from a process xi “When the value of S exceeds a certain threshold value, a change in value has been found”

CUSUM Wikipedia link

xi = xt

xt

“x sub t”

At each time period, we observe X sub t and see how far above the expectation it is. xt = observed value at time t

Dr. Sokol Lecture 6.2 (M)

 

xi = xt

C

“C”

So we include a value C to pull the running total down a little bit.

Dr. Sokol Lecture 6.2 (M)

 

C = K

σ

“sigma” lowercase

standard deviation σ = 1

NCSU slides link

σ

h

“h”, another “control Limit” default values for h are 4 or 5

For tabular CUSUMs, h is the number of standard deviations between the center line and the control limits. It is the value at which an out-of-control signal occurs.

 

Minitab site link

H = h*sigma 

 

     k

“k” a reference value,

default value for k is 0.5

For tabular CUSUMs, k is the allowable “slack” in the process. In the CUSUM point formula, k specifies the size of the shift you want to detect.

 

Minitab site link

K = k*sigma

N, N+, N-

N

N number of observations above or below the target / expected value

NCSU slides link

 

N

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