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Biological Indicator
2010
Process LethalityCalculation and
Workbook
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The biological data derived from a sterilization process is qualitative information, such as
sterile or non-sterile, established by observing either growth or no growth of a biological
challenge. The process is challenged with calibrated bacterial spores with a defined
resistance to the sterilization process. The process is effective if the spore challenge is
killed (no growth). The process is not effective when the spore challenge survives.
When we expose replicate samples to replicate physical conditions we are able to expandour knowledge of the lethality being delivered by the sterilization process. This is
usually expressed as a probabilistic value and is capable of predicting results with a high
level of certainty.
This workbook is intended to provide you with the ability to express biological
measurements in numbers using standard mathematical formulas. These biological
numbers provide the quantative assessment of the sterilization process. When used
properly, the bacterial spore provides the most accurate measure of the effectiveness of
the sterilization process.
The population of the spore challenge is established using standard microbiological platecount procedures and is used in the following mathematical equations. The D-value is
the first assessment of the resistance of a biological challenge to a particular sterilization
process. The D-value is defined as the time in minutes that it takes at a specified set of
conditions to reduce the population of the biological challenge by one log or a factor of
ten. There are two basic approaches to establish the D-value. One approach is referred to
as the survivor curve method and the other is the fraction negative method. In the
survivor curve method, high levels of spores are exposed to successive short time periods
of sterilizing conditions. The data collected is the number of spores that survived the
sterilization conditions. The exposures are performed over increasing durations of clock
time. The surviving spores are recovered using standard microbiological plate count
techniques. The data is plotted on a semi log graph. The X axis is clock time and theY axis is the log scale of the number of spores recovered at each of the exposure times.
The slope of the curve is the D-value. The coefficient of determination (r2) is also
calculated. This coefficient indicates how close the data points are to the calculated
linear regression plot.
The D-value can also be calculated using fraction negative data from units exposed in the
quantal zone. There are two approaches to analyze this data. The first approach is
referred to as the Stumbo, Murphy, Cochran formula. This method calculates a D-value
from each fraction negative data point. When more than one data set is available, the
individual point D-values are summed and divided by the number of data points. This
method is quite useful for determining a process D-value when it may be difficult to
collect more than one fraction negative data set.
The second approach using fraction negative data sets is referred to as the Limited
Holcomb, Spearmen, Karber method. This method not only focuses on the quantal zone
data points, but it looks at the shortest time to all negative units and the longest time to all
positive units. It uses all the quantal zone values and the exposure interval to calculate
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the mean time to sterility. This approach is a little more robust than the Stumbo,
Murphy, Cochran method.
Now that spore populations have been identified and D-values have been established at
specific sets of conditions, the effect of varying temperature conditions can be evaluated.
The temperature coefficient or Z-value is defined as the temperature change required toalter the D-value by one log. This temperature coefficient can be applied to steam, dry
heat and ethylene oxide processes. The Z-value is best calculated using three D-values.
This can be performed graphically as well as calculated. The graphic plot is a semi log
plot with the X axis being the linear temperature scale and the Y axis the log plot ofthe D-values. The slope of the curve is the Z-value. The formula to calculate the slope is
the same log linear regression plot used for the survivor curve. The coefficient of
determination (r2) is also calculated using the same formula as in the survivor curve
method.
The Z-value allows the integration of different lethal rates for different temperatures. A
reference temperature or process set point must be identified. As temperatures increase,spores die faster. The Z-value provides an accurate assessment of lethality over the
normal process temperature variance as seen in come-up time, hold time and come-down
time process phases.
The temperature coefficient is now used to establish an equivalent process lethality (F-
value) at a defined reference temperature. The F-value integrates the varying process
conditions into an expression of equivalent process lethality. The equivalent process
lethality is usually described as equivalent process minutes at the reference temperature.
Complete and accurate temperature profiles are required for this calculation. This
establishes an accurate accumulated lethality value for a known biological challenge and
a dynamic process.
The F equivalent process lethality is now used to establish the equivalent spore log
reductions that are delivered by this equivalent process lethality value. This is
accomplished by dividing the F-value for the process by the process D-value. The result
is the spore log reductions (SLR) provided by the process.
The spore log reduction value is used to establish the sterility assurance level (SAL). The
sterility assurance level is used to assess the microbiological lethality of the process.
This value is the probability of a non-sterile unit (PNSU) occurring in the process.
Sterility assurance level is expressed as 10-x
. X is the log of the microbial challengeeither spores or bioburden, which is labeled N0 minus the SLR value delivered by the
process.
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Calculate the D-value Using the Limited Holcomb, Spearman,
Karber Method
You have collected the following fraction negative data that you will apply to the LimitedHolcomb-Spearman-Karber equations.
The process set at 121.0 C.The initial population N0 = 1.7 x 10
5.
Twenty (20) replicate BIs were used at each exposure.
Calculate the D-value using the data sheet provided.
Exposure Time Number of Units Exposed (n) Number of Units Sterile (r)
8 20 0
9 20 2
10 20 5
11 20 11
12 20 1813 20 20
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The Limited Holcomb, Spearman, Karber Method for
Fraction Negative Data
2507.0010
NLog
TD HSK
rxn
ddTT kHSK
2
THSK = mean time to sterility
Log10 N0 = spore population0.2507 = Eulers constant
Tk
= shortest time to all units sterile
d = time interval between data points
n = number of replicate units per testr = number of units sterile
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CALCULATION OF D-VALUE USING LIMITED-HOLCOMB-
SPEARMAN-KARBER (USP)
Sample Identification #: Exposure conditions:
In the table on the right, fill in the exposure times and # of units killed where: Data
f1= exposure time or dose where all units are positive i Exposure timer
(# units negative)
(at all shorter times or doses, all units are positive) 1
and 2
fk = exposure time or dose where all units are negative
(at all longer times or doses, all units are negative)3
4
Fill in the appropriate data in the blanks below: 5
Time (Tk) for achieving results fk 6
Difference between adjacent times (d) 7
Sample size (n) 8
Sum of the negative replicates ( r) from f1 to fk-1 9
(fk-1 is the time prior to fk) 10
Average spore count per carrier (No) 11
Log No= (round to 4 decimal places) 12
Calculate mean heating time (THSK) for achieving complete kill by the equation: 13
THSK = Tk- d/2 - (d/n * r)
14
( r) from f1 to fk-1(fk-1 is the time prior to fk)
THSK = (round to 4 decimal places)
Calculate D-value (D) by the equation:
D = (THSK)/ (Log No + 0.2507)
D = (round to 4 decimal places)
D-VALUE (rounded to 1 decimal place*)* values 0.0950 are rounded to 1 decimal place.
* values 0.0949 are rounded to 2 decimal places.
Calculation by: Date:
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CALCULATION OF D-VALUE USING LIMITED-HOLCOMB-
SPEARMAN-KARBER (USP)
Sample Identification #: Exposure conditions: 121C
In the table on the right, fill in the exposure times and # of units killed where: Data
f1= exposure time or dose where all units are positive i Exposure timer
(# units negative)
(at all shorter times or doses, all units are positive) 1 8 0
and 2 9 2
fk = exposure time or dose where all units are negative
(at all longer times or doses, all units are negative)3 10 5
4 11 11
Fill in the appropriate data in the blanks below: 5 12 18
Time (Tk) for achieving results fk 13 6 13 20
Difference between adjacent times (d) 1 7
Sample size (n) 20 8
Sum of the negative replicates ( r) from f1 to fk-1 36 9
(fk-1 is the time prior to fk) 10
Average spore count per carrier (No) 1.7 x 105 11
Log No= 5.2304 (round to 4 decimal places) 12
Calculate mean heating time (THSK) for achieving complete kill by the equation: 13
THSK = Tk- d/2 - (d/n * r)
14
( r) from f1 to fk-1(fk-1 is the time prior to fk)
36
3620
1
2
113 x
7.10)8.1()5.0(13
THSK = 10.7000 (round to 4 decimal places)
Calculate D-value (D) by the equation:
D = (THSK)/ (Log No + 0.2507)
9522.14811.5
7000.10
2507.02304.5
7000.10
D = 1.9522 (round to 4 decimal places)
D-VALUE (rounded to 1 decimal place*) 2.0* values 0.0950 are rounded to 1 decimal place.
* values 0.0949 are rounded to 2 decimal places.
Calculation by: Date:
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Using the Stumbo, Murphy, Cochran Method for Calculating the D-
Value
You have collected fraction negative data; your initial intent was to use the Limited Holcomb-
Spearman-Karber equation, but your data does not include two of the necessary data points. You
do not have a data point that indicated all surviving BIs and you do not have a data point with
all BIs killed. You must use the Stumbo, Murphy, Cochran method. Your process was set tocontrol at 121.0 C.
Calculate the D-value using the formula on the reverse side of this question.
The initial population N0 = 1.7 x 105.
Exposure Time Number of Exposed Units (n) Number of Units Sterile (r)
9 20 2
10 20 5
11 20 11
12 20 18
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The Stumbo, Murphy, Cochran Fraction Negative Data
( )
n
DDDD
n++
=21
110010
1
1
loglog uNN
UD
=
Nui =r
nln
U= exposure time
N0= starting spore population
Nu = most probable number of surviving spores
n = number units exposed
r= number units sterile (negative)
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CALCULATION OF D-VALUE USING
STUMBO-MURPHY-COCHRAN METHOD
Sample Identification #: ________________________ Exposure Conditions: ___________________________
* values 0.0950 are rounded to 1 decimal place.
* values 0.0949 are rounded to 2 decimal places.
Calculation by: _________________________________________________________________________ Date: ________________
Reviewed by: __________________________________________________________________________ Date: _______________
Sample size (n) =
Average spore count per carrier (No) = ___________________
Log No =___________________
In the table on the right, fill in the exposure times and # of units
killed starting with the shortest exposure. Round all numbers to 4
decimal laces*.
iExposure
Time (U)
Number
Killed (r)
Calculated
D-value
1
2
3
4
5
6
7
8
9
D-values = ____________average D-value = ______________
D-value = ______________
(round to 1 decimal place*)
Calculation of D1
NU1 = ln (n/r) = _______________
log NU1 = __________________
D1 = U1/(log N0 log NU1) = ___________________
Calculation of D2
NU2 = ln (n/r) = _______________
log NU2 = __________________
D2 = U2/(log N0 log NU2) = ___________________
Calculation of D3
NU3 = ln (n/r) = _______________
log NU3 = __________________
D3 = U3/(log N0 log NU3) = ___________________Calculation of D7
NU7 = ln (n/r) = _______________
log NU7 = __________________
D7 = U7/(log N0 log NU7) = ___________________
Calculation of D5
NU5 = ln (n/r) = _______________
log NU5 = __________________
D5 = U5/(log N0 log NU5) = ___________________
Calculation of D8
NU8 = ln (n/r) = _______________
log NU8 = __________________
D8 = U8/(log N0 log NU8) = ___________________
Calculation of D6
NU6 = ln (n/r) = _______________
log NU6 = __________________
D6 = U6/(log N0 log NU6) = ___________________
Calculation of D4
NU4 = ln (n/r) = _______________
log NU4 = __________________
D4 = U4/(log N0 log NU4) = ___________________
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CALCULATION OF D-VALUE USING
STUMBO-MURPHY-COCHRAN METHOD
Sample Identification #: ________________________ Exposure Conditions: 121C
* values 0.0950 are rounded to 1 decimal place.
* values 0.0949 are rounded to 2 decimal places.
Calculation by: _________________________________________________________________________ Date: ________________
Reviewed by: __________________________________________________________________________ Date: _______________
Sample size (n) = 20
Average spore count per carrier (No) = 1.7 x 105
Log No = 5.2304
In the table on the right, fill in the exposure times and # of units
killed starting with the shortest exposure. Round all numbers to 4
decimal places*.
iExposure
Time (U)
Number
Killed (r)
Calculated
D-value
1 8 0 NA
2 9 2 1.8487
3 10 5 1.9652
4 11 11 2.0169
5 12 18 1.9331
6 13 20 NA
7
8
9D-values = 7.7639
average D-value = 1.9410
D-value = 1.9
(round to 1 decimal place*)
Calculation of D1
NU1 = ln (n/r) = 2.3026
log NU1 = 0.3622
D1 = U1/(log N0 log NU1) = 8487.18682.4
9=
Calculation of D2
NU2 = ln (n/r) = 1.3863
log NU2 = 0.1419
D2 = U2/(log N0 log NU2) = 9652.10885.5
10=
Calculation of D3
NU3 = ln (n/r) = 0.5978
log NU3 = -0.2234
D3 = U3/(log N0 log NU3) = 0169.24538.5
11=
Calculation of D7
NU7 = ln (n/r) = _______________
log NU7 = __________________D7 = U7/(log N0 log NU7) = ___________________
Calculation of D5
NU5 = ln (n/r) = _______________
log NU5 = __________________
D5 = U5/(log N0 log NU5) = ___________________
Calculation of D8
NU8 = ln (n/r) = _______________
log NU8 = __________________
D8 = U8/(log N0 log NU8) = ___________________
Calculation of D6
NU6 = ln (n/r) = _______________
log NU6 = __________________
D6 = U6/(log N0 log NU6) = ___________________
Calculation of D4
NU4 = ln (n/r) = 0.1054
log NU4 = -0.9772
D4 = U4/(log N0 log NU4) = 9331.12076.6
12=
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Calculate the D-value Using the Survivor Curve Method
You are performing a D-value test using the survivor curve method. You collect the followingplate count data at the various exposure times. Your process is set to run at 121.0 C. The initial
population N0 = 2.2 x 105
Calculate the survivor curve D-value using the log linear regression method on the worksheet on
the back of this question.
Calculate the coefficient of determination r2
for the data.
Data Collected
Exposure Time Population Recovered
0.0 minutes 2.2 x 105
1.8 minutes 3.0 x 10
3.6 minutes 2.6 x 103
5.4 minutes 1.0 x 103
7.2 minutes 2.1 x 10
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The Survivor Curve D-value using the Log Linear Regression
Method
m = slope of the regression line
[ ][ ] ( )( )[ ][ ] [ ]221010
)()()(log)(log
=
xxn
yxyxnm
n = number of data points
y = recovered spore population
x = exposure time
r2
= coefficient of determination which indicates how close the data points are to the
predicted line
an r2
= 1.000 indicates all data points are on the predicted line
[ ][ ]
( )( )[ ]
n
yy
n
xx
n
yxyx
r
=
2
102
10
2
2
2
10
10
)(log)(log
)()(
)(log)()(log
2
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Calculation of D-value by Log Linear Regression (Survivor Curve)Sample Identification # Round all values to 4 decimal places. Use rounded values in calculations
Recovered
Population =y
Exposure
Time =x log10y x2
x(log10y) (log10y)2
(x)=A (log10y)=B (x2
)= C [x(log10y)]= G (log10y2
)]=E
Assigned Variable A = B = C= G = E=
Calculation of slope (m
) and D-value
Number of data points (n) = ________
m = slope of the regression line
)()]()[(
)])([()]()[(2
ACn
BAGnm
=
( )( )[ ] ( )( )[ ]
( )( )[ ] ( )2
=m
( )[ ] ( )[ ]( )[ ] ( )
=m
( )[ ]( )[ ]
=m
m = __________
=
m
valueD1
1
=
11valueD
( )1=valueD
D value = __________ _______________(rounded to one decimal)
Calculation of coefficient of determination (r)
( ) ( )
( ) ( )
=
n
BE
n
AC
n
BAG
r22
2
2
( ) ( )
( ) ( )
=
22
2
2r
( ) ( )[ ][ ]( ) ( )[ ] ( ) ( )[ ]
=
2
2r
( )[ ]( )[ ] ( )[ ]
2
2=r
( )( )=2r
r2
= __________
Calculations by: ____________________________ _____________
Date
Reviewed by: ______________________________ _____________
Date
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Calculation of D-value by Log Linear Regression (Survivor Curve)Sample Identification # Round all values to 4 decimal places. Use rounded values in calculations
Recovered
Population =y
Exposure
Time =x log10y x2
x(log10y) (log10y)2
1.7 x 10 0.0 5.2304 0.0000 0.0000 27.3571
3.0 x 104
2.0 4.4771 4.0000 8.9542 20.0444
1.0 x 10 4.0 3.0000 16.0000 12.0000 9.0000
6.0 x 10 6.0 2.7782 36.0000 16.6692 7.7184
1.1 x 101 8.0 1.0414 64.0000 8.3312 1.0845
(x)=A (log10y)=B (x2
)= C [x(log10y)]= G (log10y2
)]=E
Assigned Variable A = 20 B = 16.5271 C= 120.0000 G = 45.9546 E= 65.2044
Calculation of slope (m
) and D-value
Number of data points (n) = 5
m = slope of the regression line
)()]()[(
)])([()]()[(2
ACn
BAGnm
=
( )( )[ ] ( )( )[ ]
( )( )[ ] ( )22012055271.16209546.455
=m
( )[ ] ( )[ ]( )[ ] ( )400600
5420.3307730.229
=m
( )[ ]( )[ ]200
7690.100=m
m = -0.5038
=
m
valueD1
1
=
5038.0
11valueD
( )9849.11 =valueD
D value = 1.8911 2.0(rounded to one decimal)
Calculation of coefficient of determination (r)
( ) ( )
( ) ( )
=
n
BE
n
AC
n
BAG
r22
2
2
( ) ( )
( ) ( )
=
5
5271.16
2044.655
20
120
5
5271.16209546.45
22
2
2r
( ) ( )[ ][ ]( ) ( )[ ] ( ) ( )[ ]6290.542044.6580120
1084.669546.452
2
=r
( )[ ]( )[ ] ( )[ ]5754.1040
1538.202
2 =r
( )( )0160.423
1757.4062=r
r2 = 0.9602
Calculations by: ____________________________ _____________Date
Reviewed by: ______________________________ _____________
Date
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Sterilizing Value, Minutes
Example of Plotting the Survivor Curve on Semi Log Graph Paper
1.9 Min
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Example of Plotting the Survivor Curve on Semi Log Graph Paper
Sterilizing Value, Minutes
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Calculate the Z-value Using the Following Data:
D121 = 1.9522
D124 = 1.3127
D127 = 0.8650
ISO 11138 states three D-values between 110 and 130C
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Temperature Coefficient Z-value Using the Log Linear
Regression Method
m = the slope of the regression line
( ) [ ]( ) ( )( ) ( )( )
( ) ( )[ ] ( )[ ]22
1010 loglog
=
xxn
yxyxnm
n = number of data points
y = D-value
x = exposure temperature
r2
= coefficient of determination
[ ][ ]
( ) ( )[ ]n
yy
n
xx
n
yxyx
r
=
2102
10
2
2
2
10
10
)(log)(log)()(
)(log)()(log
2
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Calculation of Z-value by Log Linear RegressionCrop or Lot Number Round all values to 4 decimal places. Use rounded values in calculations.
D value =y
Exposure
Temperature =x
log10y x2 x(log10y) (log10y)2
(x)=A (log10y)=B (x2
)= C [x(log10y)]= G (log10y2
)]=E
Assigned
VariableA = B = C= G = E=
Calculation of slope (m) and Z-value
Number of D values (n) = ________
m = slope of the regression line
)()]()[(
)])([()]()[(2ACn
BAGnm
=
( )( )[ ] ( )( )[ ]
( )( )[ ] ( )2
=m
( )[ ] ( )[ ]( )[ ] ( )
=m
( )[ ]( )[ ]
=m
m = __________
=
mvalueZ
11
=
11valueZ
( )1=valueZ
Z value = _________ ______________(rounded to one decimal)
Calculation of coefficient of determination (r)
( ) ( )
( ) ( )
=
n
BE
n
AC
n
B
AGr
22
2
2
( ) ( )
( ) ( )
=22
2
2r
( ) ( )[ ][ ]( ) ( )[ ] ( ) ( )[ ]
=
2
2r
( )[ ]( )[ ] ( )[ ]
2
2=r
( )
( )=
2r
r2
= __________
Calculations by: ____________________________ _____________
Date
Reviewed by: ______________________________ _____________
Date
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Calculation of Z-value by Log Linear RegressionCrop or Lot Number Round all values to 4 decimal places. Use rounded values in calculations.
D value =y
Exposure
Temperature =x
log10y x2 x(log10y) (log10y)2
1.9522 121 0.2905 14641 35.1505 0.0844
1.3127 124 0.1182 15376 14.6568 0.0140
0.8650 127 -0.0630 16129 -8.0010 0.0040
(x)=A (log10y)=B (x2
)= C [x(log10y)]= G (log10y2
)]=E
Assigned
VariableA = 372 B = 0.3457 C= 46146 G = 41.8063 E= 0.1024
Calculation of slope (m) and Z-value
Number of D values (n) = 3
m = slope of the regression line
)()]()[(
)])([()]()[(2
ACn
BAGnm
=
( )( )[ ] ( )( )[ ]
( )( )[ ] ( )23724614633457.03728063.413
=m
( )[ ] ( )[ ]( )[ ] ( )138384138438
6004.1284189.125
=m
( )[ ]( )[ ]54
1815.3=m
m = -0.0589
=
mvalueZ
11
=
0589.0
11valueZ
( )9779.161 =valueZ
Z value = 16.9779 17.0(rounded to one decimal)
Calculation of coefficient of determination (r)
( ) ( )
( ) ( )
=
n
BE
n
AC
n
B
AGr
22
2
2
( ) ( )
( ) ( )
=
3
3457.01024.0
3
37246146
3
3457.03728063.41
22
2
2r
( ) ( )[ ][ ]( ) ( )[ ] ( ) ( )[ ]0398.01024.04612846146
8668.428063.412
2
=r
( )[ ]( )[ ] ( )[ ]0626.018
0605.12
2 =r
( )( )1268.1
1247.12=r
r2 = 0.9981
Calculations by: ____________________________ _____________
Date
Reviewed by: ______________________________ _____________
Date
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Example of Plotting the Z-value Curve on Semi Log Graph Paper
16.8C
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Plotting the Z-value Curve on Semi Log Graph Paper
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Process Equivalent Time F
=Z
TT
AZT
Aref
AreftF 10x,
Process Equivalent Lethality ++= AiAAAAref ZTZTZTZTZT FFFFF ,....,,,, 321 tA = process clock time interval, usually 1 minute
Tref= process reference temperature
ZA = actual Z-value for the spore challenge
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Process Equivalent Time
A typical time interval is 1 minute. tA = 1 minute, Tref= 121C, ZA = 8C.
Measure average temperature during 1 minute interval to calculate the iZTiF ,
Time(Min.) Temp. Formula ProcessEquivalent Time
T1 110C
10x110xmin1,1 ==
ZTF
T2 115C
10x110xmin1,2 ==
ZTF
T3 118C
10x110xmin1,3 ==
ZTF
T4 120C
10x110xmin1,4 ==
ZTF
T5 121C
10x110xmin1,5
==
ZT
F
T6 122C
10x110xmin1,6 ==
ZTF
T7 124C
10x110xmin1,7 ==
ZTF
T8 121C
10x110xmin1,8 ==
ZTF
T9 118C
10x110xmin1,9 ==
ZTF
T10 107C
10x110xmin1,10 ==
ZTF
T11 105C10x110xmin1,11 ==
ZTF
ZTF ,
= ZTZT iref FF ,,Process
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Process Equivalent Time
A typical time interval is 1 minute. tA = 1 minute, Tref= 121C, ZA = 8C.
Measure average temperature during 1 minute interval to calculate the iZTiF ,
Time(Min.)
Temp. Formula ProcessEquivalent
Time
T1 110C3750.1
8
110121
, 10x110xmin11
==ZTF 0.0422
T2 115C7500.0
8
115121
, 10x110xmin12
==ZTF 0.1778
T3 118C3750.0
8
118121
, 10x110xmin13
==ZTF 0.4217
T4 120C1250.08
120121
, 10x110xmin14
==ZTF
0.7499
T5 121C0
8
121121
, 10x110xmin15 ==
ZTF 1.0000
T6 122C1250.08
122121
, 10x110xmin16 ==
ZTF 1.3335
T7 124C3750.0
8
124121
, 10x110xmin17 ==
ZTF 2.3714
T8 121C0
8
121121
, 10x110xmin18 ==
ZTF 1.0000
T9 118C3750.0
8
118121
, 10x110xmin19
==ZTF 0.4217
T10 107C7500.1
8
107121
, 10x110xmin110
==ZTF 0.0178
T11 105C0000.2
8
105121
, 10x110xmin111
==ZTF 0.0100
ZTF , 7.5460
= ZTZT iref FF ,,Process
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Calculate the Process Spore Log Reduction Value
SLR =value-DProcess
AZ,
refT
FTimeEquivalentProcess
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Calculate the Process Spore Log Reduction (SLR) Value
The process equivalent time is 58.5 minutes.
The process D-value is 4.5 minutes.
Calculate the spore log reduction.
SLR =value-DProcess
AZ,
refT
FTimeEquivalentProcess
SLR = =
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Process Spore Log Reduction (SLR) Value
SLR = 13min5.4min5.58 =
Your process delivers 13 spore log reductions.
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Sterility Assurance Level
( )SLRNlog 01010SAL
=
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Calculate the Sterility Assurance Level
Your process used a spore challenge of 1.5 x 106
therefore, N0 = 1.5 x 106.
Process equivalent lethality is equal to 13 spore log reductions (SLR).
Calculate the sterility assurance level.
Calculation
SAL = 10logNo SLR
N0 =
logN0 =
Process equivalent lethality =
SAL =
SAL =
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Calculate the Sterility Assurance Level
Your process used a spore challenge of 1.5 x 106 therefore, N0 = 1.5 x 106.
Process equivalent lethality is equal to 13 spore log reductions (SLR).
Calculate the sterility assurance level.
Calculation
SAL = 10logNo SLR
N0 = 1.5 x 106
logN0 = 6.176
Process equivalent lethality = 13 SLR
SAL = 10(6.176 13)
SAL = 10-6.824
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Plotting the Survivor Curve on Semi Log Graph Paper
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Calculate the D-value Using the Limited Holcomb, Spearman,
Karber Method
You have collected the following fraction negative data that you will apply to the LimitedHolcomb-Spearman-Karber equations.
The process set at 121.0 C.The initial population N0 = 1.7 x 10
5.
Twenty (20) replicate BIs were used at each exposure.
Calculate the D-value using the data sheet provided.
Exposure Time Number of Units Exposed (n) Number of Units Sterile (r)
8 20 0
9 20 2
10 20 5
11 20 11
12 20 1813 20 20
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The Limited Holcomb, Spearman, Karber Method for
Fraction Negative Data
2507.0010
NLog
TD HSK
rxn
ddTT kHSK
2
THSK = mean time to sterility
Log10 N0 = spore population0.2507 = Eulers constant
Tk
= shortest time to all units sterile
d = time interval between data points
n = number of replicate units per testr = number of units sterile
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CALCULATION OF D-VALUE USING LIMITED-HOLCOMB-
SPEARMAN-KARBER (USP)
Sample Identification #: Exposure conditions:
In the table on the right, fill in the exposure times and # of units killed where: Data
f1= exposure time or dose where all units are positive i Exposure timer
(# units negative)
(at all shorter times or doses, all units are positive) 1
and 2
fk = exposure time or dose where all units are negative
(at all longer times or doses, all units are negative)3
4
Fill in the appropriate data in the blanks below: 5
Time (Tk) for achieving results fk 6
Difference between adjacent times (d) 7
Sample size (n) 8
Sum of the negative replicates ( r) from f1 to fk-1 9
(fk-1 is the time prior to fk) 10
Average spore count per carrier (No) 11
Log No= (round to 4 decimal places) 12
Calculate mean heating time (THSK) for achieving complete kill by the equation: 13
THSK = Tk- d/2 - (d/n * r)
14
( r) from f1 to fk-1(fk-1 is the time prior to fk)
THSK = (round to 4 decimal places)
Calculate D-value (D) by the equation:
D = (THSK)/ (Log No + 0.2507)
D = (round to 4 decimal places)
D-VALUE (rounded to 1 decimal place*)* values 0.0950 are rounded to 1 decimal place.
* values 0.0949 are rounded to 2 decimal places.
Calculation by: Date:
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CALCULATION OF D-VALUE USING LIMITED-HOLCOMB-
SPEARMAN-KARBER (USP)
Sample Identification #: Exposure conditions: 121C
In the table on the right, fill in the exposure times and # of units killed where: Data
f1= exposure time or dose where all units are positive i Exposure timer
(# units negative)
(at all shorter times or doses, all units are positive) 1 8 0
and 2 9 2
fk = exposure time or dose where all units are negative
(at all longer times or doses, all units are negative)3 10 5
4 11 11
Fill in the appropriate data in the blanks below: 5 12 18
Time (Tk) for achieving results fk 13 6 13 20
Difference between adjacent times (d) 1 7
Sample size (n) 20 8
Sum of the negative replicates ( r) from f1 to fk-1 36 9
(fk-1 is the time prior to fk) 10
Average spore count per carrier (No) 1.7 x 105 11
Log No= 5.2304 (round to 4 decimal places) 12
Calculate mean heating time (THSK) for achieving complete kill by the equation: 13
THSK = Tk- d/2 - (d/n * r)
14
( r) from f1 to fk-1(fk-1 is the time prior to fk)
36
3620
1
2
113 x
7.10)8.1()5.0(13
THSK = 10.7000 (round to 4 decimal places)
Calculate D-value (D) by the equation:
D = (THSK)/ (Log No + 0.2507)
9522.14811.5
7000.10
2507.02304.5
7000.10
D = 1.9522 (round to 4 decimal places)
D-VALUE (rounded to 1 decimal place*) 2.0* values 0.0950 are rounded to 1 decimal place.
* values 0.0949 are rounded to 2 decimal places.
Calculation by: Date:
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Using the Stumbo, Murphy, Cochran Method for Calculating the D-
Value
You have collected fraction negative data; your initial intent was to use the Limited Holcomb-
Spearman-Karber equation, but your data does not include two of the necessary data points. You
do not have a data point that indicated all surviving BIs and you do not have a data point with
all BIs killed. You must use the Stumbo, Murphy, Cochran method. Your process was set tocontrol at 121.0 C.
Calculate the D-value using the formula on the reverse side of this question.
The initial population N0 = 1.7 x 105.
Exposure Time Number of Exposed Units (n) Number of Units Sterile (r)
9 20 2
10 20 5
11 20 11
12 20 18
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The Stumbo, Murphy, Cochran Fraction Negative Data
( )
n
DDDD
n++
=21
110010
1
1
loglog uNN
UD
=
Nui =r
nln
U= exposure time
N0= starting spore population
Nu = most probable number of surviving spores
n = number units exposed
r= number units sterile (negative)
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CALCULATION OF D-VALUE USING
STUMBO-MURPHY-COCHRAN METHOD
Sample Identification #: ________________________ Exposure Conditions: ___________________________
* values 0.0950 are rounded to 1 decimal place.
* values 0.0949 are rounded to 2 decimal places.
Calculation by: _________________________________________________________________________ Date: ________________
Reviewed by: __________________________________________________________________________ Date: _______________
Sample size (n) =
Average spore count per carrier (No) = ___________________
Log No =___________________
In the table on the right, fill in the exposure times and # of units
killed starting with the shortest exposure. Round all numbers to 4
decimal laces*.
iExposure
Time (U)
Number
Killed (r)
Calculated
D-value
1
2
3
4
5
6
7
8
9
D-values = ____________average D-value = ______________
D-value = ______________
(round to 1 decimal place*)
Calculation of D1
NU1 = ln (n/r) = _______________
log NU1 = __________________
D1 = U1/(log N0 log NU1) = ___________________
Calculation of D2
NU2 = ln (n/r) = _______________
log NU2 = __________________
D2 = U2/(log N0 log NU2) = ___________________
Calculation of D3
NU3 = ln (n/r) = _______________
log NU3 = __________________
D3 = U3/(log N0 log NU3) = ___________________Calculation of D7
NU7 = ln (n/r) = _______________
log NU7 = __________________
D7 = U7/(log N0 log NU7) = ___________________
Calculation of D5
NU5 = ln (n/r) = _______________
log NU5 = __________________
D5 = U5/(log N0 log NU5) = ___________________
Calculation of D8
NU8 = ln (n/r) = _______________
log NU8 = __________________
D8 = U8/(log N0 log NU8) = ___________________
Calculation of D6
NU6 = ln (n/r) = _______________
log NU6 = __________________
D6 = U6/(log N0 log NU6) = ___________________
Calculation of D4
NU4 = ln (n/r) = _______________
log NU4 = __________________
D4 = U4/(log N0 log NU4) = ___________________
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CALCULATION OF D-VALUE USING
STUMBO-MURPHY-COCHRAN METHOD
Sample Identification #: ________________________ Exposure Conditions: 121C
* values 0.0950 are rounded to 1 decimal place.
* values 0.0949 are rounded to 2 decimal places.
Calculation by: _________________________________________________________________________ Date: ________________
Reviewed by: __________________________________________________________________________ Date: _______________
Sample size (n) = 20
Average spore count per carrier (No) = 1.7 x 105
Log No = 5.2304
In the table on the right, fill in the exposure times and # of units
killed starting with the shortest exposure. Round all numbers to 4
decimal places*.
iExposure
Time (U)
Number
Killed (r)
Calculated
D-value
1 8 0 NA
2 9 2 1.8487
3 10 5 1.9652
4 11 11 2.0169
5 12 18 1.9331
6 13 20 NA
7
8
9D-values = 7.7639
average D-value = 1.9410
D-value = 1.9
(round to 1 decimal place*)
Calculation of D1
NU1 = ln (n/r) = 2.3026
log NU1 = 0.3622
D1 = U1/(log N0 log NU1) = 8487.18682.4
9=
Calculation of D2
NU2 = ln (n/r) = 1.3863
log NU2 = 0.1419
D2 = U2/(log N0 log NU2) = 9652.10885.5
10=
Calculation of D3
NU3 = ln (n/r) = 0.5978
log NU3 = -0.2234
D3 = U3/(log N0 log NU3) = 0169.24538.5
11=
Calculation of D7
NU7 = ln (n/r) = _______________
log NU7 = __________________D7 = U7/(log N0 log NU7) = ___________________
Calculation of D5
NU5 = ln (n/r) = _______________
log NU5 = __________________
D5 = U5/(log N0 log NU5) = ___________________
Calculation of D8
NU8 = ln (n/r) = _______________
log NU8 = __________________
D8 = U8/(log N0 log NU8) = ___________________
Calculation of D6
NU6 = ln (n/r) = _______________
log NU6 = __________________
D6 = U6/(log N0 log NU6) = ___________________
Calculation of D4
NU4 = ln (n/r) = 0.1054
log NU4 = -0.9772
D4 = U4/(log N0 log NU4) = 9331.12076.6
12=
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Calculate the D-value Using the Survivor Curve Method
You are performing a D-value test using the survivor curve method. You collect the followingplate count data at the various exposure times. Your process is set to run at 121.0 C. The initial
population N0 = 2.2 x 105
Calculate the survivor curve D-value using the log linear regression method on the worksheet on
the back of this question.
Calculate the coefficient of determination r2
for the data.
Data Collected
Exposure Time Population Recovered
0.0 minutes 2.2 x 105
1.8 minutes 3.0 x 10
3.6 minutes 2.6 x 103
5.4 minutes 1.0 x 103
7.2 minutes 2.1 x 10
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The Survivor Curve D-value using the Log Linear Regression
Method
m = slope of the regression line
[ ][ ] ( )( )[ ][ ] [ ]221010
)()()(log)(log
=
xxn
yxyxnm
n = number of data points
y = recovered spore population
x = exposure time
r2
= coefficient of determination which indicates how close the data points are to the
predicted line
an r2
= 1.000 indicates all data points are on the predicted line
[ ][ ]
( )( )[ ]
n
yy
n
xx
n
yxyx
r
=
2
102
10
2
2
2
10
10
)(log)(log
)()(
)(log)()(log
2
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Calculation of D-value by Log Linear Regression (Survivor Curve)Sample Identification # Round all values to 4 decimal places. Use rounded values in calculations
Recovered
Population =y
Exposure
Time =x log10y x2
x(log10y) (log10y)2
(x)=A (log10y)=B (x2
)= C [x(log10y)]= G (log10y2
)]=E
Assigned Variable A = B = C= G = E=
Calculation of slope (m
) and D-value
Number of data points (n) = ________
m = slope of the regression line
)()]()[(
)])([()]()[(2
ACn
BAGnm
=
( )( )[ ] ( )( )[ ]
( )( )[ ] ( )2
=m
( )[ ] ( )[ ]( )[ ] ( )
=m
( )[ ]( )[ ]
=m
m = __________
=
m
valueD1
1
=
11valueD
( )1=valueD
D value = __________ _______________(rounded to one decimal)
Calculation of coefficient of determination (r)
( ) ( )
( ) ( )
=
n
BE
n
AC
n
BAG
r22
2
2
( ) ( )
( ) ( )
=
22
2
2r
( ) ( )[ ][ ]( ) ( )[ ] ( ) ( )[ ]
=
2
2r
( )[ ]( )[ ] ( )[ ]
2
2=r
( )( )=2r
r2
= __________
Calculations by: ____________________________ _____________
Date
Reviewed by: ______________________________ _____________
Date
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Calculation of D-value by Log Linear Regression (Survivor Curve)Sample Identification # Round all values to 4 decimal places. Use rounded values in calculations
Recovered
Population =y
Exposure
Time =x log10y x2
x(log10y) (log10y)2
1.7 x 10 0.0 5.2304 0.0000 0.0000 27.3571
3.0 x 104
2.0 4.4771 4.0000 8.9542 20.0444
1.0 x 10 4.0 3.0000 16.0000 12.0000 9.0000
6.0 x 10 6.0 2.7782 36.0000 16.6692 7.7184
1.1 x 101 8.0 1.0414 64.0000 8.3312 1.0845
(x)=A (log10y)=B (x2
)= C [x(log10y)]= G (log10y2
)]=E
Assigned Variable A = 20 B = 16.5271 C= 120.0000 G = 45.9546 E= 65.2044
Calculation of slope (m
) and D-value
Number of data points (n) = 5
m = slope of the regression line
)()]()[(
)])([()]()[(2
ACn
BAGnm
=
( )( )[ ] ( )( )[ ]
( )( )[ ] ( )22012055271.16209546.455
=m
( )[ ] ( )[ ]( )[ ] ( )400600
5420.3307730.229
=m
( )[ ]( )[ ]200
7690.100=m
m = -0.5038
=
m
valueD1
1
=
5038.0
11valueD
( )9849.11 =valueD
D value = 1.8911 2.0(rounded to one decimal)
Calculation of coefficient of determination (r)
( ) ( )
( ) ( )
=
n
BE
n
AC
n
BAG
r22
2
2
( ) ( )
( ) ( )
=
5
5271.16
2044.655
20
120
5
5271.16209546.45
22
2
2r
( ) ( )[ ][ ]( ) ( )[ ] ( ) ( )[ ]6290.542044.6580120
1084.669546.452
2
=r
( )[ ]( )[ ] ( )[ ]5754.1040
1538.202
2 =r
( )( )0160.423
1757.4062=r
r2 = 0.9602
Calculations by: ____________________________ _____________Date
Reviewed by: ______________________________ _____________
Date
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Sterilizing Value, Minutes
Example of Plotting the Survivor Curve on Semi Log Graph Paper
1.9 Min
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Example of Plotting the Survivor Curve on Semi Log Graph Paper
Sterilizing Value, Minutes
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Calculate the Z-value Using the Following Data:
D121 = 1.9522
D124 = 1.3127
D127 = 0.8650
ISO 11138 states three D-values between 110 and 130C
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Temperature Coefficient Z-value Using the Log Linear
Regression Method
m = the slope of the regression line
( ) [ ]( ) ( )( ) ( )( )
( ) ( )[ ] ( )[ ]22
1010 loglog
=
xxn
yxyxnm
n = number of data points
y = D-value
x = exposure temperature
r2
= coefficient of determination
[ ][ ]
( ) ( )[ ]n
yy
n
xx
n
yxyx
r
=
2102
10
2
2
2
10
10
)(log)(log)()(
)(log)()(log
2
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Calculation of Z-value by Log Linear RegressionCrop or Lot Number Round all values to 4 decimal places. Use rounded values in calculations.
D value =y
Exposure
Temperature =x
log10y x2 x(log10y) (log10y)2
(x)=A (log10y)=B (x2
)= C [x(log10y)]= G (log10y2
)]=E
Assigned
VariableA = B = C= G = E=
Calculation of slope (m) and Z-value
Number of D values (n) = ________
m = slope of the regression line
)()]()[(
)])([()]()[(2ACn
BAGnm
=
( )( )[ ] ( )( )[ ]
( )( )[ ] ( )2
=m
( )[ ] ( )[ ]( )[ ] ( )
=m
( )[ ]( )[ ]
=m
m = __________
=
mvalueZ
11
=
11valueZ
( )1=valueZ
Z value = _________ ______________(rounded to one decimal)
Calculation of coefficient of determination (r)
( ) ( )
( ) ( )
=
n
BE
n
AC
n
B
AGr
22
2
2
( ) ( )
( ) ( )
=22
2
2r
( ) ( )[ ][ ]( ) ( )[ ] ( ) ( )[ ]
=
2
2r
( )[ ]( )[ ] ( )[ ]
2
2=r
( )
( )=
2r
r2
= __________
Calculations by: ____________________________ _____________
Date
Reviewed by: ______________________________ _____________
Date
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Calculation of Z-value by Log Linear RegressionCrop or Lot Number Round all values to 4 decimal places. Use rounded values in calculations.
D value =y
Exposure
Temperature =x
log10y x2 x(log10y) (log10y)2
1.9522 121 0.2905 14641 35.1505 0.0844
1.3127 124 0.1182 15376 14.6568 0.0140
0.8650 127 -0.0630 16129 -8.0010 0.0040
(x)=A (log10y)=B (x2
)= C [x(log10y)]= G (log10y2
)]=E
Assigned
VariableA = 372 B = 0.3457 C= 46146 G = 41.8063 E= 0.1024
Calculation of slope (m) and Z-value
Number of D values (n) = 3
m = slope of the regression line
)()]()[(
)])([()]()[(2
ACn
BAGnm
=
( )( )[ ] ( )( )[ ]
( )( )[ ] ( )23724614633457.03728063.413
=m
( )[ ] ( )[ ]( )[ ] ( )138384138438
6004.1284189.125
=m
( )[ ]( )[ ]54
1815.3=m
m = -0.0589
=
mvalueZ
11
=
0589.0
11valueZ
( )9779.161 =valueZ
Z value = 16.9779 17.0(rounded to one decimal)
Calculation of coefficient of determination (r)
( ) ( )
( ) ( )
=
n
BE
n
AC
n
B
AGr
22
2
2
( ) ( )
( ) ( )
=
3
3457.01024.0
3
37246146
3
3457.03728063.41
22
2
2r
( ) ( )[ ][ ]( ) ( )[ ] ( ) ( )[ ]0398.01024.04612846146
8668.428063.412
2
=r
( )[ ]( )[ ] ( )[ ]0626.018
0605.12
2 =r
( )( )1268.1
1247.12=r
r2 = 0.9981
Calculations by: ____________________________ _____________
Date
Reviewed by: ______________________________ _____________
Date
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Example of Plotting the Z-value Curve on Semi Log Graph Paper
16.8C
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Plotting the Z-value Curve on Semi Log Graph Paper
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Process Equivalent Time F
=Z
TT
AZT
Aref
AreftF 10x,
Process Equivalent Lethality ++= AiAAAAref ZTZTZTZTZT FFFFF ,....,,,, 321 tA = process clock time interval, usually 1 minute
Tref= process reference temperature
ZA = actual Z-value for the spore challenge
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Process Equivalent Time
A typical time interval is 1 minute. tA = 1 minute, Tref= 121C, ZA = 8C.
Measure average temperature during 1 minute interval to calculate the iZTiF ,
Time(Min.) Temp. Formula ProcessEquivalent Time
T1 110C
10x110xmin1,1 ==
ZTF
T2 115C
10x110xmin1,2 ==
ZTF
T3 118C
10x110xmin1,3 ==
ZTF
T4 120C
10x110xmin1,4 ==
ZTF
T5 121C
10x110xmin1,5
==
ZT
F
T6 122C
10x110xmin1,6 ==
ZTF
T7 124C
10x110xmin1,7 ==
ZTF
T8 121C
10x110xmin1,8 ==
ZTF
T9 118C
10x110xmin1,9 ==
ZTF
T10 107C
10x110xmin1,10 ==
ZTF
T11 105C10x110xmin1,11 ==
ZTF
ZTF ,
= ZTZT iref FF ,,Process
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Process Equivalent Time
A typical time interval is 1 minute. tA = 1 minute, Tref= 121C, ZA = 8C.
Measure average temperature during 1 minute interval to calculate the iZTiF ,
Time(Min.)
Temp. Formula ProcessEquivalent
Time
T1 110C3750.1
8
110121
, 10x110xmin11
==ZTF 0.0422
T2 115C7500.0
8
115121
, 10x110xmin12
==ZTF 0.1778
T3 118C3750.0
8
118121
, 10x110xmin13
==ZTF 0.4217
T4 120C1250.08
120121
, 10x110xmin14
==ZTF
0.7499
T5 121C0
8
121121
, 10x110xmin15 ==
ZTF 1.0000
T6 122C1250.08
122121
, 10x110xmin16 ==
ZTF 1.3335
T7 124C3750.0
8
124121
, 10x110xmin17 ==
ZTF 2.3714
T8 121C0
8
121121
, 10x110xmin18 ==
ZTF 1.0000
T9 118C3750.0
8
118121
, 10x110xmin19
==ZTF 0.4217
T10 107C7500.1
8
107121
, 10x110xmin110
==ZTF 0.0178
T11 105C0000.2
8
105121
, 10x110xmin111
==ZTF 0.0100
ZTF , 7.5460
= ZTZT iref FF ,,Process
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Calculate the Process Spore Log Reduction Value
SLR =value-DProcess
AZ,
refT
FTimeEquivalentProcess
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Calculate the Process Spore Log Reduction (SLR) Value
The process equivalent time is 58.5 minutes.
The process D-value is 4.5 minutes.
Calculate the spore log reduction.
SLR =value-DProcess
AZ,
refT
FTimeEquivalentProcess
SLR = =
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Process Spore Log Reduction (SLR) Value
SLR = 13min5.4min5.58 =
Your process delivers 13 spore log reductions.
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Sterility Assurance Level
( )SLRNlog 01010SAL
=
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Calculate the Sterility Assurance Level
Your process used a spore challenge of 1.5 x 106
therefore, N0 = 1.5 x 106.
Process equivalent lethality is equal to 13 spore log reductions (SLR).
Calculate the sterility assurance level.
Calculation
SAL = 10logNo SLR
N0 =
logN0 =
Process equivalent lethality =
SAL =
SAL =
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Calculate the Sterility Assurance Level
Your process used a spore challenge of 1.5 x 106 therefore, N0 = 1.5 x 106.
Process equivalent lethality is equal to 13 spore log reductions (SLR).
Calculate the sterility assurance level.
Calculation
SAL = 10logNo SLR
N0 = 1.5 x 106
logN0 = 6.176
Process equivalent lethality = 13 SLR
SAL = 10(6.176 13)
SAL = 10-6.824
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Plotting the Survivor Curve on Semi Log Graph Paper
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Biological Indicator
2010
Process LethalityCalculation and
Workbook
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The biological data derived from a sterilization process is qualitative information, such as
sterile or non-sterile, established by observing either growth or no growth of a biological
challenge. The process is challenged with calibrated bacterial spores with a defined
resistance to the sterilization process. The process is effective if the spore challenge is
killed (no growth). The process is not effective when the spore challenge survives.
When we expose replicate samples to replicate physical conditions we are able to expandour knowledge of the lethality being delivered by the sterilization process. This is
usually expressed as a probabilistic value and is capable of predicting results with a high
level of certainty.
This workbook is intended to provide you with the ability to express biological
measurements in numbers using standard mathematical formulas. These biological
numbers provide the quantative assessment of the sterilization process. When used
properly, the bacterial spore provides the most accurate measure of the effectiveness of
the sterilization process.
The population of the spore challenge is established using standard microbiological platecount procedures and is used in the following mathematical equations. The D-value is
the first assessment of the resistance of a biological challenge to a particular sterilization
process. The D-value is defined as the time in minutes that it takes at a specified set of
conditions to reduce the population of the biological challenge by one log or a factor of
ten. There are two basic approaches to establish the D-value. One approach is referred to
as the survivor curve method and the other is the fraction negative method. In the
survivor curve method, high levels of spores are exposed to successive short time periods
of sterilizing conditions. The data collected is the number of spores that survived the
sterilization conditions. The exposures are performed over increasing durations of clock
time. The surviving spores are recovered using standard microbiological plate count
techniques. The data is plotted on a semi log graph. The X axis is clock time and theY axis is the log scale of the number of spores recovered at each of the exposure times.
The slope of the curve is the D-value. The coefficient of determination (r2) is also
calculated. This coefficient indicates how close the data points are to the calculated
linear regression plot.
The D-value can also be calculated using fraction negative data from units exposed in the
quantal zone. There are two approaches to analyze this data. The first approach is
referred to as the Stumbo, Murphy, Cochran formula. This method calculates a D-value
from each fraction negative data point. When more than one data set is available, the
individual point D-values are summed and divided by the number of data points. This
method is quite useful for determining a process D-value when it may be difficult to
collect more than one fraction negative data set.
The second approach using fraction negative data sets is referred to as the Limited
Holcomb, Spearmen, Karber method. This method not only focuses on the quantal zone
data points, but it looks at the shortest time to all negative units and the longest time to all
positive units. It uses all the quantal zone values and the exposure interval to calculate
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the mean time to sterility. This approach is a little more robust than the Stumbo,
Murphy, Cochran method.
Now that spore populations have been identified and D-values have been established at
specific sets of conditions, the effect of varying temperature conditions can be evaluated.
The temperature coefficient or Z-value is defined as the temperature change required toalter the D-value by one log. This temperature coefficient can be applied to steam, dry
heat and ethylene oxide processes. The Z-value is best calculated using three D-values.
This can be performed graphically as well as calculated. The graphic plot is a semi log
plot with the X axis being the linear temperature scale and the Y axis the log plot ofthe D-values. The slope of the curve is the Z-value. The formula to calculate the slope is
the same log linear regression plot used for the survivor curve. The coefficient of
determination (r2) is also calculated using the same formula as in the survivor curve
method.
The Z-value allows the integration of different lethal rates for different temperatures. A
reference temperature or process set point must be identified. As temperatures increase,spores die faster. The Z-value provides an accurate assessment of lethality over the
normal process temperature variance as seen in come-up time, hold time and come-down
time process phases.
The temperature coefficient is now used to establish an equivalent process lethality (F-
value) at a defined reference temperature. The F-value integrates the varying process
conditions into an expression of equivalent process lethality. The equivalent process
lethality is usually described as equivalent process minutes at the reference temperature.
Complete and accurate temperature profiles are required for this calculation. This
establishes an accurate accumulated lethality value for a known biological challenge and
a dynamic process.
The F equivalent process lethality is now used to establish the equivalent spore log
reductions that are delivered by this equivalent process lethality value. This is
accomplished by dividing the F-value for the process by the process D-value. The result
is the spore log reductions (SLR) provided by the process.
The spore log reduction value is used to establish the sterility assurance level (SAL). The
sterility assurance level is used to assess the microbiological lethality of the process.
This value is the probability of a non-sterile unit (PNSU) occurring in the process.
Sterility assurance level is expressed as 10-x
. X is the log of the microbial challengeeither spores or bioburden, which is labeled N0 minus the SLR value delivered by the
process.
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