JP2009192221A - Deterioration evaluator and deterioration evaluation method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a deterioration evaluator and a deterioration evaluation method for evaluating the deterioration process of an object, including unobservable or hard-to-observe heterogeneous factors. <P>SOLUTION: When the state of soundness determined by an administrator having inspected a plurality of objects is inputted through an input device, a data-receiving part 10 is used to receive it as inspection data. A deterioration characteristic calculating part 12 is used to calculate the average value Aveθ<SP>k</SP><SB>i</SB>of the deterioration characteristics θ<SB>i</SB>(1<SB>k</SB>) of the object, based on the data on the soundness of the plurality of objects received by the receiving part 10. A heterogeneity parameter calculating part 16 is used to calculate a heterogeneity parameter ε<SP>k</SP>for each of the unobservable or hard-to-observe heterogeneous factors, causing deviation in the deterioration characteristics θ<SB>i</SB>(1<SB>k</SB>). A benchmark part 18 is used to evaluate the effect of the heterogeneous factors on the deterioration characteristics by using the heterogeneity parameters, while an output part 20 outputs the evaluation results. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a deterioration evaluation apparatus and a deterioration evaluation method.

  In asset management of bridges, roads, etc., it is an important issue to seek an optimal repair strategy for reducing the life cycle cost associated with maintenance and repair. For this reason, conventionally, various methods for quantitatively predicting deterioration of civil engineering facilities such as bridges and roads have been proposed.

For example, Patent Literature 1 below discloses a bridge maintenance management plan support system that quantitatively and objectively evaluates the soundness of members constituting a bridge and predicts long-term deterioration.
JP 2006-177080 A

  However, in the above conventional technology, the difference in degradation process caused by heterogeneity factors that are unobservable or difficult to observe is evaluated based on the environmental conditions in which civil engineering facilities are installed and the difference in quality during construction. There was a problem that I could not.

  The present invention has been made in view of the above-described conventional problems, and a purpose of the present invention is to provide a deterioration evaluation apparatus and a deterioration evaluation that can evaluate a deterioration process of an object including a heterogeneity factor that is unobservable or difficult to observe. It is to provide a method.

  In order to achieve the above-mentioned object, the invention of the multiple object degradation evaluation apparatus according to claim 1 provides the degradation characteristics of the multiple objects for each observable degradation factor based on the soundness of the multiple objects. A deterioration characteristic calculation means for calculating, a heterogeneity parameter calculation means for calculating a heterogeneity parameter that is an indicator of the deviation of the deterioration characteristics for each unobservable or difficult to observe heterogeneity factor that causes a deviation in the deterioration characteristics; It is characterized by providing.

  According to a second aspect of the present invention, there is provided the benchmarking means for the deterioration evaluation apparatus for a plurality of objects according to the first aspect to further evaluate the influence of the heterogeneity factor on the deterioration characteristic based on the magnitude relationship of the heterogeneity parameters. It is characterized by providing.

  The invention according to claim 3 is the logarithm representing the co-occurrence probability density of the deterioration process of the plurality of objects in the deterioration evaluation apparatus for the plurality of objects according to claim 1 or claim 2. The deterioration characteristic is obtained as a maximum likelihood estimation value that maximizes the likelihood function.

  According to a fourth aspect of the present invention, in the apparatus for evaluating deterioration of a plurality of objects according to any one of the first to third aspects, the heterogeneity parameter calculating means generates an object having the heterogeneity factor. A partial log likelihood representing the co-occurrence probability density is obtained, and the heterogeneity parameter is obtained as an optimum solution when the condition is maximized conditionally.

  The invention according to claim 5 is the multiple object deterioration evaluation apparatus according to any one of claims 2 to 4, wherein the deterioration evaluation apparatus further includes an output unit, and the benchmarking unit includes: Taking the elapsed time on the horizontal axis and the soundness on the vertical axis, creating a degradation curve that relatively represents the degradation characteristics of each object, and the output means creates individual curves created based on the values of the heterogeneity parameters. A deterioration curve is output.

  The invention of the degradation evaluation method for multiple objects according to claim 6 acquires the degradation rates of the multiple objects, and calculates the degradation characteristics of the multiple objects for each observable degradation factor based on the degradation rates. In addition, a heterogeneity parameter that is an index of the deviation of the degradation characteristic is calculated for each heterogeneity factor that is unobservable or difficult to observe that causes a deviation in the degradation characteristic.

  According to the first aspect of the present invention, it is possible to evaluate the deterioration process of an object including a heterogeneity factor that cannot be observed or is difficult to observe.

  According to the inventions of claims 2 and 5, the influence of the heterogeneity factor on the deterioration characteristics can be easily evaluated.

  According to the third and fourth aspects of the invention, the deterioration characteristic and the heterogeneity parameter can be appropriately calculated.

  According to the invention of claim 6, it is possible to provide a deterioration evaluation method for a plurality of objects that can evaluate the deterioration process of the object including heterogeneity factors that are not observable or difficult to observe.

  Hereinafter, the best mode for carrying out the present invention (hereinafter referred to as an embodiment) will be described with reference to the drawings.

  FIG. 1 shows a functional block diagram of an embodiment of a deterioration evaluation apparatus according to the present invention. In FIG. 1, the deterioration evaluation apparatus is realized on a computer, and includes a data reception unit 10, a deterioration characteristic calculation unit 12, a heterogeneity factor storage unit 14, a heterogeneity parameter calculation unit 16, a benchmarking unit 18, and an output unit 20. It is configured.

  The data receiving unit 10 is realized by including a central processing unit (for example, a CPU can be used) and a program for controlling the processing operation of the CPU, and a bridge, road, etc. input from the input device by the manager of the object Receive data (observed values) on the soundness of civil engineering facilities and other objects. The input device may be configured with, for example, a keyboard, a pointing device, or the like, may be configured with an appropriate disk drive device, and further configured with an appropriate communication interface such as a USB (Universal Serial Bus) port or a network port. May be. In addition, the soundness level represents a state in which deterioration of a target object has progressed over time after new construction and the function or performance to be reduced is expressed by a rating in which the degree of deterioration is classified into multiple stages. Say.

  FIG. 2 shows an example of the soundness level. FIG. 2 is a seven-stage rating evaluation standard for visual inspection established by New York City for RC floor slabs, which are important members for maintenance, because direct wheel loads act on bridge members. In FIG. 2, “1” representing the newly installed state is the best, and “7” is set according to the extent to which the state of the RC floor slab obtained by visual observation deteriorates thereafter. Therefore, in this example, the larger the rating value, the more deteriorated the RC floor slab.

  Returning to FIG. 1, the deterioration characteristic calculation unit 12 is realized by including a CPU and a program for controlling the processing operation of the CPU, and based on data on the soundness level of a plurality of objects received by the data reception unit 10. The deterioration characteristics of a plurality of objects are calculated for each possible deterioration factor. Here, the observable deterioration factor is a deterioration factor that can be quantified, for example, in the case of a bridge or a road, such as traffic volume, weather conditions at the installation site, material, and construction year. The deterioration characteristic is a probability density function representing the probability that the rating deteriorates by one step when a certain time has elapsed since construction. This probability density function is called a hazard function and will be described in detail later.

  The heterogeneity factor storage unit 14 includes a computer-readable storage device such as a RAM (Random Access Memory) and a hard disk device, and a program for controlling them by the CPU, and cannot be observed to cause a deviation in deterioration characteristics. Or store heterogeneity factors that are difficult to observe. Here, the heterogeneity factor includes factors that are impossible or difficult to quantitatively observe, such as factors specific to individual bridges in bridges having the same characteristic values such as construction conditions and RC slabs. These heterogeneity factors are stored in association with the object.

The heterogeneity parameter calculation unit 16 is realized including a CPU and a program for controlling the processing operation of the CPU, and is an index of the deviation of the deterioration characteristic for each heterogeneity factor stored in the heterogeneity factor storage unit 14. The heterogeneity parameter (ε ^k ) is calculated. Note that the heterogeneity factor may be specified by an administrator instead of being acquired from the heterogeneity factor storage unit 14. The heterogeneity parameter will be described later.

  The benchmarking unit 18 is realized including a CPU and a program for controlling the processing operation of the CPU, and the heterogeneity factor affects the deterioration characteristics based on the magnitude relationship of the heterogeneity parameters calculated by the heterogeneity parameter calculation unit 16. Assess the impact. Here, as an example of the evaluation method, for example, there is a method of creating a degradation curve that relatively represents degradation characteristics of individual objects.

  The output unit 20 is realized including a CPU and a program for controlling the processing operation of the CPU, and outputs an evaluation result performed by the benchmarking unit 18 to a data output unit such as a display device such as a display or a printing device.

  Next, a process performed by the deterioration characteristic calculation unit 12 for calculating deterioration characteristics of a plurality of objects for each observable deterioration factor will be described.

FIG. 3 shows an explanatory diagram of a deterioration process of an object such as a bridge. In FIG. 3, the horizontal axis is the elapsed time τ from when the object is newly established, and the vertical axis is the soundness level. In this example, the state (rating) indicating the soundness is represented by a state variable i (i is an integer), and this is shown in three stages i, i + 1, and i + 2. In addition, the manager checks the object at two time points τ _A and τ _{B based on} specific deterioration factors such as traffic volume and materials, and confirms the soundness level.

In the case of FIG. 3, examples of four types of deterioration processes are shown. In pass 1, the deterioration does not proceed at two inspection intervals (between τ _A and τ _B ), and the state i is observed as the soundness level of the object in two inspections. In pass 2 and pass 3, the soundness deteriorates from state i to i + 1 at times τ ₄ and τ ₃ , respectively, and state i + 1 is observed at the second inspection time point (τ _B ). Furthermore, in pass 4, the soundness level changes from i to i + 1 and from i + 1 to i + _{2 at} times τ ₁ and τ ₂ , respectively. In each case described above, the administrator can observe the soundness level at the time of two inspections, but the time when the soundness actually changes (τ ₁ , τ ₂ , τ ₃ , τ ₄ ). Cannot be observed. For this reason, a stochastic process (Markov degradation model) is introduced to estimate the transition of the soundness (degradation process).

と表現できる。なお、補修がなされない場合には劣化が改善されることはないので、ｉ＞ｊではπ_ｉｊ＝０となる。また、推移確率の定義より、

である。 The degradation process shown in FIG. 3 is a Markov degradation model, the state of health of the object observed at time τ _A is the state variable h (τ _A ), and the state of health of the object observed at time τ _B is the state. when expressed as a variable h (τ _B), the time tau _a soundness h (tau _a) observed in = when a there was i, soundness h during inspection in tau _B is a future time (tau _B) = The conditional transition probability (Markov transition probability) of j is
Pr [h (τ _B ) = j | h (τ _A ) = i] = π _ij
It expresses. When such transition probabilities are obtained for the combination of soundness (i, j), the Markov transition probability matrix is

Can be expressed as Note that if no repair is performed, the deterioration is not improved, so that π _ij = 0 when i> j. From the definition of transition probability,

It is.

が成立する。さらに、初期時点ｙ_ｉ＝０（時刻τ_ｉ−１）から点検時点ｙ_ｉまでに健全度がｉのまま推移する確率は、
Ｐｒ｛ζ_ｉ≧ｙ_ｉ｝＝Ｆ’_ｉ（ζ_ｉ）＝１−Ｆ_ｉ（ζ_ｉ）
と定義できる。ここで、健全度が時点ｙ_ｉまで状態ｉで推移し、かつ期間［ｙ_ｉ，ｙ_ｉ＋Δｙ_ｉ）中に状態ｉ＋１に劣化する条件付確率は、

と表現できる。この確率密度λ_ｉ（ｙ_ｉ）をハザード関数と呼ぶ。健全度の状態数−１個のハザード関数を定義することができる。なお、ハザード関数の値が小さいほど劣化速度が小さいことを意味する。 FIG. 4 is an explanatory diagram of a method for formulating the Markov transition probability. In FIG. 4, it is assumed that the soundness level changes from i-1 to i at time τ _i−1 , and the soundness level changes from i to i + 1 at time τ _i . Here, a time axis with the time τ _i−1 as an initial time point (y _i = 0) is set. At this time, time τ _A is y _A on the time axis, and time τ _B is y _B. Further, the length of the period during which the soundness level of the object remains at i (lifetime of the soundness level i) is ζ _i = y _C as shown in FIG. The life ζ _i of the soundness _i is a random variable, and follows the probability density function f _i (ζ _i ) and distribution function F _i (ζ _i ),

Is established. Further, the probability that the soundness level remains _i from the initial time point y _i = 0 (time τ _i-1 ) to the inspection time point y _i is:
Pr {ζ _i ≧ y _i } = F ′ _i (ζ _i ) = 1−F _i (ζ _i )
Can be defined. Here, the conditional probability that the soundness changes in the state _i until the time point y _i and deteriorates to the state i + 1 during the period [y _i , y _i + Δy _i ) is

Can be expressed as This probability density λ _i (y _i ) is called a hazard function. It is possible to define a hazard function of the number of states of soundness minus one. In addition, it means that deterioration rate is so small that the value of a hazard function is small.

As described above, when the deterioration process is a Markov deterioration model and the hazard function does not depend on time and always takes a constant value, the exponential hazard function λ _i (y _i ) = θ _i (θ _i is a positive constant) )
Is established. In this way, since the exponent hazard function takes a constant value without depending on time, it is possible to express the Markov property that the deterioration process does not depend on the past history. In addition, the probability F ′ _i (y _i ) that the lifetime of the soundness level i is y _i or more is
F ′ _i (y _i ) = exp (−θ _i y _i )
It becomes.

ただし、ｚは１回目と２回目の点検の間隔（ｙ_Ｂ−ｙ_Ａ）である。 Here, when the exponential hazard function is used, the Markov transition probability π _ij (i = 1,..., I−) in which the soundness transitions from i to j between two inspections (τ _A and τ _B ). 1; j = i + 1,..., I) can be formulated as:

However, z is the interval between the first inspection and the second inspection (y _B -y _A ).

The deterioration characteristic calculation unit 12 calculates the exponent hazard function θ _i described above as the deterioration characteristic of the object.

  Next, a process performed by the heterogeneity parameter calculation unit 16 to calculate a heterogeneity parameter, which is an index of deterioration characteristic deviation, will be described.

First, the degradation characteristic calculation unit 12 divides a plurality of objects into K groups, and degradation characteristics (exponential hazard function) for each element l _k belonging to each group k (k = 1, 2,..., K). An average value (Aveθ ^k _i ) of θ _i (l _k ) is calculated. Here, the element l _{k of} each group may be a building such as a bridge belonging to the group, or may be a member constituting the building. For example, in the case of a bridge, this group can be configured by classifying the traffic volume as an observable degradation factor into large, medium, and small according to an appropriate standard, and classifying a plurality of bridges according to the traffic volume.

Next, heterogeneity parameter calculating unit 16 sets the heterogeneity factor causing deviation deterioration characteristics for each element l _k in each group k, calculates the heterogeneity parameter epsilon ^k is an index of deviation. The heterogeneity parameter ε ^k does not depend on the rating i. This heterogeneity parameter ε ^k is a random variable representing the degree to which the deterioration characteristic deviates from the average value (Aveθ ^k _i ) for each group k, and ε ^k > 0. ε ^k = 1 corresponds to the average value of the degradation characteristics of each group k, and the larger the value of the heterogeneity parameter ε ^k is, the faster the degradation rate of the object is with respect to the average value. It represents that the degradation rate of the object is slow relative to the average value. The deterioration characteristic θ _i (l _k ) for each element l _k is expressed by the following equation as a mixed index hazard function.
θ _i (l _k ) = Ave θ ^k _i × ε ^k (1)

と表される。 Here, for example, if the heterogeneity parameter ε ^k is a probability sample extracted from a gamma distribution with an average of 1 and a variance of 1 / φ, the Markov transition probability representing the average deterioration transition is

It is expressed.

と定式化される。さらには、異質性パラメータの同時生起確率を表す部分対数尤度関数は、

と表される。ここで、ｘ^ｌｋは、劣化予測の対象となる対象物の任意の観測可能な特性ベクトルを示す。また、

は指数ハザード関数の平均値及び異質性パラメータの確率分布に関する最尤推定値を表している。 At this time, the log-likelihood function representing the co-occurrence probability expressing the probability that the observed values of the soundness (ratings) of all objects are obtained simultaneously is

Is formulated. Furthermore, the partial log likelihood function representing the co-occurrence probability of heterogeneity parameters is

It is expressed. Here, x ^lk represents an arbitrary observable characteristic vector of the target object for which deterioration is predicted. Also,

Represents the maximum likelihood estimate for the mean value of the exponential hazard function and the probability distribution of the heterogeneity parameter.

  In addition, the hat (^) attached | subjected to the code | symbol in each said numerical formula represents the estimated value, the tilde (-) represents the average value, and the bar | burr (-) represents the observed value, respectively.

In the above case, the deterioration characteristic calculation unit 12 uses the maximum likelihood estimation value that maximizes the log likelihood function representing the co-occurrence probability that expresses the probability that the observed values of the soundness (ratings) of all objects are obtained simultaneously. Then, an average value (Aveθ ^k _i ) of an exponential hazard function that represents an average deterioration characteristic that does not consider the heterogeneity of the deterioration characteristic is ^obtained . Further, the heterogeneity parameter calculation unit 16 uses the average value (Aveθ ^k _i ) of the exponent hazard function, for example, to calculate a partial log likelihood representing the co-occurrence probability of the heterogeneity parameter of the target object belonging to the group k. Then, the heterogeneity parameter ε ^k of each group ^k is calculated as an optimal solution to be maximized (that is, on the assumption that the average value of the exponential hazard function becomes Ave θ ^k _i ).

As described above, the heterogeneity parameter ε ^k is based on individual heterogeneity factors that are difficult to observe. For example, the heterogeneity parameter ε ^k is calculated for each heterogeneity factor stored in advance in the heterogeneity factor storage unit 14. It can be. Moreover, it is good also as a structure which an administrator sets in the case of examination of a degradation characteristic.

  FIG. 5 shows a flow of an operation example of the deterioration evaluation apparatus according to the present invention. In FIG. 5, the state of health and the date and time of inspection determined by the administrator inspecting a plurality of objects are input from the input device, and the data receiving unit 10 receives them as inspection data (S1). This check is performed several times at an appropriate time.

Based on the data (state) regarding the soundness of a plurality of objects received by the data receiving unit 10, the deterioration characteristic calculating unit 12 averages (Aveθ) the deterioration characteristics θ _i (l _k ) of the objects for each deterioration factor. ^k _i ) is calculated (S2).

The heterogeneity parameter calculation unit 16 calculates the heterogeneity parameter ε ^k for each heterogeneity factor stored in the heterogeneity factor storage unit 14 or designated by the administrator (S3).

  Next, the benchmarking unit 18 evaluates the influence of the heterogeneity factor on the degradation characteristics based on the magnitude relationship of the heterogeneity parameters calculated by the heterogeneity parameter calculation unit 16 (S4), and the output unit 20 sets the benchmarking unit. 18 evaluation results are output (S5). In this case, the benchmarking unit 18 can create a deterioration curve and an average deterioration curve shown in FIG. 7 described later, for example, and the output unit 20 can output the deterioration curve and the average deterioration curve.

FIG. 6 shows a conceptual diagram of the magnitude relationship of the heterogeneity parameters output by the output unit 20. In FIG. 6, the horizontal axis represents the deterioration characteristic θ _i (l _k ), and the vertical axis _represents the number (frequency) of the elements l _k for each deterioration characteristic θ _i (l _k ). Further, the average value (Aveθ ^k _i ) of the deterioration characteristics θ _i (l _k ) is indicated by a vertical line. The heterogeneity parameter ε ^k is indicated by the distance in the horizontal axis direction from the average value (Aveθ ^k _i ).

In FIG. 6, the heterogeneity factors are indicated by A, B, and C. Further, the heterogeneity parameter ε ^k is indicated by the distance in the horizontal axis direction from the average value (Aveθ ^k _i ). Here, the heterogeneity factor is, for example, a condition peculiar to an individual bridge in a bridge having the same characteristic value such as a construction condition or an RC floor slab. Degradation characteristic theta _{i (l k),} since it indicates that higher degradation rate less is low, the heterogeneity parameter epsilon ^k defining equation (1), heterogeneity parameter as the degradation rate is smaller epsilon ^k that is small Become. For this reason, the deterioration factors A, B, and C increase in this order (A <B <C). As described above, the superiority or inferiority of each heterogeneous factor can be determined based on the deterioration characteristic θ _i (l _k ), and the factor that cannot be quantitatively observed or difficult can be evaluated.

となる。本式より、初期時点（レーティングが１の場合）からの経過年数と対象物の平均的なレーティングとの対応関係である劣化曲線を求めることができる。また、劣化曲線は、グループ毎に作成することも、グループの別なく全対象物を対象に作成することもできる。 By using the Markov degradation model, it is possible to obtain the expected rating life (the expected length of time from when the specified rating is reached for the first time until degradation progresses to the next rating), which is a risk management index in asset management. . That is, by integrating the probability F ′ _i (y _i ) that the life of the soundness i becomes y _i or more from time 0 to infinity, the rating expected life RMD _i is

It becomes. From this equation, it is possible to obtain a deterioration curve that is a correspondence relationship between the number of years elapsed from the initial time point (when the rating is 1) and the average rating of the object. In addition, the deterioration curve can be created for each group, or can be created for all objects regardless of the group.

FIG. 7 shows an example of a degradation curve and an average degradation curve (reference curve; benchmark curve) created by the benchmarking unit 18 from the expected rating life and its average value (corresponding to the heterogeneity parameter ε ^k = 1). An object positioned above the average deterioration curve (corresponding to ε ^k <1) has a slower deterioration than the average, and conversely, an object positioned below the average deterioration curve (corresponding to ε ^k > 1) is averaged. It can be seen that the deterioration is faster than

  By referring to this result and analyzing in detail objects that have a large deviation from the average deterioration curve, it is possible to grasp factors that affect the deterioration rate in addition to the factors that were foreseen at the time of the initial group division. it can.

  In this example, the deterioration curve has been described as an example, but the secular change of the stochastic deterioration distribution (rating probability distribution) is obtained for each heterogeneous parameter, and the factors affecting the deterioration speed are understood by comparing these. Is also possible.

It is a functional block diagram of one embodiment of a degradation evaluation device concerning the present invention. It is a figure which shows the example of a soundness degree. It is explanatory drawing of the degradation process of a target object. It is explanatory drawing of the formulation method of a Markov transition probability. It is a flowchart of the operation example of the degradation evaluation apparatus concerning this invention. It is a conceptual diagram of the magnitude relationship of a heterogeneity parameter. It is explanatory drawing of the relative evaluation of a degradation curve.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 10 Data reception part, 12 Deterioration characteristic calculation part, 14 Heterogeneity factor storage part, 16 Heterogeneity parameter calculation part, 18 Benchmarking part, 20 Output part

Claims (6)

A deterioration characteristic calculating means for calculating deterioration characteristics of the plurality of objects for each observable deterioration factor based on the soundness of the plurality of objects;
Heterogeneity parameter calculating means for calculating a heterogeneity parameter that is an indicator of the deviation of the deterioration characteristic for each unobservable or difficult to observe heterogeneity factor that causes a deviation in the deterioration characteristic;
A deterioration evaluation apparatus for a plurality of objects, comprising:   The deterioration evaluation apparatus for a plurality of objects according to claim 1, further comprising benchmarking means for evaluating the influence of the heterogeneity factor on the deterioration characteristics based on the magnitude relationship of the heterogeneity parameters. Equipment for evaluating deterioration of objects.   2. The deterioration characteristic calculating means obtains the deterioration characteristic as a maximum likelihood estimation value that maximizes a log likelihood function representing a co-occurrence probability density of deterioration processes of the plurality of objects. Item 3. The deterioration evaluation apparatus for multiple objects according to Item 2.   The heterogeneity parameter calculation means obtains a partial log likelihood representing a co-occurrence probability density in which an object having the heterogeneity factor occurs, and obtains the heterogeneity parameter as an optimal solution when the condition is maximized conditionally. The deterioration evaluation apparatus for a plurality of objects according to any one of claims 1 to 3, wherein: The deterioration evaluation apparatus further includes output means,
The benchmarking means takes the elapsed time on the horizontal axis and the soundness on the vertical axis, and creates a deterioration curve that relatively represents the deterioration characteristics of individual objects,
5. The multi-object degradation evaluation apparatus according to claim 2, wherein the output unit outputs an individual degradation curve created based on the value of the heterogeneity parameter. 6. . Get the degradation rate of multiple objects,
Based on the degradation rate, calculate degradation characteristics of the plurality of objects for each observable degradation factor,
Calculating a heterogeneity parameter that is an indicator of the deviation of the degradation characteristic for each unobservable or difficult to observe heterogeneity factor that causes a deviation in the degradation characteristic;
A method for evaluating deterioration of multiple objects.

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