Standard practice for applying statistics to analysis of corrosion data
Some standard content:
National Standard of the People's Republic of China
Standard method for statistical analysis of corrosion data
Standard practice for applying statistics analysis of corrosion data 1 Main content and scope of application
GB12336—90
1.1 This standard aims to provide a general method for statistical analysis of corrosion test data. This standard provides methods for designing corrosion tests, analyzing corrosion data, and determining the reliability of corrosion data. 1.2 This standard includes the following contents:
Errors and their identification and treatment
Standard error
Probability curve
Curve fitting-least square method
Confidence interval estimation of the true value of the mean
Comparison of near-means
Data comparison on probability curve
Sample population
Variance analysis
Three-water semi-factorial experimental design
1.3 The above methods can be selected according to the needs of processing corrosion data. 2 Errors and their identification and treatment
2.1 Whether it is laboratory research or field failure analysis, various measurements must be made: However, measurements cannot be very accurate and errors will always occur. For this reason, a certain measurement is usually repeated many times. This repetition allows us to use statistical methods to determine the accuracy of the measurement data.
2.2 Statistical methods cannot eliminate errors, but they can estimate the size of errors. The premise of statistical analysis is that the errors obey a normal distribution or a specific distribution. Errors come from the test process and the data processing process. In order to reduce errors and ensure that all sources of errors can be clearly identified, it is extremely important to be careful and meticulous during the experiment and calculation process. 2.2.1 Normal distribution
If a batch of corrosion specimens of a certain thickness are prepared from an alloy beech, it is obvious that all the specimens cannot have exactly the same thickness. There will always be some errors, which are called random errors. The number of specimens in a certain thickness range is plotted against the thickness, and a histogram curve is obtained. The shape of this curve is similar to the characteristics shown in Figure 1. This is the normal distribution function. It should be noted that not all experimental errors obey the normal distribution. The histogram can be used to determine whether the data obeys the normal distribution, but the largest number of data, at least one, should be obtained.
Approved by the National Technical Supervision Bureau on April 27, 1990 and implemented on December 1, 1990
2.2.2 Systematic reading
GB 12336-90
The product of the number of samples measured by the test is 73%
Figure 1 Normal distribution curve
In the above example, if different people measure the thickness of the corrosion samples and draw a graph according to the above method, each person can obtain a normal distribution curve based on their own data, and the maximum value of the curve will be located on the left and right of the maximum value of the curve in Figure 1 respectively. This error is called systematic error, not random error.
2.2.3 Negligence Error
In experiments and data calculations, the abnormal values caused by the error are called negligence errors and should be eliminated. Otherwise, they will have an adverse effect on the statistical processing of the data and will also lead to incorrect conclusions when analyzing problems: abnormal values can be identified by statistical methods because the probability of such values is low.
2.2.4 Significant Figures
2.2.4.1 When reporting results, the correct number of significant figures should be given. For example, 2700 indicates four significant figures, that is, accurate to ±1; 2.7×103 indicates two significant figures, that is, accurate to ±100. 2.2.4.2 In the calculation process, the method of retaining one non-significant figure can be used to reduce rounding errors, but the non-significant figures should be discarded when the results are finally given. For example. The correct result of 2 700 "7.07" is 2 707, not 2 707.07. 2.2.5 Transfer of errors in calculation
2.2.5.1 Mathematical operations on data will inevitably cause changes in the original errors of the data. Generally, two types of errors need to be considered: (1) maximum error and (2) possible error. The maximum error can be obtained from the manual of the measuring instrument, which includes both systematic error and random error. The possible error is related to the standard deviation caused by random error when the systematic error is known or negligible. 2.2.5. 2 The maximum error can be calculated according to formula (1): (1)
In the formula, the quantity to be calculated is the function of the observed variable, % the maximum error:
Ax. The maximum error of an independent variable
Formula (1) All X are assumed to be independent variables, otherwise the partial differential values of the non-independent variables should be merged in brackets to form the partial differential of the independent variable. When merging, the signs of the partial differentials should be noted. 2.2.5.3 If the standard deviation is known, then
is: ) The standard deviation of
;
. The standard deviation of
,
2.2. 5. 4 If it is assumed that each X is independent, when GB 1233690
Q(XX..X.) - AxX..X
, formula (1) can be simplified to:
=(+[)+ +
4-ax x I +sx.
, formula (1) can be simplified to:
A nax, + x— + x,
3 standard deviation
(3)
3.1 The twenty-four × values in Table 3 are the weight loss values of a special alloy after being exposed to seawater for several months, in mg/(dm\·d). All data can be described as: (1) the average value, which is the arithmetic mean of all numbers. (2) the median, which is the middle value of the data arranged in ascending order (because it is a false number, it is equal to the average of the first and third data). When individual data deviate significantly from the rest of the data: the median is more meaningful than the average. (3) standard deviation α. 3. 2 The standard deviation of a set of data is defined as follows: 7)
, = X,-
, where: -
standard deviation:
number of data;
experimental data:
the overall mean value of the data.
If we cannot express our opinion independently, then for the observation with limited desire, we can get the estimated value of the standard deviation S: $-Edon
（8）
G 12336—90
(n — 1)
Where: S·Estimated value of standard deviation, also commonly called standard deviation:
: (test data,: the average value of a group of data):——number of data.
The square of the standard deviation is called variance. The calculation results are listed in Table 1. Table 1
Weight loss data of a certain alloy in seawater and its average value and standard deviation da
d-/xS=d/(n-1)—/2 642/23—10.724Probability curve
mg/(dm\d)
When the data obey the normal distribution, they will be distributed near a straight line in the normal probability paper. Before drawing the graph, arrange the data in increasing order according to 4.1
Gu, and determine the cumulative probability of each data according to formula (11): P(%) = 100(-: 0.375)/+0.25))Where: ——-The position of the data point in the increasing sequence: n—-The total number of data points. The cumulative probability of the data in Table 1 is shown in Table 2,
Note: MTDD
P data
mg/(dm +d).
GB12336.90
Cumulative probability of the test data in Table 1
P data
4.2 In the normal probability coordinate, the mean value is plotted at 50% of the horizontal coordinate, and then the sum of the mean value and the standard deviation (1S) is used as a point at 84.13% of the horizontal coordinate. The straight line passing through these two points is the fitting straight line of these data points. The difference between the mean value and the standard deviation (-S) can also be used as the difference between the two points. At this time, its corresponding horizontal coordinate is 15.87 light. The distribution of the data in Table 2 in the normal probability coordinate is shown in Figure 2.
mgiidmt-d)
155jin
—=166,:5
Average price in sample-
Standard 8= 10.72
T+F -187. H9
= J77. J7
黑积书
Figure 2 Distribution of the data in Table 2 in normal probability coordinates 15
4.3 When the data obey the lognormal distribution, they are distributed near a straight line in the lognormal probability coordinates. For example, the stress corrosion cracking time of lead alloy in salt solution obeys the lognormal distribution. Table 3 and Figure 3 show the endurance time of stress corrosion cracking of lead alloy GB 12336
and their logarithmic end-state probability curves. The fitting straight line of the data is made based on the logarithmic mean (at 50% of the horizontal axis) and the sum or difference of the logarithmic mean and the logarithmic standard deviation (at 84% and 16% of the horizontal axis). Table 3 Stress corrosion cracking endurance time of AI-5%Mg aluminum alloy in 3%NaCT solution 66
108,
Constant current
Constant potential
— 0. 34 V
{relative saturation
calomel electrode）
108,
Average value -103.2
126,
Logarithm (10g)>Average value 2.014
Logarithm (10g) Standard error 0.0841
Average value = 80.15
Logarithm (log) Average value —1.90387
Logarithm (1g) Standard error 0.04 4
100,
116,
100,
106,
135,
107,
105,
105,
after logarithmic persistence
.1 .2 .s 1||tt| |GU 12336--90
Constant current
Constant potential
Extreme probability, %
Figure 3 Distribution of the test data in Table 3 in normal probability coordinates 99.8
4.4 The extreme value distribution is a special distribution that can be used to analyze the maximum pitting depth for a given set of corrosion specimens. Although the distribution of the pitting depth of each specimen obeys the exponential function distribution, the maximum pitting depth of all specimens obeys the extreme value distribution. Although the mathematical representation of the extreme value distribution is very complicated, the use of extreme value probability paper can simplify the application of this technology. 4.5 For example, extreme value probability coordinate paper is used to study the pitting corrosion of aluminum alloys. Table 4 lists the extreme value distribution of nine or ten specimens. The maximum pitting depths of the test samples composed of samples were exposed to tap water for one period of time to one year. These data are arranged in inverse ascending order. The position of each data in the series is determined by n/(n-1), where n represents the sequence number and n represents the total number of samples. 4.6 Figure 4 is the distribution of the data in Table 4 in the extreme value probability coordinate. They are all distributed near the straight line, which means that the data obeys the extreme value distribution. Some predictions can be made by extrapolating the line. For example, according to the data with an exposure time of two weeks, it can be seen that the probability of obtaining a pitting depth equal to or less than 760um is 99.90%, the probability of not obtaining a pitting depth greater than 760um is 0.1%, and the maximum pitting depth observed is 680um
2 Week
QiuAlcan
Graph point location January
GB 12336
Maximum pitting depth (um), 3S-0
immersion time, sample number and graph point location Graph point location
0, 2 7
.818 1
Graph point location
. 200
Graph point location
0. 099
(1. 272 7
0. 636 Station
Graph point location
0. 5-45 4
Graph point location
.454 5
chemical variable, Y
smooth rate ()
5 curve fitting one
GE 12336·90
reply to show
2 another period
58 (measurement depth)
measured variable,
maximum foundation depth. μm
same period
average
Distribution of the test data in Table 4 in extreme value probability coordinates Least squares method
5.1 If a linear curve in the form of Y=+10 is used to fit the data, the following two equations must be solved: X4
(126)
(12c 2
{ 12d )
(J3b)
(13c)
5.2 Table 5 lists the data obtained when the tin-zinc alloy specimen was exposed to 400℃, 106kg/cm2 steam. It is known that the corrosion kinetics of zirconium-tin alloy in 4-core steam obeys two rate laws. The initial corrosion rate increases with time according to the power law, and after about forty days, the rate becomes a linear increase. The data in Table 5 are the initial reaction kinetics data, which obey the power function law: W=Ka
Where: W—weight gain,
K——rate constant:
time:
dimensionless constant.
The above inverse equation is expressed in logarithmic form as follows:
logW=mlogt:logK
It can be seen that the logarithm of weight gain and the logarithm of time are in a linear relationship. As long as: Y=logW
-logt
h-lugK
, the least squares method of the straight line can be used to fit the data. 1 day
GB 12336
Weight gain data of zinc-tin alloy dew in 400 ℃ steam 3 days
5.3 Table 6 lists the logarithms of the data in Table 5 and the sum of the curve fitting results. After calculation: m=0.469
Therefore, the best fitting curve equation for the data is: W = 7. 89 tn.469
Table 6 Least squares calculation of logarithmic time of test data of zirconium engraved alloy in 400℃ steam1
Logarithmic weight gain
2x— 27. 75
Zy—39.92
Zry=41.303
mg/dm?
2*-- 35. 001 5
5.4The above curve is plotted on the double logarithmic coordinates shown in Figure 5, and the 95% confidence interval of the regression line is also plotted in the figure. When the independent variable is an independent variable (such as time), the confidence interval is calculated by the following formula: logW-logkalogt±28
its-
(Y—)/(n—2)
W=. H9 I
Exposure time, d
2.5Isosorbide-5-Nitrae
Figure 5 The trajectory of the best fitting equation for the corrosion rate of zirconium-tin alloy in the double logarithmic plane 6 Estimation of confidence interval of the true value of the mean
6.1 For a set of test data, the limits of the confidence interval of the true value of the mean are calculated according to formula (14): Proof
In the formula: $standard deviation,
the limits of the confidence interval of the true value of the mean; x
the mean value of the test data,
a given positive number, (1-α) is called confidence interval; to(w-1): after α and n are determined, they can be obtained by looking up Appendix A (Supplement) Table A1. After the limits of the confidence interval of the true value of the mean are determined, the confidence interval of the true value of the mean is (-4, double + 4). 6.2 Test data of miscast alloys after exposure to 400 steam (see Table 5) Confidence interval of mean value Estimated mean value: to 25.9
Standard deviation: 8--1.15
Number of data: n=5
(1α) -- 0, 50, tm.t4: —0, 741(1: α) - 0. 95, tn.025( 2. 776(1-α) = 0. 99, to. tos) = 4. 604 Calculated results:2
126，
log(10g)>mean2.014
log(10g)standarderror0.0841
mean=80.15
log(1og)mean—1.90387
log(1g1standarderror0.04 4
100，
116，
106，
106，
106，
135，
107，
105，
105，
logpersistenceafter
.1 .2 .s 1
GU 12336--90
Constant current
Constant potential
Extreme probability, %
Figure 3 Distribution of the test data in Table 3 in normal probability coordinates 99.8
4.4 The extreme value distribution is a special distribution that can be used to analyze the maximum pitting depth for a given set of corrosion specimens. Although the distribution of the pitting depth of each specimen obeys the exponential function distribution, the maximum pitting depth of all specimens obeys the extreme value distribution. Although the mathematical representation of the extreme value distribution is very complicated, the use of extreme value probability paper can simplify the application of this technology. 4.5 For example, extreme value probability coordinate paper is used to study the pitting corrosion of aluminum alloys. Table 4 lists the extreme value distribution of nine or ten specimens. The maximum pitting depths of the test samples composed of samples were exposed to tap water for one period of time to one year. These data are arranged in inverse ascending order. The position of each data in the series is determined by n/(n-1), where n represents the sequence number and n represents the total number of samples. 4.6 Figure 4 is the distribution of the data in Table 4 in the extreme value probability coordinate. They are all distributed near the straight line, which means that the data obeys the extreme value distribution. Some predictions can be made by extrapolating the line. For example, according to the data with an exposure time of two weeks, it can be seen that the probability of obtaining a pitting depth equal to or less than 760um is 99.90%, the probability of not obtaining a pitting depth greater than 760um is 0.1%, and the maximum pitting depth observed is 680um
2 Week
QiuAlcan
Graph point location January
GB 12336
Maximum pitting depth (um), 3S-0
immersion time, sample number and graph point location Graph point location
0, 2 7
.818 1
Graph point location
. 200
Graph point location
0. 099
(1. 272 7
0. 636 Station
Graph point location
0. 5-45 4
Graph point location
.454 5
chemical variable, Y
smooth rate ()
5 curve fitting one
GE 12336·90
reply to show
2 another period
58 (measurement depth)
measured variable,
maximum foundation depth. μm
same period
average
Distribution of the test data in Table 4 in extreme value probability coordinates Least squares method
5.1 If a linear curve in the form of Y=+10 is used to fit the data, the following two equations must be solved: X4
(126)
(12c 2
{ 12d )
(J3b)
(13c)
5.2 Table 5 lists the data obtained when the tin-zinc alloy specimen was exposed to 400℃, 106kg/cm2 steam. It is known that the corrosion kinetics of zirconium-tin alloy in 4-core steam obeys two rate laws. The initial corrosion rate increases with time according to the power law, and after about forty days, the rate becomes a linear increase. The data in Table 5 are the initial reaction kinetics data, which obey the power function law: W=Ka
Where: W—weight gain,
K——rate constant:
time:
dimensionless constant.
The above inverse equation is expressed in logarithmic form as follows:
logW=mlogt:logK
It can be seen that the logarithm of weight gain and the logarithm of time are in a linear relationship. As long as: Y=logW
-logt
h-lugK
, the least squares method of the straight line can be used to fit the data. 1 day
GB 12336
Weight gain data of zinc-tin alloy dew in 400 ℃ steam 3 days
5.3 Table 6 lists the logarithms of the data in Table 5 and the sum of the curve fitting results. After calculation: m=0.469
Therefore, the best fitting curve equation for the data is: W = 7. 89 tn.469
Table 6 Least squares calculation of logarithmic time of test data of zirconium engraved alloy in 400℃ steam1
Logarithmic weight gain
2x— 27. 75
Zy—39.92
Zry=41.303
mg/dm?
2*-- 35. 001 5
5.4The above curve is plotted on the double logarithmic coordinates shown in Figure 5, and the 95% confidence interval of the regression line is also plotted in the figure. When the independent variable is an independent variable (such as time), the confidence interval is calculated by the following formula: logW-logkalogt±28
its-
(Y—)/(n—2)
W=. H9 I
Exposure time, d
2.5Isosorbide-5-Nitrae
Figure 5 The trajectory of the best fitting equation for the corrosion rate of zirconium-tin alloy in the double logarithmic plane 6 Estimation of confidence interval of the true value of the mean
6.1 For a set of test data, the limits of the confidence interval of the true value of the mean are calculated according to formula (14): Proof
In the formula: $standard deviation,
the limits of the confidence interval of the true value of the mean; x
the mean value of the test data,
a given positive number, (1-α) is called confidence interval; to(w-1): after α and n are determined, they can be obtained by looking up Appendix A (Supplement) Table A1. After the limits of the confidence interval of the true value of the mean are determined, the confidence interval of the true value of the mean is (-4, double + 4). 6.2 Test data of miscast alloys after exposure to 400 steam (see Table 5) Confidence interval of mean value Estimated mean value: to 25.9
Standard deviation: 8--1.15
Number of data: n=5
(1α) -- 0, 50, tm.t4: —0, 741(1: α) - 0. 95, tn.025( 2. 776(1-α) = 0. 99, to. tos) = 4. 604 Calculated results:2
126，
log(10g)>mean2.014
log(10g)standarderror0.0841
mean=80.15
log(1og)mean—1.90387
log(1g1standarderror0.04 4
100，
116，
106，
106，
106，
135，
107，
105，
105，
logpersistenceafter
.1 .2 .s 1
GU 12336--90
Constant current
Constant potential
Extreme probability, %
Figure 3 Distribution of the test data in Table 3 in normal probability coordinates 99.8
4.4 The extreme value distribution is a special distribution that can be used to analyze the maximum pitting depth for a given set of corrosion specimens. Although the distribution of the pitting depth of each specimen obeys the exponential function distribution, the maximum pitting depth of all specimens obeys the extreme value distribution. Although the mathematical representation of the extreme value distribution is very complicated, the use of extreme value probability paper can simplify the application of this technology. 4.5 For example, extreme value probability coordinate paper is used to study the pitting corrosion of aluminum alloys. Table 4 lists the extreme value distribution of nine or ten specimens. The maximum pitting depths of the test samples composed of samples were exposed to tap water for one period of time to one year. These data are arranged in inverse ascending order. The position of each data in the series is determined by n/(n-1), where n represents the sequence number and n represents the total number of samples. 4.6 Figure 4 is the distribution of the data in Table 4 in the extreme value probability coordinate. They are all distributed near the straight line, which means that the data obeys the extreme value distribution. Some predictions can be made by extrapolating the line. For example, according to the data with an exposure time of two weeks, it can be seen that the probability of obtaining a pitting depth equal to or less than 760um is 99.90%, the probability of not obtaining a pitting depth greater than 760um is 0.1%, and the maximum pitting depth observed is 680um
2 Week
QiuAlcan
Graph point location January
GB 12336
Maximum pitting depth (um), 3S-0
immersion time, sample number and graph point location Graph point location
0, 2 7
.818 1
Graph point location
. 200
Graph point location
0. 099
(1. 272 7
0. 636 Station
Graph point location
0. 5-45 4
Graph point location
.454 5
chemical variable, Y
smooth rate ()
5 curve fitting one
GE 12336·90
reply to show
2 another period
58 (measurement depth)
measured variable,
maximum foundation depth. μm
same period
average
Distribution of the test data in Table 4 in extreme value probability coordinates Least squares method
5.1 If a linear curve in the form of Y=+10 is used to fit the data, the following two equations must be solved: X4
(126)
(12c 2
{ 12d )
(J3b)
(13c)
5.2 Table 5 lists the data obtained when the tin-zinc alloy specimen was exposed to 400℃, 106kg/cm2 steam. It is known that the corrosion kinetics of zirconium-tin alloy in 4-core steam obeys two rate laws. The initial corrosion rate increases with time according to the power law, and after about forty days, the rate becomes a linear increase. The data in Table 5 are the initial reaction kinetics data, which obey the power function law: W=Ka
Where: W—weight gain,
K——rate constant:
time:
dimensionless constant.
The above inverse equation is expressed in logarithmic form as follows:
logW=mlogt:logK
It can be seen that the logarithm of weight gain and the logarithm of time are in a linear relationship. As long as: Y=logW
-logt
h-lugK
, the least squares method of the straight line can be used to fit the data. 1 day
GB 12336
Weight gain data of zinc-tin alloy dew in 400 ℃ steam 3 days
5.3 Table 6 lists the logarithms of the data in Table 5 and the sum of the curve fitting results. After calculation: m=0.469
Therefore, the best fitting curve equation for the data is: W = 7. 89 tn.469
Table 6 Least squares calculation of logarithmic time of test data of zirconium engraved alloy in 400℃ steam1
Logarithmic weight gain
2x— 27. 75
Zy—39.92
Zry=41.303
mg/dm?
2*-- 35. 001 5
5.4The above curve is plotted on the double logarithmic coordinates shown in Figure 5, and the 95% confidence interval of the regression line is also plotted in the figure. When the independent variable is an independent variable (such as time), the confidence interval is calculated by the following formula: logW-logkalogt±28
its-
(Y—)/(n—2)
W=. H9 I
Exposure time, d
2.5Isosorbide-5-Nitrae
Figure 5 The trajectory of the best fitting equation for the corrosion rate of zirconium-tin alloy in the double logarithmic plane 6 Estimation of confidence interval of the true value of the mean
6.1 For a set of test data, the limits of the confidence interval of the true value of the mean are calculated according to formula (14): Proof
In the formula: $standard deviation,
the limits of the confidence interval of the true value of the mean; x
the mean value of the test data,
a given positive number, (1-α) is called confidence interval; to(w-1): after α and n are determined, they can be obtained by looking up Appendix A (Supplement) Table A1. After the limits of the confidence interval of the true value of the mean are determined, the confidence interval of the true value of the mean is (-4, double + 4). 6.2 Test data of miscast alloys after exposure to 400 steam (see Table 5) Confidence interval of mean value Estimated mean value: to 25.9
Standard deviation: 8--1.15
Number of data: n=5
(1α) -- 0, 50, tm.t4: —0, 741(1: α) - 0. 95, tn.025( 2. 776(1-α) = 0. 99, to. tos) = 4. 604 Calculated results:5 For example, extreme value probability coordinate paper is used to study the pitting corrosion of aluminum alloy. Table 4 lists the maximum pitting depths of a sample group consisting of nine or ten samples exposed to tap water for one year to one year. These data are arranged in reverse order. The position of each data in the series in the figure is determined by n/(n-1), where n represents the sequence number and n represents the total number of samples. 4.6 Figure 4 is the distribution of the data in Table 4 in extreme value probability coordinates. They are all distributed near the straight line, which means that the data obeys the extreme value distribution. Extrapolating the line can make some predictions. For example, according to the data of exposure time of two weeks, the probability of obtaining a pitting with a depth equal to or less than 760um is 99.90, the rate of not obtaining a pitting with a depth greater than 760um is 0.1%, and the maximum observed pitting depth is 680um
2 week
Foot Alcan
Graph point position1 month
GB 12336
Maximum pitting depth of alloy in tap water (unit: um), 3S-0
Immersion time, sample number and graph point positionGraph point position
0, 2 7
.818 1
Graph point position
. 200
Graph point position
0. 09心9
(1. 272 7
0. 636 Station
Graph point location
0. 5-45 4
Graph point location
.454 5
of the variable, Y
success rate ()
5curve fitting-
GE 12336·90
Reply to the statement
2 Another period
58 (depth)
Measured variable,
Maximum depth. μm
Same period
Average
Distribution of the experimental data in Table 4 in the extreme value probability coordinates Least squares methodbzxZ.net
5.1 If the data is fitted with a self-curve in the form of book × +, the following two equations must be solved: X
（12a）
GB12336—90
If the data is fitted with a field curve in the form of Y=+10, the following three equations must be solved: X4
(126）
（12c 2
{ 12d )
（J3b）
(13c）
5.2 Table 5 lists the data obtained when the zirconium-tin alloy sample was exposed to 400℃, 106kg/cm steam. It is known that the corrosion kinetics of zirconium-tin alloy in 4-core steam obeys two rate laws. The corrosion rate increases with time according to the power law at the beginning, and after about forty days, the rate becomes a linear increase. The data in Table 5 are the initial reaction kinetic data, which obey the power function law: W=Ka
Where: W—weight gain, K——rate constant: time: dimensionless constant. The inverse equation is expressed in logarithmic form as follows: logW=mlogt: logK
It can be seen that the logarithm of weight gain and the logarithm of time are linearly related. As long as: Y=logW
-logt
h-lugK
The data can be fitted by the least square method of straight line. 1 day
GB 12336
Weight gain data of zinc-tin alloy dew in 400℃ steam 3 days
5.3 Table 6 lists the logarithms and the sum of the data in Table 5 for curve fitting. After calculation: m=0.469
Therefore, the best fitting curve equation for the data is: W = 7. 89 tn.469
Table 6 Least squares calculation of logarithmic time of test data of zirconium engraved alloy in 400℃ steam1
Logarithmic weight gain
2x— 27. 75
Zy—39.92
Zry=41.303
mg/dm?
2*-- 35. 001 5
5.4The above curve is plotted on the double logarithmic coordinates shown in Figure 5, and the 95% confidence interval of the regression line is also plotted in the figure. When the independent variable is an independent variable (such as time), the confidence interval is calculated by the following formula: logW-logkalogt±28
its-
(Y—)/(n—2)
W=. H9 I
Exposure time, d
2.5Isosorbide-5-Nitrae
Figure 5 The trajectory of the best fitting equation for the corrosion rate of zirconium-tin alloy in the double logarithmic plane 6 Estimation of confidence interval of the true value of the mean
6.1 For a set of test data, the limits of the confidence interval of the true value of the mean are calculated according to formula (14): Proof
In the formula: $standard deviation,
the limits of the confidence interval of the true value of the mean; x
the mean value of the test data,
a given positive number, (1-α) is called confidence interval; to(w-1): after α and n are determined, they can be obtained by looking up Appendix A (Supplement) Table A1. After the limits of the confidence interval of the true value of the mean are determined, the confidence interval of the true value of the mean is (-4, double + 4). 6.2 Test data of miscast alloys after exposure to 400 steam (see Table 5) Confidence interval of mean value Estimated mean value: to 25.9
Standard deviation: 8--1.15
Number of data: n=5
(1α) -- 0, 50, tm.t4: —0, 741(1: α) - 0. 95, tn.025( 2. 776(1-α) = 0. 99, to. tos) = 4. 604 Calculated results:5 For example, extreme value probability coordinate paper is used to study the pitting corrosion of aluminum alloy. Table 4 lists the maximum pitting depths of a sample group consisting of nine or ten samples exposed to tap water for one year to one year. These data are arranged in reverse order. The position of each data in the series in the figure is determined by n/(n-1), where n represents the sequence number and n represents the total number of samples. 4.6 Figure 4 is the distribution of the data in Table 4 in extreme value probability coordinates. They are all distributed near the straight line, which means that the data obeys the extreme value distribution. Extrapolating the line can make some predictions. For example, according to the data of exposure time of two weeks, the probability of obtaining a pitting with a depth equal to or less than 760um is 99.90, the rate of not obtaining a pitting with a depth greater than 760um is 0.1%, and the maximum observed pitting depth is 680um
2 week
Foot Alcan
Graph point position1 month
GB 12336
Maximum pitting depth of alloy in tap water (unit: um), 3S-0
Immersion time, sample number and graph point positionGraph point position
0, 2 7
.818 1
Graph point position
. 200
Graph point position
0. 09心9
(1. 272 7
0. 636 Station
Graph point location
0. 5-45 4
Graph point location
.454 5
of the variable, Y
success rate ()
5curve fitting-
GE 12336·90
Reply to the statement
2 Another period
58 (depth)
Measured variable,
Maximum depth. μm
Same period
Average
Distribution of the experimental data in Table 4 in the extreme value probability coordinates Least squares method
5.1 If the data is fitted with a self-curve in the form of book × +, the following two equations must be solved: X
（12a）
GB12336—90
If the data is fitted with a field curve in the form of Y=+10, the following three equations must be solved: X4
(126）
（12c 2
{ 12d )
（J3b）
(13c）
5.2 Table 5 lists the data obtained when the zirconium-tin alloy sample was exposed to 400℃, 106kg/cm steam. It is known that the corrosion kinetics of zirconium-tin alloy in 4-core steam obeys two rate laws. The corrosion rate increases with time according to the power law at the beginning, and after about forty days, the rate becomes a linear increase. The data in Table 5 are the initial reaction kinetic data, which obey the power function law: W=Ka
Where: W—weight gain, K——rate constant: time: dimensionless constant. The inverse equation is expressed in logarithmic form as follows: logW=mlogt: logK
It can be seen that the logarithm of weight gain and the logarithm of time are linearly related. As long as: Y=logW
-logt
h-lugK
The data can be fitted by the least square method of straight line. 1 day
GB 12336
Weight gain data of zinc-tin alloy dew in 400℃ steam 3 days
5.3 Table 6 lists the logarithms and the sum of the data in Table 5 for curve fitting. After calculation: m=0.469
Therefore, the best fitting curve equation for the data is: W = 7. 89 tn.469
Table 6 Least squares calculation of logarithmic time of test data of zirconium engraved alloy in 400℃ steam1
Logarithmic weight gain
2x— 27. 75
Zy—39.92
Zry=41.303
mg/dm?
2*-- 35. 001 5
5.4The above curve is plotted on the double logarithmic coordinates shown in Figure 5, and the 95% confidence interval of the regression line is also plotted in the figure. When the independent variable is an independent variable (such as time), the confidence interval is calculated by the following formula: logW-logkalogt±28
its-
(Y—)/(n—2)
W=. H9 I
Exposure time, d
2.5Isosorbide-5-Nitrae
Figure 5 The trajectory of the best fitting equation for the corrosion rate of zirconium-tin alloy in the double logarithmic plane 6 Estimation of confidence interval of the true value of the mean
6.1 For a set of test data, the limits of the confidence interval of the true value of the mean are calculated according to formula (14): Proof
In the formula: $standard deviation,
the limits of the confidence interval of the true value of the mean; x
the mean value of the test data,
a given positive number, (1-α) is called confidence interval; to(w-1): after α and n are determined, they can be obtained by looking up Appendix A (Supplement) Table A1. After the limits of the confidence interval of the true value of the mean are determined, the confidence interval of the true value of the mean is (-4, double + 4). 6.2 Test data of miscast alloys after exposure to 400 steam (see Table 5) Confidence interval of mean value Estimated mean value: to 25.9
Standard deviation: 8--1.15
Number of data: n=5
(1α) -- 0, 50, tm.t4: —0, 741(1: α) - 0. 95, tn.025( 2. 776(1-α) = 0. 99, to. tos) = 4. 604 Calculated results:2 Table 5 lists the data obtained when the zirconium-tin alloy sample was exposed to 400℃, 106kg/cm steam. It is known that the corrosion kinetics of zirconium-tin alloy in 400℃ steam obeys two rate laws. The initial corrosion rate increases with time according to the power law, and after about forty days, the rate becomes a linear increase. The data in Table 5 are the initial reaction kinetics data, which obey the power function law: W=Ka
Where: W—weight gain,
K——rate constant:
time:
dimensionless constant.
The above inverse equation is expressed in logarithmic form as follows:
logW=mlogt:logK
It can be seen that the logarithm of weight gain and the logarithm of time are linearly related. As long as: Y=logW
-logt
h-lugK
, the least squares method of the straight line can be used to fit the data. 1 day
GB 12336
Weight gain data of zinc-tin alloy dew in 400 ℃ steam 3 days
5.3 Table 6 lists the logarithms of the data in Table 5 and the sum of the curve fitting results. After calculation: m=0.469
Therefore, the best fitting curve equation for the data is: W = 7. 89 tn.469
Table 6 Least squares calculation of logarithmic time of test data of zirconium engraved alloy in 400℃ steam1
Logarithmic weight gain
2x— 27. 75
Zy—39.92
Zry=41.303
mg/dm?
2*-- 35. 001 5
5.4The above curve is plotted on the double logarithmic coordinates shown in Figure 5, and the 95% confidence interval of the regression line is also plotted in the figure. When the independent variable is an independent variable (such as time), the confidence interval is calculated by the following formula: logW-logkalogt±28
its-
(Y—)/(n—2)
W=. H9 I
Exposure time, d
2.5Isosorbide-5-Nitrae
Figure 5 The trajectory of the best fitting equation for the corrosion rate of zirconium-tin alloy in the double logarithmic plane 6 Estimation of confidence interval of the true value of the mean
6.1 For a set of test data, the limits of the confidence interval of the true value of the mean are calculated according to formula (14): Proof
In the formula: $standard deviation,
the limits of the confidence interval of the true value of the mean; x
the mean value of the test data,
a given positive number, (1-α) is called confidence interval; to(w-1): after α and n are determined, they can be obtained by looking up Appendix A (Supplement) Table A1. After the limits of the confidence interval of the true value of the mean are determined, the confidence interval of the true value of the mean is (-4, double + 4). 6.2 Test data of miscast alloys after exposure to 400 steam (see Table 5) Confidence interval of mean value Estimated mean value: to 25.9
Standard deviation: 8--1.15
Number of data: n=5
(1α) -- 0, 50, tm.t4: —0, 741(1: α) - 0. 95, tn.025( 2. 776(1-α) = 0. 99, to. tos) = 4. 604 Calculated results:2 Table 5 lists the data obtained when the zirconium-tin alloy sample was exposed to 400℃, 106kg/cm steam. It is known that the corrosion kinetics of zirconium-tin alloy in 400℃ steam obeys two rate laws. The initial corrosion rate increases with time according to the power law, and after about forty days, the rate becomes a linear increase. The data in Table 5 are the initial reaction kinetics data, which obey the power function law: W=Ka
Where: W—weight gain,
K——rate constant:
time:
dimensionless constant.
The above inverse equation is expressed in logarithmic form as follows:
logW=mlogt:logK
It can be seen that the logarithm of weight gain and the logarithm of time are linearly related. As long as: Y=logW
-logt
h-lugK
, the least squares method of the straight line can be used to fit the data. 1 day
GB 12336
Weight gain data of zinc-tin alloy dew in 400 ℃ steam 3 days
5.3 Table 6 lists the logarithms of the data in Table 5 and the sum of the curve fitting results. After calculation: m=0.469
Therefore, the best fitting curve equation for the data is: W = 7. 89 tn.469
Table 6 Least squares calculation of logarithmic time of test data of zirconium engraved alloy in 400℃ steam1
Logarithmic weight gain
2x— 27. 75
Zy—39.92
Zry=41.303
mg/dm?
2*-- 35. 001 5
5.4The above curve is plotted on the double logarithmic coordinates shown in Figure 5, and the 95% confidence interval of the regression line is also plotted in the figure. When the independent variable is an independent variable (such as time), the confidence interval is calculated by the following formula: logW-logkalogt±28
its-
(Y—)/(n—2)
W=. H9 I
Exposure time, d
2.5Isosorbide-5-Nitrae
Figure 5 The trajectory of the best fitting equation for the corrosion rate of zirconium-tin alloy in the double logarithmic plane 6 Estimation of confidence interval of the true value of the mean
6.1 For a set of test data, the limits of the confidence interval of the true value of the mean are calculated according to formula (14): Proof
In the formula: $standard deviation,
the limits of the confidence interval of the true value of the mean; x
the mean value of the test data,
a given positive number, (1-α) is called confidence interval; to(w-1): after α and n are determined, they can be obtained by looking up Appendix A (Supplement) Table A1. After the limits of the confidence interval of the true value of the mean are determined, the confidence interval of the true value of the mean is (-4, double + 4). 6.2 Test data of miscast alloys after exposure to 400 steam (see Table 5) Confidence interval of mean value Estimated mean value: to 25.9
Standard deviation: 8--1.15
Number of data: n=5
(1α) -- 0, 50, tm.t4: —0, 741(1: α) - 0. 95, tn.025( 2. 776(1-α) = 0. 99, to. tos) = 4. 604 Calculated results:
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