Daniel,
Sorry for the terse initial post. I mistakenly assumed that the remainder of the code was irrelevant, Here is an example of the complete code.
In[1]:= Clear["Global`*"]
In[2]:= f[x_, b_, p_] =
DiracDelta[x] (1 - Exp[-b/p]) + Exp[-(x + b)/p]/p
Out[2]= E^((-b - x)/p)/p + (1 - E^(-(b/p))) DiracDelta[x]
In[3]:= capF[s_] =
Assuming[b \[Element] Reals && b > 0,
Simplify[LaplaceTransform[f[x, b, p], x, s]]]
Out[3]= (1 + p s - E^(-(b/p)) p s)/(1 + p s)
In[4]:= g[s_, k_] =
capF[s] /. {b -> Subscript[b, k], p -> Subscript[p, k]}
Out[4]= (1 + s Subscript[p, k] -
E^(-(Subscript[b, k]/Subscript[p, k])) s Subscript[p, k])/(1 +
s Subscript[p, k])
In[5]:= fSum[y_] =
InverseLaplaceTransform[Expand[Product[g[s, k], {k, 1, 6}]], s, y];
In[6]:= bdb = {83, 92, 96, 99, 100, 95} - 15 - 80
Out[6]= {-12, -3, 1, 4, 5, 0}
In[7]:= setb = Table[Subscript[b, k] -> 10^(.1 bdb[[k]]), {k, 1, 6}]
Out[7]= {Subscript[b, 1] -> 0.0630957, Subscript[b, 2] -> 0.501187,
Subscript[b, 3] -> 1.25893, Subscript[b, 4] -> 2.51189,
Subscript[b, 5] -> 3.16228, Subscript[b, 6] -> 1.}
In[8]:= setp =
Table[Subscript[p, k] -> 10^(.1 (bdb[[k]] + 15)), {k, 1, 6}]
Out[8]= {Subscript[p, 1] -> 1.99526, Subscript[p, 2] -> 15.8489,
Subscript[p, 3] -> 39.8107, Subscript[p, 4] -> 79.4328,
Subscript[p, 5] -> 100., Subscript[p, 6] -> 31.6228}
In[9]:= pfa = .01;
initThresh = 700
Out[10]= 700
In[11]:= threshold =
FindRoot[Integrate[
fSum[y] /. Catenate[{setb, setp}], {y, detThresh, \[Infinity]}] ==
pfa, {detThresh, initThresh}]
During evaluation of In[11]:= FindRoot::nlnum: The function value {False} is not a list of numbers with dimensions {1} at {detThresh} = {700.}. >>
During evaluation of In[11]:= FindRoot::nlnum: The function value {False} is not a list of numbers with dimensions {1} at {detThresh} = {700.}. >>
Out[11]= FindRoot[\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(detThresh\), \
\(\[Infinity]\)]\(\((fSum[y] /.
Catenate[{setb, setp}])\) \[DifferentialD]y\)\) ==
pfa, {detThresh, initThresh}]
In[12]:= threshold =
FindRoot[Integrate[
fSum[y] /. Catenate[{setb, setp}], {y, detThresh, \[Infinity]}] -
pfa, {detThresh, initThresh}]
{detThresh -> 697.83}
The notebook doesn't look quite like the code above so I am also including an image. If it would help I can also attach the file.