semi合集-English.pdf - 第246页
SEMI E35-0305 © SEMI 1995, 2005 15 – P [Item is conforming, All gauges show conforming] A1-5.2.4 The overall value, T , is calculated from the equation: T = n i i 1 (10) NOTE 3: This equation is based on th…
SEMI E35-0305 © SEMI 1995, 2005 14
xxf
xLSL
LSL
M
d1
(5)
A1-4.4.3 For a characteristic with both upper and lower specifications limits, use the following equations to
calculate
and
:
USL
LSL
M
USL
LSL
M
xxf
xLSL
xxf
xUSL
d
d1
(6)
xxf
xLSLxUSL
xxf
xLSLxUSL
USL
MM
LSL
MM
d
d
(7)
A1-5 Extensions of the Methodology to More Complex Situations
A1-5.1 In general, when a single characteristic on a unit is measured once on a single gauge and 100% sampling is
employed, the model will take the form described earlier. If the situation is more complex, the nature of the model
will be different. Factors that can affect the nature of the model include the following:
number of units examined (lot acceptance sampling vs. 100% sampling),
number of times a unit is inspected (single vs. multiple),
effect of the inspection process on the unit (destructive vs. non-destructive),
number of item characteristics examined for a single decision (one vs. many), and
cost functions associated with the business decisions (fixed vs. variable).
A1-5.2 Extension to Multiple Gauges
A1-5.2.1 To extend the model to multiple gauges, one must make the additional assumption that all measuring
gauges are measuring the same characteristic.
A1-5.2.1.1 In addition, define a conforming item as one that all gauges show the measured characteristic to be in
specification.
A1-5.2.1.2 A nonconforming item is taken to be one in which at least one gauge shows the measured characteristic
to be outside of specification.
A1-5.2.2 It is then possible to define a set of
and
error rates for each gauge. Let
1
,
2
, …,
n
be the
values
and
1
,
2
, …,
n
be the
values associated with the n different gauges.
A1-5.2.3 The overall
value,
T
, is calculated from the equation:
T
=
n
i
i
1
1
(9)
where:
xxf
USL
d
, and
f(x) = PDF of the characteristic being measured.
NOTE 2: This equation is based on the probability P that the item is conforming but that one or more gauges give a conforming
result:
T
= P[Item is conforming, 1 gauges show nonconforming]
= P[Item is conforming]
SEMI E35-0305 © SEMI 1995, 2005 15
– P[Item is conforming, All gauges show conforming]
A1-5.2.4 The overall
value,
T
, is calculated from the equation:
T
=
n
i
i
1
(10)
NOTE 3: This equation is based on the probability P that the item is nonconforming but that all gauges give a conforming result:
T
= P[Item is nonconforming, All gauges show pass]
A1-5.3 Extension to Multiple Inspections with the Same Metrology System
A1-5.3.1 Multiple inspection with the same metrology system is a special case of inspection with multiple gauges.
If the same measurement system is used to measure the item characteristic repeatedly, one merely lets
i
=
and
i
=
for all i, as the
and
error rates will not change for the same gauge.
A1-5.4 Extension to Decisions Based on Multiple Characteristics
A1-5.4.1 It is also possible to develop a model where a decision is based on more than one characteristic. As with
the case of multiple gauges, several assumptions must be made.
A1-5.4.1.1 The characteristics being measured are independent or an independent combination of their values is
used.
A1-5.4.1.2 All tests are performed before a decision to reject or pass is made.
A1-5.4.1.3 F(x) has been deconvolved from F·G.
A1-5.4.1.4 A conforming unit is defined as one in which all measured characteristics are shown to be within
specification.
A1-5.4.1.5 A nonconforming unit is taken to be one in which at least one characteristic is outside of specification.
A1-5.4.2 It is then possible to define a set of
and
errors for each gauge. Let
1
,
2
, …,
n
be the
values and
1
,
2
, …,
n
be the
values associated with the n different characteristics.
A1-5.4.3 The overall
value,
T
, is calculated from the equation:
T
=
n
i
n
i
ii
11
1
(11)
where:
USL
ii
xxf d
, and
f
i
(x) = PDF of the characteristic i.
This equation is based on the probability P that all characteristics conform, but that at least one test failed:
T
= P[All characteristics conform, At least one test failed]
= P[All characteristics conform]
– P[All characteristics conform, All tests passed]
A1-5.4.4 The overall
value,
T
, is calculated from the equation:
T
=
n
i
n
i
ii
P
11
1
(12)
where:
P
i
= proportion of observations within specification for characteristic i.
This equation is based on the probability P that one or more characteristics are nonconforming but that all tests
passed:
T
= P[1 characteristic nonconforming, All tests passed]
SEMI E35-0305 © SEMI 1995, 2005 16
= P[All pass]
– P[All characteristics conform, All tests passed]