Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 15 ppsx

3.3 Analytic Development of Reliability and Performance in Engineering Design 123
Computation:
(only X) and (only Y)andG ⇒ (only Range (G, X, Y))
Flow [corners (Q,
η
,
ω
)] = (0.0375, 0.075, 0.45, 0.9) m
3
/min
Flow [range (Q,
η
,
ω
)] = < flow 2.25 54 > m
3
/h
Propagation result:
Flow (Q ) = < all-parts only flow 2.25 54 >
Elimination condition:
(only X
1
) and (only X
2
)andNot(X
1
∩X
2
)
Subset interval:
System requirement: X

1
= < flow 1.50 60 > m
3
/h
Subset interval: X
2
= < flow 2.25 54 > m
3
/h
Computation:
(X
1
∩X
2
) = < flow 2.25 54 > m
3
/h
Elimination result:
Condition: Not (X
1
∩X
2
) ⇒true
Description:
With the labelled interval o f displacement between 0.5 ×10
−3
and 6 ×10
−3
cu-
bic metre per revolution and the labelled interval of RPM in the interval of 75

to 150RPM, the pumpscan produce flows only in the interval of2 .25 to 54m
3
/h.
The elimination condition is true in that the labelled interval of flow does no t
meet the system requirement of:
System requirement: X
1
= < flow 1.50 60 > m
3
/h
Subset interval: X
2
= < flow 2.25 54 > m
3
/h
3.3.1.6 Labelled Interval Calculus in Designing for Reliability
An approach to designing for reliability th at integrates functional failure as well as
functional performance considerations so that a maximum safety margin is achieved
with respect to all performance criteria is considered (Thompson et al. 1999). This
approach has b een expanded to represent sets of systems functioning under sets of
failure and performance intervals. The labelled interval calculus (LIC) formalises
an approach for reasoning about these sets. The application of LIC in designing
for reliability produces a design that has the highest possible safety margin with
respect to intervals of performance values relating to specific system datasets. The
most significant advantage of this expanded method is that, besides not having to
rely on the propagation of single estimated values of failure data, it also does not
have to rely on the determination of single values of maximum and minimum ac-
ceptable limits of performance for each criterion. Instead, constraint propagation of
intervals about sets of performance values is applied, making it possible to compute
a multi-objective optimisation of conceptual design solution sets to different sets of

performance intervals.
124 3 Reliability and Performance in Engineering Design
Multi-objective optimisation of c onceptual design problems can be computed by
applying LIC inference rules, which draw conclusions about the sets of systems
under consideration to determine optimal solution sets to d ifferent intervals of per-
formance values. Considering the performance limits represented diagram matically
in Figs. 3.23, 3.24and 3.25, where an example of two performancelimits, one upper
perfor mance limit, and one lower performance limit is given, the determination of
datasets using LIC would include the following.
a) Determination of a Data Point: Two Sets of L imit Intervals
The proximity of actual performance to the minimum, nominal or maximum sets of
limit intervals of performance for each performance criterion relates to a measure
of the safety margin range.
The data point x
ij
is the value closest to the nominal design condition that ap-
proaches either minimu m or maximum limit interval. The value of x
ij
always lies
in the range 0–10. Ideally, when the design condition is at the mid-range, then the
data point is 10. A set of data points can thus be obtained for each system with re-
spect to the performance parameters that are relevant to that system. In this case, the
data point x
ij
approaching the maximum limit interval is the performance variable
of temperature
x
ij
=
Max. Temp. T

1
−Nom. T High (×20)
Max. Temp. T
1
−Min. Temp. T
2
(3.83)
Given relationship: dataset:
(Max. Temp. T
1
−Nom. T High)/(Max. Temp. T
1
−Min. Temp. T
2
) ×20
where
Max. Temp. T
1
= maximum performance interval
Min. Temp. T
2
= minimum performance interval
Nom. T High = nominal performance interval high
Labelled intervals:
Max. Temp. T
1
= < all-parts only T
1
t
1l

t
1h
>
Min. Temp. T
2
= < all-parts only T
2
t
2l
t
2h
>
Nom.T High = < all-parts only T
H
t
Hl
t
Hh
>
where
t
1l
= lowest temperature value in interval of
maximum performance interval.
t
1h
= highest temperature value in interval of
maximum performance interval.
t
2l

= lowest temperature value in interval of
minimum performance interval.
t
2h
= highest temperature value in interval of
minimum performance interval.
3.3 Analytic Development of Reliability and Performance in Engineering Design 125
t
Hl
= lowest temperature value in interval of
nominal performance interval high.
t
Hh
= highest temperature value in interval of
nominal performance interval high.
Computation: propagation rule 1:
(only X) and (only Y)andG ⇒ (only Range (G, X, Y))
x
ij
[corners (Max. Temp. T
1
,Nom.T High, Min. Temp. T
2
)]
=(t
1h
−t
Hl
/t
1l

−t
2h
) ×20 , (t
1h
−t
Hl
/t
1l
−t
2l
) ×20 ,
(t
1h
−t
Hl
/t
1h
−t
2h
) ×20 , (t
1h
−t
Hl
/t
1h
−t
2l
) ×20 ,
(t
1l

−t
Hl
/t
1l
−t
2h
) ×20 , (t
1l
−t
Hl
/t
1l
−t
2l
) ×20 ,
(t
1l
−t
Hl
/t
1h
−t
2h
) ×20 , (t
1l
−t
Hl
/t
1h
−t

2l
) ×20 ,
(t
1h
−t
Hh
/t
1l
−t
2h
) ×20 , (t
1h
−t
Hh
/t
1l
−t
2l
) ×20 ,
(t
1h
−t
Hh
/t
1h
−t
2h
) ×20 , (t
1h
−t

Hh
/t
1h
−t
2l
) ×20 ,
(t
1l
−t
Hh
/t
1l
−t
2h
) ×20 , (t
1l
−t
Hh
/t
1l
−t
2l
) ×20 ,
(t
1l
−t
Hh
/t
1h
−t

2h
) ×20 , (t
1l
−t
Hh
/t
1h
−t
2l
) ×20 ,
x
ij
[range (Max. Temp. T
1
,Nom.T High, Min. Temp. T
2
)]
=(t
1l
−t
Hh
/t
1h
−t
2l
) ×20 , (t
1h
−t
Hl
/t

1l
−t
2h
) ×20
Propagation result:
x
ij
= < all-parts only
x
ij
(t
1l
−t
Hh
/t
1h
−t
2l
) ×20 , (t
1h
−t
Hl
/t
1l
−t
2h
) ×20 >
where x
ij
is dimensionless.

Description:
The generation of data points with respect to performance limits using the la-
belled interval calculus, approaching the maximum limit interval.
This is where the data point x
ij
approaching the maximum limit interval, with x
ij
in the range (Max.Temp.T
1
,Nom.T High, Min. Temp. T
2
), and the data point x
ij
being dimensionless,has a propagationresult equivalent to the following labelled
interval:
< all-parts only x
ij
(t
1l
−t
Hh
/t
1h
−t
2l
)×20 , (t
1h
−t
Hl
/t

1l
−t
2h
)×20 > ,which
represents the relationship:
x
ij
=
Max. Temp. T
1
−Nom. T High (×20)
Max. Temp. T
1
−Min. Temp. T
2
In the case of the data point x
ij
approaching the minimum limit interval,where
the performance variable is temperature
x
ij
=
Nom. T Low−Min. Temp. T
2
(×20)
Max. Temp. T
1
−Min. Temp. T
2
(3.84)

126 3 Reliability and Performance in Engineering Design
Given relationship: dataset:
(Max. Temp. T
1
−Nom. T High)/(Max. Temp. T
1
−Min. Temp. T
2
) ×20
where
Max. Temp. T
1
= maximum performance interval
Min. Temp. T
2
= minimum performance interval
Nom. T Low = nominal performance interval low
Labelled intervals:
Max. Temp. T
1
= < all-parts only T
1
t
1l
t
1h
>
Min. Temp. T
2
= < all-parts only T

2
t
2l
t
2h
>
Nom. T Low = < all-parts only T
L
t
Ll
t
Lh
>
where
t
1i
= lowest temperature value in interval of
maximum performance interval
t
1h
= highest temperature value in interval of
maximum performance interval
t
2l
= lowest temperature value in interval of
minimum performance interval
t
2h
= highest temperature value in interval of
minimum performance interval

t
Ll
= lowest temperature value in interval of
nominal performance interval low
t
Lh
= highest temperature value in interval of
nominal performance interval low
Computation: propagation rule 1 :
(only X) and (only Y)andG ⇒ (only Range (G, X, Y))
x
ij
[corners (Max. Temp. T
1
,Nom.T High, Min. Temp. T
2
)]
=(t
Lh
−t
2l
/t
1l
−t
2h
) ×20 , (t
Lh
−t
2l
/t

1l
−t
2l
) ×20 ,
(t
Lh
−t
2l
/t
1h
−t
2h
) ×20 , (t
Lh
−t
2l
/t
1h
−t
2l
) ×20 ,
(t
Ll
−t
2l
/t
1l
−t
2h
) ×20 , (t

Ll
−t
2l
/t
1l
−t
2l
) ×20 ,
(t
Ll
−t
2l
/t
1h
−t
2h
) ×20 , (t
Ll
−t
2l
/t
1h
−t
2l
) ×20 ,
(t
Lh
−t
2h
/t

1l
−t
2h
) ×20 , (t
Lh
−t
2h
/t
1l
−t
2l
) ×20 ,
(t
Lh
−t
2h
/t
1h
−t
2h
) ×20 , (t
Lh
−t
2h
/t
1h
−t
2l
) ×20 ,
(t

Ll
−t
2h
/t
1l
−t
2h
) ×20 , (t
Ll
−t
2h
/t
1l
−t
2l
) ×20 ,
(t
Ll
−t
2h
/t
1h
−t
2h
) ×20 , (t
Ll
−t
2h
/t
1h

−t
2l
) ×20 ,
x
ij
[range (Max. Temp. T
1
,Nom.T High, Min. Temp. T
2
)]
=(t
Ll
−t
2h
/t
1h
−t
2l
) ×20 , (t
Lh
−t
2l
/t
1l
−t
2h
) ×20
3.3 Analytic Development of Reliability and Performance in Engineering Design 127
Propagation result:
x

ij
= < all-parts only
x
ij
(t
Ll
−t
2h
/t
1h
−t
2l
) ×20 , (t
Lh
−t
2l
/t
1l
−t
2h
) ×20 >
where x
ij
is dimensionless.
Description:
The generation of data points with respect to performance limits using the la-
belled interval calculus, in the case of the data point x
ij
approachingthe minimum
limit interval, with x

ij
in the range (Max. Temp. T
1
,Nom.T High, Min. Temp.
T
2
), and x
ij
dimensionless, has a propagation result equivalent to the following
labelled interval:
< all-parts only x
ij
(t
Ll
−t
2h
/t
1h
−t
2l
) ×20 , (t
Lh
−t
2l
/t
1l
−t
2h
) ×20 >
which represents the relationship:

x
ij
=
Nom. T Low−Min. Temp. T
2
(×20)
Max. Temp. T
1
−Min. Temp. T
2
b) Determination of a Data Point: One Upper Limit I nterval
If there is one operating limit set only, then the data point is obtained as shown in
Figs. 3.24 and 3.25, where the upper or lower limit is known. A set of data points
can be obtained for each system with respect to the performance parameters that are
relevant to that system. In the case of the data point x
ij
approaching the upper limit
interval
x
ij
=
Highest Stress Level−Nominal Stress Level (×10)
Highest Stress Level−Lowest Stress Est.
(3.85)
Given relationship: dataset:
(HSL−NSL)/(HSL−LSL) ×10
Labelled intervals:
HSI = highest stress interval < all-parts only HSI s
1l
s

1h
>
LSI = lowest stress interval < all-parts only LSI s
2l
s
2h
>
NSI = nominal stress interval < all-parts only NSI s
Hl
s
Hh
>
where:
s
1l
= lowest stress value in interval of highest stress interval
s
1h
= highest stress value in interval of highest stress interval
s
2l
= lowest stress value in interval of lowest stress interval
s
2h
= highest stress value in interval of lowest stress interval
s
Hl
= lowest stress value in interval of nominal stress interval
s
Hh

= highest stress value in interval of nominal stress interval
128 3 Reliability and Performance in Engineering Design
Computation: propagation rule 1 :
(only X) and (only Y)andG ⇒(only Range (G, X, Y))
x
ij
[corners (HSL, NSL, LSL)]
=(s
1h
−s
Hl
/s
1l
−s
2h
) ×10 , (s
1h
−s
Hl
/s
1l
−s
2l
) ×10 ,
(s
1h
−s
Hl
/s
1h

−s
2h
) ×10 , (s
1h
−s
Hl
/s
1h
−s
2l
) ×10 ,
(s
1l
−s
Hl
/s
1l
−s
2h
) ×10 , (s
1l
−s
Hl
/s
1l
−s
2l
) ×10 ,
(s
1l

−s
Hl
/s
1h
−s
2h
) ×10 , (s
1l
−s
Hl
/s
1h
−s
2l
) ×10 ,
(s
1h
−s
Hh
/s
1l
−s
2h
) ×10 , (s
1h
−s
Hh
/s
1l
−s

2l
) ×10 ,
(s
1h
−s
Hh
/s
1h
−s
2h
) ×10 , (s
1h
−s
Hh
/s
1h
−s
2l
) ×10 ,
(s
1l
−s
Hh
/s
1l
−s
2h
) ×10 , (s
1l
−s

Hh
/s
1l
−s
2l
) ×10 ,
(s
1l
−s
Hh
/s
1h
−s
2h
) ×10 , (s
1l
−s
Hh
/s
1h
−s
2l
) ×10 ,
x
ij
[range (HSL, NSL, LSL)]
=(s
1l
−s
Hh

/s
1h
−s
2l
) ×10 , (s
1h
−s
Hl
/s
1l
−s
2h
) ×10
Propagation result:
x
ij
= < all-parts only
x
ij
(s
1l
−s
Hh
/s
1h
−s
2l
) ×10 , (s
1h
−s

Hl
/s
1l
−s
2h
) ×10 >
where x
ij
is dimensionless.
Description:
The data point x
ij
approachingthe upperlimit interval, with x
ij
in the range (High
Stress Level, Nominal Stress Level, Lowest Stress Level), and x
ij
dimensionless,
has a propagation result equivalent to the following labelled interval:
< all-parts only x
ij
(s
Ll
−s
2h
/s
1h
−s
2l
) ×20 , (s

Lh
−s
2l
/s
1l
−s
2h
) ×20 > ,
which represents the relationship:
x
ij
=
Highest Stress Level−Nominal Stress Level (×10)
Highest Stress Level−Lowest Stress Est.
c) Determination o f a Data Point: One Lower Limit I nterval
In the case of the data point x
ij
approaching the lower limit interval
x
ij
=
Nominal Capacity−Min. Capacity Level (×10)
Max. Capacity Est.−Min. Capacity Level
(3.86)
Given relationship: dataset:
(Nom. Cap. L−Min. Cap. L)/(Max. Cap. L−Min. Cap. L) ×10
where
Max. Cap. C
1
= m a ximum capacity interval

Min. Cap. C
2
= m inimum capacity interval
Nom. Cap. C
L
= nominal capacity interval low
3.3 Analytic Development of Reliability and Performance in Engineering Design 129
Labelled intervals:
Max. Cap. C
1
= < all-parts only C
1
c
1l
c
1h
>
Min. Cap. C
2
= < all-parts only C
2
c
2l
c
2h
>
Nom. Cap. C
L
= < all-parts only C
L

c
Ll
c
Lh
>
where
c
1l
= lowest capacity value in interval of maximum
capacity interval
c
1h
= highest capacity value in interval of maximum
capacity interval
c
2l
= lowest capacity value in interval of minimum
capacity interval
c
2h
= highest capacity value in interval of minimum
capacity interval
c
Ll
= lowest capacity value in interval of nominal capacity
interval low
c
Lh
= highest capacity value in interval of nominal
capacity interval low

Computation: propagation rule 1:
(only X) and (only Y)andG ⇒ (only Range (G, X, Y))
x
ij
[corners (Max. Cap. Min. Cap. C
2
,Nom.Cap.C
L
)]
=(c
Lh
−c
2l
/c
1l
−c
2h
) ×10 , (c
Lh
−c
2l
/c
1l
−c
2l
) ×10 ,
(c
Lh
−c
2l

/c
1h
−c
2h
) ×10 , (c
Lh
−c
2l
/c
1h
−c
2l
) ×10 ,
(c
Ll
−c
2l
/c
1l
−c
2h
) ×10 , (c
Ll
−c
2l
/c
1l
−c
2l
) ×10 ,

(c
Ll
−c
2l
/c
1h
−c
2h
) ×10 , (c
Ll
−c
2l
/c
1h
−c
2l
) ×10 ,
(c
Lh
−c
2h
/c
1l
−c
2h
) ×10 , (c
Lh
−c
2h
/c

1l
−c
2l
) ×10 ,
(c
Lh
−c
2h
/c
1h
−c
2h
) ×10 , (c
Lh
−c
2h
/c
1h
−c
2l
) ×10 ,
(c
Ll
−c
2h
/c
1l
−c
2h
) ×10 , (c

Ll
−c
2h
/c
1l
−c
2l
) ×10 ,
(c
Ll
−c
2h
/c
1h
−c
2h
) ×10 , (c
Ll
−c
2h
/c
1h
−c
2l
) ×10 ,
x
ij
[range (Max. Cap. Min. Cap. C
2
,Nom.Cap.C

L
)]
=(c
Ll
−c
2h
/c
1h
−c
2l
) ×10 , (c
Lh
−c
2l
/c
1l
−c
2h
) ×10
Propagation result:
x
ij
= < all-parts only
x
ij
(c
Ll
−c
2h
/c

1h
−c
2l
) ×10 , (c
Lh
−c
2l
/c
1l
−c
2h
) ×10 >
where x
ij
is dimensionless.
Description:
The generation of data points with respect to performance limits using the la-
belled interval calculus for the lower limit interval is the following:
130 3 Reliability and Performance in Engineering Design
The data pointx
ij
approachingthe lower limitinterval, with x
ij
in the range (Max.
Capacity Level, Min. Capacity Level, Nom. Capacity Level), and x
ij
dimension-
less, has a propagation result equivalent to the following labelled interval:
< all-parts only x
ij

(c
Ll
−c
2h
/c
1h
−c
2l
) ×10 , (c
Lh
−c
2l
/c
1l
−c
2h
) ×10 >
with x
ij
in the range (Max. Cap. Min. Cap. C
2
,Nom.Cap.C
L
), representing the
relationship:
x
ij
=
Nominal Capacity−Min. Capacity Level(×10)
Max. Capacity Est.−Min. Capacity Level

d) Analysis of the Interval Matrix
In Fig. 3.26, the performance measures of each system of a process are described
in matrix form containing data points relating to pr ocess systems and single pa-
rameters that describe their performance. The matrix can be analysed by rows and
columns in order to evaluate the performance characteristics of the process. Each
data point of x
ij
refers to a single parameter. Similar ly, in the expande d method
using labelled interval calculus (LIC), the performance measures of each system of
a process are described in an interval matrix form, containing datasets relatin g to
systems and labelled intervals that describe their performance. Each row of the in-
terval matrix reveals whether the process has a consistent safety margin with respect
to a specific set o f p erformance values.
A parameter performance index, PPI, can be calculated for each row
PPI = n

n
∑
j= 1
1

x
ij

−1
(3.87)
where n is th e number of systems in row i.
The calculation of PPI is accomplished using LIC inference rules that draw con-
clusions about the system datasets of each matrix row under consideration. The
numerical value of PPI lies in the range 0–10, irrespective of the number of datasets

in each row (i.e. the number of process systems). A comparison of PPIs can be made
to judge whether specific performance criteria, such as reliability, are acceptable.
Similarly, a system performance index, SPI, can be calculated for each column as
SPI = m

m
∑
i=1
1

x
ij

−1
(3.88)
where m is the number of parameters in column i.
The calculation of SPI is accomplished using LIC inference rules that draw con-
clusions about performance labelled intervals of each matrix column under con-
sideration. The numerical value of SPI also lies in the range 0–10, irrespective of
the number of labelled in tervals in each column (i.e. the number of performance
3.3 Analytic Development of Reliability and Performance in Engineering Design 131
parameters). A comparison of SPIs can be made to assess whether there is accept-
able performance with respect to any performance criteria of a specific system.
Finally, an overall performance index, OPI, can be calculated (Eq. 3.89). The
numerical value of OPI lies in the range 0–100 and can be indicated as a percentage
value.
OPI =
1
mn


m
∑
i=1
n
∑
j= 1
(PPI)(SPI)

(3.89)
where m is the number of performance parameters, and n is the number of systems.
Description of Example
Acidic gases, such as sulphur dioxide, are removed from the combustion gas emis-
sions of a non-ferrous metal smelter by passing these through a reverse jet scrub-
ber. A reverse jet scrubber consists of a scrubber vessel containing jet-spray nozzles
adapted to spray,under high pressure, a caustic scrubbing liquid counter to the high-
velocity combustion gas stream emitted by the smelter, whereby the combustion gas
stream is scrubbed and a clear gas stream is recovered downstream. The reverse jet
scrubber consists of a scrubber vessel and a subset of three centrifugal pumps in
parallel, any two of which are continually operational, with the following labelled
intervals for the specific performance parameters (Tables 3.10 and 3.11):
Propagation result:
x
ij
= < all-parts only
x
ij
(x
1l
−x
Hh

/x
1h
−x
2l
) ×10 , (x
1h
−x
Hl
/x
1l
−x
2h
) ×10 >
Table 3.10 Labelled intervals for specific performance parameters
Parameters Vessel Pump 1 Pump 2 Pump 3
Max. flow < 65 75 ><55 60 ><55 60 ><65 70 >
Min. flow < 30 35 ><20 25 ><20 25 ><30 35 >
Nom. flow < 50 60 ><40 50 ><40 50 ><50 60 >
Max. pressure < 10000 12500 ><8500 10000 ><8500 10000 ><12500 15000 >
Min. pressure < 1000 1500 ><1000 1250 ><1000 1250 ><2000 2500 >
Nom. pressure < 5000 7500 ><5000 6500 ><5000 6500 ><7500 10000 >
Max. temp. < 80 85 ><85 90 ><85 90 ><80 85 >
Min. temp. < 60 65 ><60 65 ><60 65 ><55 60 >
Nom. temp. < 70 75 ><75 80 ><75 80 ><70 75 >
Table 3.11 Parameter interval matrix
Parameters Vessel Pump 1 Pump 2 Pump 3
Flow (m
3
/h) < 1.18.3 ><1.36.7 ><1.36.7 ><1.18.3 >
Pressure (kPa) < 2.28.8 ><2.26.9 ><2.26.9 ><1.97.5 >

Temp. (
◦
C) < 2.010.0 ><1.77.5 ><1.77.5 ><1.75.0 >
132 3 Reliability and Performance in Engineering Design
Labelled intervals—flow:
Vessel interval: = < all-parts only x
ij
1.18.3 >
Pump1interval:= < all-parts only x
ij
1.36.7 >
Pump2interval:= < all-parts only x
ij
1.36.7 >
Pump3interval:= < all-parts only x
ij
1.18.3 >
Labelled intervals—pressure:
Vessel interval: = < all-parts only x
ij
2.28.8 >
Pump1interval:= < all-parts only x
ij
2.26.9 >
Pump2interval:= < all-parts only x
ij
2.26.9 >
Pump3interval:= < all-parts only x
ij
1.97.5 >

Labelled intervals—temperature:
Vessel interval: = < all-parts only x
ij
2.010.0 >
Pump1interval:= < all-parts only x
ij
1.77.5 >
Pump2interval:= < all-parts only x
ij
1.77.5 >
Pump3interval:= < all-parts only x
ij
1.75.0 >
The parameter performance index, PPI, can be calculated for each row
PPI = n

n
∑
j= 1
1

x
ij

−1
(3.90)
where n is th e number of systems in row i.
Labelled intervals:
Flow (m
3

/h) PPI = < all-parts only PPI 1.27.4 >
Pressure (kPa) PPI = < all-parts only PPI 2.17.5 >
Temp. (
◦
C) PPI = < all-parts only PPI 1.87.1 >
The system performance index, SPI, can be calculated for each column
SPI = m

m
∑
i=1
1

x
ij

−1
(3.91)
where m is the number of parameters in column i.
Labelled intervals:
Vessel SPI = < all-parts only 1.69.0 >
Pump 1 SPI = < all-parts only 1.77.0 >
Pump 2 SPI = < all-parts only 1.77.0 >
Pump 3 SPI = < all-parts only 1.56.6 >
Description:
The parameter performance index, PPI,andthesystem performance index, SPI,
indicate whether there is acceptable overall performance of the operational pa-
rameters (PPI), and what contribution an item makes to the overall effectiveness
of the system (SPI).