Initial Tolerance Allocation
After the flowdown has been completed in a qualitative respect and specification limits and a target value for a systemlevel critical parameter have been set, the next step is to allocate tolerances from the critical parameter to the subordinate y's and x's involved in the flowdown.
Initial tolerance allocation is the quantitative part of the critical parameter flowdown. Tolerances may be available from suppliers for some of the subordinate y's and x's. For others, the initial tolerance may be the start of communication with the suppliers and assembly and manufacturing areas involved in the supply chain. If the supplier already has a proposed tolerance, it could be helpful for the engineering team to compare the tolerances proposed by the suppliers to a baseline to ascertain whether the suppliers' tolerances align with reasonable or expected tolerances.
The approach described in this section can be used for a variety of situations:
 Schedule allocation: Starting with best case/most likely/worst case durations for developing features, and allocating these to subtasks required to develop the feature.
 Timing/delay allocation: Starting with a range or mean and standard deviation for overall timing for a feature or function, and allocating the total timing or delay to the individual tasks.
 Mechanical tolerance allocation: Allocating tolerances that are additive, like tolerances for components in a gap analysis.
 Electrical tolerance allocation: Allocating tolerances for a function to its subfunctions when the transfer function is not necessarily additive and some of the subordinate y's or x's might be in different units than the Y (for example, the Y may be frequency in MHz and the x's might be capacitance in pF and inductance in nH).
A stepbystep approach for allocating tolerances to the subordinate y's and x's is provided here. The Excel template shown in Figure 10.17 can be downloaded to assist with these calculations. The subordinate y's and x's are both referred to as subordinate y's and treated the same in this approach. If the transfer function is a simple additive or sum of terms function, then the slopes will be set to unity. If the transfer function is a simple multiplicative or product of terms function, then a logarithmic transform could allow the same approach to be used, with the slopes similarly set to unity.
 Determine Tolerance for Y: Target, USL and LSL.
 Determine Target or Most Likely Values for subordinate y's: Y_{T,i} and slopes: b_{i} = dY/dy_{i}.
 Estimate the constant percent tolerance for each subordinate y_{i}
:
 For each subordinate y, set USL(y_{i} ) = y_{T,i} (1 + k _{max}).
 If the Tolerance for Y is symmetrical, set LSL(y_{i} ) = y_{T,i} (1  k _{max}).
 If the Tolerance for Y is not symmetrical:
 Determine the constant percent tolerance for each subordinate y to its lower limit:
 Set LSL(y_{i} ) = y_{T,i} (1  k _{min}).
 Determine the constant percent tolerance for each subordinate y to its lower limit:
Figure 10.17. Excel worksheet for quantitative flowdown of allocated tolerances
Units 
LSL 
Target 
USL 
kmin 
kmax 

Frequency 
MHz 
2.4 
2.5 
2.7 
0.07 
0.13 

Subordinate y's 
Units 
Slope 
Target 
Allocated LSL 
Target 
Allocated USL 

Capacitor 1 
pF 
0.24793 
2 
1.9 
2.0 
2.3 

Capacitor 2 
pF 
0.24793 
1 
0.9 
1.0 
1.1 

Varactor Sensitivity 
pF/V 
0.48868 
1 
0.9 
1.0 
1.1 

Inductor 
nH 
0.15582 
8 
7.5 
8.0 
9.0 

Voltage 
V 
0.24793 
2 
1.9 
2.0 
2.3 
As illustrated in Figure 10.2, these allocated tolerances should be shared with suppliers and manufacturing and assembly engineers, or with supply chain experts who can work with suppliers and manufacturers.
The quantitative aspect of the flowdown described in the previous section will be applied through an Excel worksheet set up as a template, as shown in Figure 10.17. Figure 10.15 includes a subordinate y called "center frequency." The quantitative flowdown for the subordinate y of center frequency for the VCO is illustrated in Figure 10.17, using the template that can be downloaded from http://www.sigmaexperts.com/dfss/chapter10allocation. The transfer function for the center frequency is not additive; it is a constant divided by the square root of the product of the inductor value and the sum of the capacitances for the two capacitors and the varactor. This transfer function was evaluated to obtain slopes for frequency versus each factor for use with the spreadsheet template.