
614 Current Trends in Bayesian Methodology with Applications
FIGURE 29.2
A pro file of surface roughness (R
a
).
0.00031 mm and 0.0 0082 mm. After lapping, based mainly on the capability
of the lapping process itself and the equipment, the typical obtained surface
roughness produced is a pproximately between 0.00005 mm and 0.00050 mm
[1].
29.5.2 Fuzzy Bayesian inference
The obtained surface roughness (X) is modeled with an expo nential distribu-
tion a nd fuzzy gamma density as a-priori density for the parameter θ ∈ (0 , ∞).
X ∼ Ex
θ
ˆ=f(x|θ) =
1
θ
exp
h
−
x
θ
i
·1
(0,∞)
(x)
The a-priori density π(·) for
˜
θ (mean value of obtained surface rough-
ness) is assumed to be