
# <center>ANAVAR method</center>  

To calculate the GRR and Cpc by using the ANAVAR method, the statistical analyses of the Fisher test are used:

|Source variability|	Sum of squares|	Degree of freedom|	Average of squares|	F statistic|
|:-|:-|:-|-|-|
|Operator |SSA|	a-1|	![equation]("MSA"="SSA"/(a-1)) |![equation]("F"="MSA"/"MSE")|
|Parts| SSB	|b-1|	![equation]("MSB"="SSB"/(b-1)) |	 ![equation]("F"="MSB"/"MSE")|
|Interaction (Operator/part)| SSAB	|(a-1)(b-1)|![equation]("MSAB"="SSAB"/((a-1)*(b-1)))|  ![equation]("F"="MSAB"/"MSE")|
|Instrument |SSE|	ab(n-1)|	 ![equation]("MSE"="SSE"/(a*b*(n-1))) ||
|Total| TSS|	N-1|||	  
	
 <center>a =number of operators </center>

 <center>b = number of parts</center>

 <center>n = number of repetitions </center>

 <center>N = total number of measurements = abn </center>

![equation]("SSA"=sum_a(Y_i^2/(b*n)-Y_{"**"}^2/N))

![equation]("SSB"=sum_b(Y_i^2/(a*n)-Y_{"**"}^2/N))
![equation]("SSAB"=sum_a(sum_b(Y_{ij}^2/(n)-Y_{"**"}^2/N-SSA-SSB)))
![equation]("TSS"=sum_a(sum_b(sum_n(Y_{ijk}^2-Y_{"**"}^2/N))))
![equation]("SSE"="TSS"-"SSA"-"SSB"-"SSAB")

The repeatability of the measurement system is given by:
![equation]("Repeatability"=5.15*sqrt("MSE"))

The reproducibility of the measurement system is given by:
![equation]("Reproducibility"=5.15*sqrt(("MSA"-"MSAB")/(b*n)))

The interaction is given by:![equation]("Interaction"=5.15*sqrt(("MSAB"-"MSE")/(n)))

The variability of the measurement system is given by
![equation]("Dispersion_mesure"=sqrt("Repeatbility"^2+"Reproducibility"^2+"Interaction"^2))

Final calculation:
![equation]("Cpc"="IT"/"Dispersion_mesure")
and
![equation]("GRR"="Dispersion_mesure"/"IT")


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ANAVAR method

Eine Komplettlösung für Industrie 4.0

Source variability	Sum of squares	Degree of freedom
Operator	SSA	a-1
Parts	SSB	b-1
Interaction (Operator/part)	SSAB	(a-1)(b-1)
Instrument	SSE	ab(n-1)
Total	TSS	N-1