Question

the two-inch din if to statistical interchangeability is used. 002

Answer 1

GIVEN DATA :

A = 2.000 $\pm$ 0.003.

B = 4.000 $\pm$ 0.003.

C = 2.000 $\pm$ 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$\sigma$ 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 ( $\sigma$ _A )= ( 0.003 + 0.003 ) / (2 x 3 ) = 0.006 / 6 = 0.001.

Therefore, Standard deviation for Dimension - B ( $\sigma$ _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.

$\sigma$_B = [ ( $\sigma$ _A )² + ( $\sigma$ _C )² ]^1/2 --------------------------- Q

Assume, Tolerance Value for C - dimension = 0.001.

Therefore, Standard deviation for C -Dimension Tolerance Value ( $\sigma$ _C )= ( 0.001 + 0.001 ) / (2 x 3 ) = 0.002 / 6 = 0.000333.

If we are substituting the above value in equation - A,

$\sigma$_B = [ ( 0.001 )² + ( 0.000333 )² ]^1/2

$\sigma$_B = [ ( 1 x 10^-6 )+ ( 1.11 x 10^-7 ) ]^1/2 = 0.00105

Therefore, $\sigma$ _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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