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  μ = µ0  
T  “T Target Value”  Center line, the target value, T, of the quality characteristic  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. 
K = k*sigma  
C_{i} C_{i}+, C_{i}–  C_{i} 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 C_{i}+, C_{i}–and control limits at ±H,  C_{i = }S_{t}  
i  “i” index  i, j, and k (sometimes l or h) are often used to denote varying integers or indices in an indexed family  t = i
 
S_{t}  “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)
 C_{i = }S_{t} 
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 C_{i}+ or C_{i}– exceeds a decision interval H. 

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 onesided control chart) and “Upper”  Dr. Sokol Lecture 6.2 (M)
 H = T (T threshold) Note: T threshold is different than T Target variable

x_{i}  “x sub i”  Samples from a process x_{i} “When the value of S exceeds a certain threshold value, a change in value has been found”  x_{i =} x_{t }  
x_{t}  “x sub t”  At each time period, we observe X sub t and see how far above the expectation it is. x_{t = }observed value at time t  Dr. Sokol Lecture 6.2 (M)
 x_{i =} x_{t} 
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  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 outofcontrol signal occurs. 
 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. 
 K = k*sigma 
N, N+, N  N  N number of observations above or below the target / expected value 
 N 