JP6389804B2 - Failure rate estimation device, failure rate estimation method, and program - Google Patents

Description

  The present invention relates to a technique for estimating a failure rate of an apparatus, and more particularly to a technique for estimating a failure rate of an apparatus due to an earthquake.

  Various devices are used for social infrastructure such as communication, electricity, gas, and water. Since such a device is basically required to always operate normally, for example, it is estimated that aging deterioration is estimated and the deterioration device is repaired or replaced before failure occurs.

  However, when a large earthquake occurs, equipment failure is inevitable. Estimating how many devices will fail depending on the seismic intensity when a large earthquake occurs is important in planning the response when an earthquake occurs.

  Here, in general, when there are n devices, and if a failure occurs in m devices, if the failure occurs independently in each device, the number of failures (number of devices in which the failure occurs) is binomial distribution B In order to comply with (n, p), for failure rate p, p = m / n is the maximum likelihood estimate (Non-Patent Document 1).

Isao Yoshimura, Mathematical Statistics, pp.130-131, Baifukan, October 30, 1978

  In order to accurately estimate the device failure rate, a large amount of sample data is generally required. However, since there is a small amount of sample data related to damage caused by a large earthquake, it is required to appropriately estimate the failure rate from a small number of sample data.

  Here, to appropriately estimate the failure rate is to estimate a failure rate that satisfies natural demands related to the magnitude of seismic intensity and the effects of aging with respect to the size of the failure rate.

  However, when the number of sample data is small, the estimated value according to the prior art does not satisfy this requirement. Specifically, when the seismic intensity is high, the failure rate should be greater than when the seismic intensity is low. However, in the case where there is only one device in a place where the seismic intensity is high, if the device does not fail, it is estimated that the failure rate is 0, and there was a failure for 100 devices in the place where the seismic intensity was low. When the number of devices is 10, the failure rate is estimated to be 0.1, and the device failure rate due to earthquake is unnatural as the seismic intensity of the earthquake decreases. Similarly, for the same seismic intensity, even when an old device is requested to have a higher failure rate than a new device, an estimate that does not satisfy this requirement may occur simply by estimation according to the prior art.

  The present invention has been made in view of the above points, and an object of the present invention is to provide a technique that can appropriately estimate the failure rate of an apparatus due to an earthquake even when sample data is small.

According to an embodiment of the present invention, a failure rate estimation device for estimating a failure rate of a device due to an earthquake,
The probability of obtaining the observed number of failed devices under the assumption that the number of failed devices out of the total number of devices subjected to the earthquake follows a predetermined distribution function determined in advance with respect to the total number of devices and the failure rate of the device, Expressed as a function of the failure rate,
The property to be satisfied by the failure rate is expressed as a conditional expression of the failure rate,
An input means for inputting the function and the conditional expression;
Computing means for calculating a value of the failure rate that maximizes the probability represented by the function under the condition represented by the conditional expression;
And a failure rate estimation apparatus comprising: an output unit configured to output the failure rate value as an estimated value.

Moreover, according to the embodiment of the present invention, there is a failure rate estimation method executed by a failure rate estimation device that estimates a failure rate of a device due to an earthquake,
The probability of obtaining the observed number of failed devices under the assumption that the number of failed devices out of the total number of devices subjected to the earthquake follows a predetermined distribution function determined in advance with respect to the total number of devices and the failure rate of the device, Expressed as a function of the failure rate,
The property to be satisfied by the failure rate is expressed as a conditional expression of the failure rate,
An input step for inputting the function and the conditional expression;
An operation step of calculating a value of the failure rate that maximizes the probability represented by the function under the condition represented by the conditional expression;
An output step of outputting the failure rate value as an estimated value is provided.

  According to the embodiment of the present invention, there is provided a technique capable of appropriately estimating the failure rate of an apparatus due to an earthquake even when sample data is small.

It is a block diagram of the failure rate estimation apparatus 100 which concerns on embodiment of this invention. It is a figure which shows the total number n (s, t | i) of the checked pipe line. It is a figure which shows the total number v (s, t | i) of the pipe line where damage was seen as a result of inspection. It is a figure which shows the failure rate p when each failure occurs independently. It is a figure which shows the failure rate p calculated using the technique which concerns on this invention.

  Embodiments of the present invention will be described below with reference to the drawings. The embodiment described below is only an example, and the embodiment to which the present invention is applied is not limited to the following embodiment. For example, in the embodiment described below, a binomial distribution is used as an example of a predetermined known distribution function, but this is only an example, and the predetermined known distribution function is a binomial distribution. It is not limited to.

  Note that the “apparatus” that is the target of failure rate estimation in the present embodiment includes equipment such as pipeline equipment.

(Device configuration)
FIG. 1 shows a configuration diagram of a failure rate estimation apparatus 100 according to the present embodiment. The failure rate estimation apparatus 100 according to the present embodiment is an apparatus that estimates a failure rate that satisfies a natural request related to the magnitude of seismic intensity and the influence of aging based on data relating to the apparatus failure actually collected at the time of the occurrence of an earthquake. is there.

  As illustrated in FIG. 1, the failure rate estimation apparatus 100 according to the present embodiment includes an input unit 101, a data storage unit 102, a calculation unit 103, and an output unit 104.

  From the input unit 101, an equation for estimating the failure rate, data on actual device failure, and the like are input. The data storage unit 102 stores these formulas and data. The operation unit 103 performs an operation described later to estimate the failure rate of the device. The output unit 104 outputs the failure rate estimated by the calculation unit 103. For example, the output failure rate is displayed on a display.

  The failure rate estimation apparatus 100 according to the present embodiment can be realized by causing a computer to execute a program describing the processing contents described in the present embodiment. In other words, the functions of the device can be realized by executing a program corresponding to processing executed by the device using hardware resources such as a CPU, memory, and hard disk built in the computer. is there. The above-mentioned program can be recorded on a computer-readable recording medium (portable memory or the like), stored, or distributed. It is also possible to provide the program through a network such as the Internet or electronic mail.

(Processing content)
The processing contents for estimating the failure rate that satisfies the natural requirements related to the magnitude of seismic intensity and the effects of aging will be described in detail below.

  The failure rate estimation apparatus 100 according to the present embodiment uses the device type and the year (or year classification) as attribute pairs, and estimates the failure rate of the device for each seismic intensity for each attribute pair. In the present embodiment, the number of attributes is two, but this is an example, and the number of attributes may be one or three or more. Further, “attribute pair” may be regarded as one attribute.

  The device type is a criterion when categorizing the device according to some criterion. For example, when the device subject to failure rate estimation is a pipeline facility, its material (steel pipe, vinyl pipe, etc.) ) Is an example of type.

  The number of years represents the age (newness) of the equipment, and is the year in which the equipment subject to failure rate estimation was installed (eg, 1975), the number of years that have passed since installation (to the time of failure rate estimation), etc. is there. Further, the year may be the year division in which the apparatus is installed (eg, 1941 to 1969, after 1970, etc.). In the following, “years” includes years. The seismic intensity is the seismic intensity at the installation position of the device subject to failure rate estimation.

  In this embodiment, when estimating the failure rate of the apparatus for each seismic intensity for each attribute pair, the failure rate when the seismic intensity is large for the same attribute pair is low. Include a condition that the failure rate is higher than the failure rate (increased seismic intensity). Similarly, the following conditions 1) and 2) may be included.

  1) The same type of equipment with older years has the same or greater failure rate for the same seismic intensity than newer ones (aging degradation).

  2) When the seismic resistance is superior or inferior between the types of equipment (with or without reinforcing equipment, etc.), the failure rate of the equipment with earthquake resistance is less than the failure rate of the equipment without the earthquake (earthquake resistance) ).

  In estimating the failure rate, all of the above three conditions (intensity related to seismic intensity, secular deterioration, and earthquake resistance) may be used as conditions, or any two may be used as conditions. May be used as a condition. The above three conditions are examples, and conditions other than the three conditions may be used.

  In the present embodiment, the failure data of the device that is the target of failure rate estimation is obtained in the form of device type, number of years, device position, and presence / absence of device failure for each device. In addition, the seismic intensity at the location of the device is obtained from seismic intensity information from each place from the Japan Meteorological Agency and seismic intensity meter information of each station. As a result, for each device, the device type s, the year t, the seismic intensity i of the device position, and the device failure presence / absence j can be obtained as failure data vectors.

Here, if the failure data vector value of the a-th device is s (a), t (a), i (a), j (a), the failure of device type s, years t, and seismic intensity i at the device position The number of devices v (s, t | i)
Equation (1) v (s, t | i) = Σ _a I (s (a) = s, t (a) = t, i (a) = i) j (a)
Can be obtained at Here, in Expression (1), I (x) is a function that becomes 1 when x is true and 0 when it is false. That is, I (s (a) = s, t (a) = t, i (a) = i) is the case where the device type, age, and seismic intensity of the a-th device are s, t, and i, respectively. 1 J (a) is 1 when there is a failure in the a-th device, and 0 when there is no failure. Therefore, by adding I (s (a) = s, t (a) = t, i (a) = i) j (a) for a, the device type s, the year t, and the seismic intensity i of the device position The number of failed devices (v (s, t | i)) can be obtained.

  Further, if the failure rate in the case of seismic intensity i for a device having the attribute pair (s, t) is p (s, t | i), the condition for increasing the seismic intensity is expressed by the following equation (2).

Equation (2) p (s, t | i) <= p (s, t | i + 1)
Further, the aging deterioration condition is expressed by the following formula (3).

Equation (3) p (s, t | i) <= p (s, t + 1 | i)
Further, when the device s_1 has an earthquake resistance advantage over the device s_2, the condition of the earthquake resistance is expressed by the following formula (4).

Equation (4) p (s_1, t | i) <= p (s_2, t | i)
In the present embodiment, it is assumed that the failure of the device of the attribute pair (s, t) occurs independently by the failure rate based on the seismic intensity i of the device position for the device. In this case, when the device type s, the number of years t, and the seismic intensity i are n (s, t | i), the number of failed devices v (s, t | i) is the binomial distribution B (n ( s, t | i), p (s, t | i)).

  Therefore, the probability (likelihood) that the number of failed devices v (s, t | i) = m is given by f (m | n (s, t | i), p (s, t | i)). f (m | n, p) is given by the following equation (5). The following formula (5) itself is a general formula obtained from the definition of binomial distribution.

Formula (5) f (m | n, p) = nCm p ^m (1-p) ^(nm)
Here, as failure data (including the number of failed devices obtained by equation (1)), N sets of data (device type, year, seismic intensity, number of affected devices, number of failed devices are N sets) are obtained. For the k-th (k = 1 ,,, N) data, the device type is s_k, the year is t_k, the seismic intensity at the device position is i_k, and the number of failed devices at s_k, t_k, i_k is m_k. And As described above, since the probability that the number of failed devices v (s, t | i) = m is f (m | n (s, t | i), p (s, t | i)), The probability that the obtained N events occur is the probability f (m | n (s, t | i), for each k (k = 1 ,,, N), as shown in Equation (6) below. It is multiplied by p (s, t | i)).

(6) f (m_1 | n (s_1, t_1 | i_1), p (s_1, t_1 | i_1)) × f (m_2 | n (s_2, t_2 | i_2), p (s_2, t_2 | i_2)) × ... xf (m_N | n (s_N, t_N | i_N), p (s_N, t_N | i_N))
The failure rate estimation apparatus 100 receives the information of the above equations and failure data and stores them in the data storage unit 102. The calculation unit 103 uses the information stored in the data storage unit 102 to maximize the failure rate p (s_k, t_k | i_k) (6) with the conditions of the equations (2)-(4). k = 1,... N) is calculated. By using the failure rate p (s_k, t_k | i_k) (k = 1,, N) obtained by calculation as an estimated value, an estimated value that satisfies the demands such as the increase in seismic intensity can be obtained. This conditional maximization calculation itself can be performed by many conventional techniques. In addition, when there are multiple requests for seismic superiority, the condition equivalent to equation (4) may be increased by the number of requests, and if there is no request for deterioration over time, the condition may be deleted.

(Example)
Next, an embodiment in which failure rate estimation processing by the failure rate estimation apparatus 100 is applied to specific data will be described. The present embodiment is an example in which the failure rate of the pipeline equipment when an earthquake occurs is obtained.

  The apparatus type s of the pipe line in this embodiment is {tube type A, pipe type B, pipe type C, pipe type D}. Also, the year division t as “years” is given only to tube types B, C, and D. Specifically, tube types B and C are given the age category t as {after 1970, 1941-1969, before 1940}, and tube type D as {after 1970, before 1969}. Year division t is given. Seismic intensity i is given as {5 weak, 5 strong, 6 weak, 6 strong}.

  FIG. 2 shows the total number n (s, t | i) of pipes inspected because of the earthquake. For example, it is shown that the number of pipes subjected to shaking with a seismic intensity of 6 or more is 960 for pipe type B pipes whose age category is 1941-1969.

  FIG. 3 shows the total number of pipes v (s, t | i) in which damage was found as a result of inspection. For example, it is shown that the number of pipes that are damaged due to shaking with a seismic intensity of 6 or more is 6 for pipe type B pipes whose age category is 1941-1969.

  FIG. 4 shows the failure rate p in the case where each failure occurs independently based on the data shown in FIG. 2 and FIG. 3 using the prior art, v (s, t | i) / n (s, t | The estimated result is shown as i). As shown in FIG. 4, it can be seen that the failure rate that satisfies various requirements cannot be estimated in the prior art.

  Hereinafter, estimation of the failure rate p when a request is made for the failure rate using the failure rate estimation apparatus 100 according to the present embodiment will be described.

  Here, first, the data of FIG. 2 and FIG. 3 and the equation (6) are input from the input unit 101 from the input unit 101 of the failure rate estimation apparatus 100. Data and formula information input from the input unit 101 are stored in the data storage unit 102. When inputting an expression, it is not always necessary to input the expression in the same format as the expression described in this specification. For example, the expression conforms to the specification of the nonlinear optimization tool that provides the function of the calculation unit 103. (Script etc.) In addition, with respect to the equation (6), the part (m, n in the equation (6)) in which the data of FIGS. 2 and 3 is input is input as a variable, and the arithmetic unit 103 stores the data in the variable (6) May be generated, or the equation (6) including the data of FIGS. 2 and 3 may be input from the input unit 101.

  In addition, as a request given to the failure rate p from the input unit 101 of the failure rate estimation apparatus 100, an equation (2) that is a conditional expression for increasing seismic intensity and an equation (3) that is a conditional equation for secular deterioration Enter a conditional expression that indicates the seismic resistance of the device. Regarding the conditional expression indicating the seismic resistance of the apparatus, in this embodiment, all of the pipe types B, C, and D have a seismic superiority over the pipe type A (the same 3 as the expression (4)). Two expressions). For tube types B and C, the condition that the failure rate is equal when the year division and seismic intensity are the same is given by the following equation (7) and input from the input unit 101. In the formula (7), for example, s_3 indicates the tube type B, and s_4 indicates the tube type C.

Equation (7) p (s_3, t | i) = p (s_4, t | i)
The calculation unit 103 of the failure rate estimation apparatus 100 calculates a failure rate p that maximizes the equation (6) under given conditions. In this embodiment, Rsolnp, which is a nonlinear optimization tool for R, is used as a program corresponding to the calculation unit 103.

  FIG. 5 shows the calculation result of the failure rate p in this example. In FIG. 5, it can be confirmed that the failure rate satisfying various requirements can be estimated. That is, even when the number of sample data is small, it is possible to perform failure rate estimation that satisfies natural requirements.

  The present invention is not limited to the above-described embodiments, and various modifications and applications are possible within the scope of the claims.

DESCRIPTION OF SYMBOLS 100 Failure rate estimation apparatus 101 Input part 102 Data storage part 103 Operation part 104 Output part

Claims (8)

A failure rate estimation device that estimates the failure rate of a device due to an earthquake,
The probability of obtaining the observed number of failed devices under the assumption that the number of failed devices out of the total number of devices subjected to the earthquake follows a predetermined distribution function determined in advance with respect to the total number of devices and the failure rate of the device, Expressed as a function of the failure rate,
The property to be satisfied by the failure rate is expressed as a conditional expression of the failure rate,
An input means for inputting the function and the conditional expression;
Computing means for calculating a value of the failure rate that maximizes the probability represented by the function under the condition represented by the conditional expression;
And an output means for outputting the value of the failure rate as an estimated value. If the device attribute is the device type s and the year t, and the seismic intensity of the earthquake received by the device is the seismic intensity i, the failure rate p (s, t | i) for the device type s, year t, seismic intensity i should be satisfied The conditional expression indicating the property is expressed by an equality or inequality of the failure rate p (s, t | i),
The total number of devices in device type s, years t, seismic intensity i is n (s, t | i), the number of failed devices is v (s, t | i) = m, and the probability that the number of failed devices is m is f. where (m | n (s, t | i), p (s, t | i)), the function yields the probability f (m | n (s, t, i) for each (s, t, i) The failure rate estimation apparatus according to claim 1, which is a function obtained by multiplying | i), p (s, t | i)). The properties to be failure rate satisfies the failure rate when seismic intensity is large, the first property that seismic intensity is not less than the failure rate when it is small, the failure rate of the old device, the failure rate of the new device The second property that it is above, or the failure rate of a device with earthquake resistance is a third property that is equal to or less than the failure rate of a device without earthquake resistance. The failure rate estimation apparatus described. The first property is represented by p (s, t | i) <= p (s, t | i + 1), and the second property is p (s, t | i) <= p (s, t + 1 | i), and the third property is that p (s_1, t | i) <= p (s_2, t | in the case where the device s_1 has an earthquake resistance superior to the device s_2. The failure rate estimation device according to claim 3, which is dependent on claim 2, characterized by i). A failure rate estimation method executed by a failure rate estimation device that estimates a failure rate of a device due to an earthquake,
The probability of obtaining the observed number of failed devices under the assumption that the number of failed devices out of the total number of devices subjected to the earthquake follows a predetermined distribution function determined in advance with respect to the total number of devices and the failure rate of the device, Expressed as a function of the failure rate,
The property to be satisfied by the failure rate is expressed as a conditional expression of the failure rate,
An input step for inputting the function and the conditional expression;
An operation step of calculating a value of the failure rate that maximizes the probability represented by the function under the condition represented by the conditional expression;
An output step for outputting the value of the failure rate as an estimated value. If the device attribute is the device type s and the year t, and the seismic intensity of the earthquake received by the device is the seismic intensity i, the failure rate p (s, t | i) for the device type s, year t, seismic intensity i should be satisfied The conditional expression indicating the property is expressed by an equality or inequality of the failure rate p (s, t | i),
The total number of devices in device type s, years t, seismic intensity i is n (s, t | i), the number of failed devices is v (s, t | i) = m, and the probability that the number of failed devices is m is f. where (m | n (s, t | i), p (s, t | i)), the function yields the probability f (m | n (s, t, i) for each (s, t, i) 6. The failure rate estimation method according to claim 5, which is a function obtained by multiplying | i), p (s, t | i)). The property to be satisfied by the failure rate is that the failure rate when the seismic intensity is high is higher than the failure rate when the seismic intensity is low, the failure rate of the old device is higher than the failure rate of the new device. The failure rate estimation method according to claim 5 or 6, wherein the failure rate of the device having earthquake resistance or the failure rate of the device having earthquake resistance is equal to or less than the failure rate of the device having no earthquake resistance.   The program for functioning a computer as each means in the failure rate estimation apparatus of any one of Claims 1 thru | or 4.

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