A First Course in Quality Engineering, 2nd Edition

188 A First Course in Quality Engineering

3.3.3.4  The RSS Formula

Suppose L

1

and L

2

are the lengths of two components (see Figure 3�12a) and

L = L

1

+ L

2

� Let t

1

and t

2

be the tolerances on L

1

and L

2

, respectively� Then the

tolerance on L is given by

t t t

L

= +

1

2

2

2

.

We need the assumption that L

1

and

L

2

are independent� Similarly, in the Figure 3�12b L = L

1

− L

2

, and if t

1

and t

2

are the tolerances on L

1

and L

2

respectively, then, assuming independence

between L

1

and L

2

, the tolerance on L is also given by

t t t

L

= +

1

2

2

2

.

Notice

that the “+” sign inside the radical of both formulas irrespective of whether L

is the sum or the difference of L

1

and ...