US 2011/0213587 A1 · METHOD AND COMPUTER PROGRAM PRODUCT FOR FINDING STATISTICAL BOUNDS, CORRESPONDING PARAMETER CORNERS, AND A PROBABILITY DENSITY FUNCTION OF A PERFORMANCE TARGET FOR A CIRCUIT

Abstract

Disclosed are embodiments of a method and an associated computer program product for finding the statistical bounds, the corresponding parameter corners and the probability density function of one or more performance targets for a circuit without requiring Monte Carlo simulation runs. To accomplish this, a joint probability density function for independent parameters that affect the performance target can be constructed. Then, based on the joint probability density function, the statistical bounds of the performance target can be found by constructing an equal-probability-density surface of the joint probability density function and solving a constrained optimization problem on that equal-probability-density surface. Once the statistical bounds are determined, the corresponding parameter corners for the performance target can also be determined. After obtaining multiple statistical bounds corresponding to different accumulated probability density, the probability density function of the performance target can also be obtained.

Claims25

Dependent claims

A method of finding statistical bounds for a performance target F of a circuit affected by M independent statistical model parameters (x1, x2, . . . , xM), where M is an integer, said method comprising:

determining, by a computer, a nominal value xj0, a standard deviation σj, and a probability density function {tilde over (p)}(xj;
xj0, σj) for each parameter xj, where j=1, 2, . . . , M;
constructing, by said computer, a joint probability density function {tilde over (P)}(x1, x2, . . . , xM), for all of said M independent statistical model parameters (x1, x2, . . . , xM), where
P
~

(
x
1
,
x
2
,
…

,
x
M
)
=
∏
j
=
1
M

p
~

(
x
j
;
x
j


0
,
σ
j
)
;
and,
based on said joint probability density function {tilde over (P)}(x1, x2, . . . , xM), determining, by said computer, said statistical bounds of said performance target F as defined by a symmetric interval from a lower statistical bound −Kσ to an upper statistical bound +Kσ by performing the following:
constructing a Kσ equal-probability-density surface S(x1, x2, . . . , xM;
K)=0 of said joint probability density function {tilde over (P)}(x1, x2, . . . , xM), and
solving a constrained optimization problem on said Kσ equal-probability-density surface S(x1, x2, . . . , xM;
K)=0 to determine said lower statistical bound −Kσ and said upper statistical bound +Kσ.

46 more elements

determining, by a computer, a nominal value xj0, a standard deviation uj, and a probability density function {tilde over (p)}(xj;
xj0, σj) for each parameter xj, where j=1, 2, . . . , M;
normalizing, by said computer, said M independent statistical model parameters (x1, x2, . . . , xM) to create M normalized parameters (u1, u2, . . . , uM);
constructing, by said computer, a joint probability density function P(u1, u2, . . . , uM) for all of said M normalized parameters (u1, u2, . . . , uM), where
P

(
u
1
,
y
2
,
…

,
u
M
)
=
∏
j
=
1
M

p

(
u
j
)


and


u
j
=
(
x
j
-
x
j


0
)
/
σ
j
;
and,
based on said joint probability density function P(u1, u2, . . . , uM), determining, by said computer, said statistical bounds of said performance target F as defined by a symmetric interval from a lower statistical bound −Kσ to an upper statistical bound +Kσ by performing the following:
constructing a Kσ equal-probability-density surface s(u1, u2, . . . , uM;
K)=0 of said second joint probability density function P(u1, u2, . . . , uM);
and
solving a constrained optimization problem on said Kσ equal-probability-density surface s(u1, u2, . . . , uM;
K)=0 to determine said lower statistical bound −Kσ and said upper statistical bound +Kσ.

58 more elements

A computer program product for performing a method of finding statistical bounds for a performance target F of a circuit affected by M independent statistical model parameters (x1, x2, . . . , xM), where M is an integer, said computer program product comprising:

a computer readable storage medium having computer readable program code embodied therewith, said computer readable program code configured to perform said method, said method comprising:
determining a nominal value xj0, a standard deviation σj, and a probability density function {tilde over (p)}(xj;
xj0, σj) for each parameter xj, where j=1, 2, . . . , M;
normalizing said M independent statistical model parameters (x1, x2, . . . , xM) to create M normalized parameters (u1, u2, . . . , uM);
constructing a joint probability density function P(u1, u2, . . . , uM) for all of said M normalized parameters (u1, u2, . . . , uM), where
P

(
u
1
,
y
2
,
…

,
u
M
)
=
∏
j
=
1
M

p

(
u
j
)


and


u
j
=
(
x
j
-
x
j


0
)
/
σ
j
;
and,
based on said joint probability density function P(u1, u2, . . . , uM), determining said statistical bounds of said performance target F as defined by a symmetric interval from a lower statistical bound −Kσ to an upper statistical bound +Kσ by performing the following:
constructing a Kσ equal-probability-density surface s(u1, u2, . . . , uM;
K)=0 of said second joint probability density function P(u1, u2, . . . , uM);
solving a constrained optimization problem on said Kσ equal-probability-density surface s(u1, u2, . . . , uM;
K)=0 to determine said lower statistical bound −Kσ and said upper statistical bound +Kσ.

58 more elements

Dependencies are inferred from the claim text.

Method and computer program product for finding statistical bounds, corresponding parameter corners, and a probability density function of a performance target for a circuit

Life of this patent

Method and computer program product for finding statistical bounds, corresponding parameter corners, and a probability density function of a performance target for a circuit

Life of this patent

Abstract

Claims25