GIVEN DATA :
A = 2.000 0.003.
B = 4.000 0.003.
C = 2.000 X.
SOLUTION :
For 100 % Interchangeability, and to find the required Tolerance value,we have to use Statistical Tolerance Stack - up Analysis such as Root Sum Square ( RSS ) method.
STEP - 1 : Calculate Standard deviation for each Tolerance considering process is 3 Capable ).
Mathematically, Standard deviation is equal to two times of process capability.
Therefore, Standard deviation = Total Tolerance / (2 x 3 ).
Therefore, Standard deviation for Dimension - A ( A )= ( 0.003 + 0.003 ) / (2 x 3 ) = 0.006 / 6 = 0.001.
Therefore, Standard deviation for Dimension - B ( B )= ( 0.003 + 0.003 ) / (2 x 3 ) = 0.006 / 6 = 0.001. ------------------ P
As per Statistical Tolerance Stack - up and Root Sum Square ( RSS ) method.
B = [ ( A )2 + ( C )2 ]1/2 --------------------------- Q
Assume, Tolerance Value for C - dimension = 0.001.
Therefore, Standard deviation for C -Dimension Tolerance Value ( C )= ( 0.001 + 0.001 ) / (2 x 3 ) = 0.002 / 6 = 0.000333.
If we are substituting the above value in equation - A,
B = [ ( 0.001 )2 + ( 0.000333 )2 ]1/2
B = [ ( 1 x 10-6 )+ ( 1.11 x 10-7 ) ]1/2 = 0.00105
Therefore, B = 0.001. ------------------ R.
Compare the equation P & R Value. Both are same.
Therefore, the Tolerance Value for C - dimension ( X ) = 0.001.
NOTE : The above C - dimension tolerance value ( 0.001 ) ( assumed value ), i have arrived by means trial and error by of substituting the different values in the equation - Q.
ANSWER :
For 100 % Interchangeability of the Tolerance Value for C - dimension ( X ) = 0.001.
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