CN112950036A - Reliability analysis method for high-speed railway traction substation system - Google Patents

Reliability analysis method for high-speed railway traction substation system Download PDF

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CN112950036A
CN112950036A CN202110247185.6A CN202110247185A CN112950036A CN 112950036 A CN112950036 A CN 112950036A CN 202110247185 A CN202110247185 A CN 202110247185A CN 112950036 A CN112950036 A CN 112950036A
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张海刚
刘飘
刘小钊
陈璇
张文
罗俊
赵德成
邹劲柏
杨明来
童中祥
杨俊�
孙平飞
王燕锋
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Abstract

The invention discloses a reliability analysis method for a high-speed railway traction substation system, which comprises the following steps of 1: defining an evaluation system of a high-speed railway traction substation system, namely, specifying a system range and determining a system reliability index; step 2: determining a successful guide criterion and a reliability index of reliability modeling of a high-speed railway traction substation system; and step 3: taking the main electrical wiring of the high-speed railway traction substation as a research object, determining the signal FLOW direction of GO-FLOW and selecting a proper operator, and establishing a GO-FLOW diagram of the main electrical wiring of the traction substation; and 4, step 4: inputting reliability parameters of the operational characters; and 5: obtaining steady-state and dynamic reliability indexes of the GO-FLOW through quantitative calculation and analysis of each operational character; step 6: and completing the reliability evaluation of the high-speed railway traction substation system.

Description

Reliability analysis method for high-speed railway traction substation system
Technical Field
The invention relates to the field of railway traction power supply, in particular to a reliability analysis method for a high-speed railway traction substation system.
Background
With the large-scale construction of high-speed railways in China, people pay high attention to the reliability problem of a traction power supply system. The traction substation is used as the core of a traction power supply system and plays a role of a bridge for connecting an external power system and a contact network. Therefore, its failure will affect the normal operation of the high-speed railway and cause huge losses. In order to ensure the safe and stable running of the locomotive group, the power supply reliability of the high-speed railway traction power substation must be ensured.
China starts earlier in the aspect of reliability research of electric power systems, and has more achievements, but has less reliability research on traction power supply systems. At present, the fault tree analysis method (FTA) is applied to the reliability research of a traction power supply system in Chenshaoshao and Wanyi, the fault tree of an electric main connection wire and a contact network of a traction substation is established, and qualitative and quantitative analysis is completed; thanks to the selection of Weibull distribution as a reliability model by Sword, an artificial intelligence algorithm based on a genetic algorithm is provided, goodness-of-fit inspection is carried out, and fitting accuracy is improved; the Li military intelligence and Zhao Jian put forward a successful flow method (GO) and successfully applied to a traction substation, thereby finding out a simple, convenient, clear and practical method for researching the reliability of the traction substation. Takeshi Matsuoka et al further supplements and perfects the principle and method of GO-FLOW, theoretically establishes a knowledge structure of the application of the GO-FLOW, and analyzes the reliability of a reactor core emergency cooling system of a boiling water reactor and the like and the reliability of a product production process by using a GO-FLOW method. In addition, the GO-FLOW process is also used to address common cause failures. In practical application, the GO-FLOW method is used for analyzing the reliability and safety of systems such as nuclear power stations and the like, and is also used in other fields. The aging problem of nuclear power plants was studied by the GO-FLOW method by Tadatsugi Okazaki, Nobuo Mitomo, and the like, Japan Ship research institute. And the Takeshi Matsuoka adopts a dynamic event tree and a GO-FLOW method to perform reliability analysis on the relay delay system.
Disclosure of Invention
GO-FLOW is a new probability risk evaluation method, which is mainly used for the probability of occurrence of complex time sequence or state. The GO-FLOW method adopts a graphical deduction mode, takes successful operation as a basis of reliability modeling, selects corresponding operational characters, directly establishes a GO-FLOW diagram according to a schematic diagram or a block diagram of the system, calculates the probability of occurrence of various states of the system, has good precision of calculation results and small calculation amount, and provides a reliable scientific basis for the maintenance plan of the whole equipment of a traction power supply station system.
In order to achieve the above purpose, the technical solution for solving the technical problem is as follows:
a reliability analysis method for a high-speed railway traction substation system comprises the following steps:
step 1: defining an evaluation system of a high-speed railway traction substation system, namely, specifying a system range and determining a system reliability index;
step 2: determining a successful guide criterion and a reliability index of reliability modeling of a high-speed railway traction substation system;
and step 3: taking the main electrical wiring of the high-speed railway traction substation as a research object, determining the signal FLOW direction of GO-FLOW and selecting a proper operator, and establishing a GO-FLOW diagram of the main electrical wiring of the traction substation;
and 4, step 4: inputting reliability parameters of the operational characters;
and 5: obtaining steady-state and dynamic reliability indexes of the GO-FLOW through quantitative calculation and analysis of each operational character;
step 6: and completing the reliability evaluation of the high-speed railway traction substation system.
Further, in the step 1: from the aspect of reliability, the traction substation is an engineering redundancy repairable system, all primary partial equipment, subsystems and systems of the traction substation are assumed to be subjected to exponential distribution and have the system average characteristic in a stable operation stage, main component equipment of the high-speed railway traction substation comprises a bus, a traction transformer, a circuit breaker, an isolating switch, a voltage transformer and a current transformer, two groups of traction transformers (T1, T2) and (T3 and T4) which are mutually hot standby are adopted to meet the continuous power supply requirement, and an external power supply is a 220 kv-grade power supply.
Further, in the step 2: the method is characterized in that normal power supply of an uplink and downlink contact network of a high-speed railway traction substation is used as a successful guidance criterion for reliability modeling, and reliability indexes mainly comprise fault rate lambda, maintenance rate, reliability, mean time to failure, mean maintenance time, mean life cycle, steady-state mean working probability, mean shutdown probability and mean failure times.
Further, the step 2 specifically includes the following steps:
step 21: the reliability R (t) and the unreliability F (t) are respectively expressed as:
R(t)＝P(T＞t)(0＜t＜∞) (1)
F(t)＝1-R(t) (2)
wherein T is the lifetime of the system component;
step 22: the fault rate lambda (t) is expressed as:
Figure BDA0002964515810000031
this gives a relation to the reliability:
Figure BDA0002964515810000032
step 23: the maintenance rate is a probability index for measuring the maintenance performance of the product, and is expressed by mu (t), and the formula is as follows:
Figure BDA0002964515810000033
in the formula, TDRepairing time for the product;
step 24: mean Time Between Failures (MTBF), where MTBF is an average value of working times of a component between two adjacent failures when the component fails, for a repairable component, and the MTBF is expressed as:
Figure BDA0002964515810000034
step 25: mean time to repair MTTR, MTTR is the average number of component repair times and is the ratio of total repair time to the number of repairs, and the MTTR is expressed as:
Figure BDA0002964515810000035
step 26: the steady-state availability A, also called the average working probability, is the availability of the element when the time tends to infinity, and the expression is as follows:
Figure BDA0002964515810000041
i.e. unavailability
Figure BDA0002964515810000042
Expressed, its expression is:
Figure BDA0002964515810000043
step 27: the average life-cycle MCT is expressed as:
MCT＝MTBF+MTTR (10)
step 28: the average failure frequency f is expressed as:
Figure BDA0002964515810000044
further, in the step 3: in the GO-FLOW method, a connection line representing an input-output relationship between operators is called a signal line, and the signal FLOW strength represents the reliability of a system, namely the probability of successful operation of the system, and the specific steps are as follows:
step 31: the GO-FLOW method defines 14 types of standard operators, wherein at a time point t, the strength of an output signal is represented by R (t), the strength of a main input signal is represented by S (t), and the number of time points is represented by n;
step 32: the functions and characteristics of operators in the GO-FLOW method are generally distinguished by type numbers, and each specific type number corresponds to a specific operation rule:
(1) type 21 operator-two-state element
Type 21 operators are used to represent two state elements, PgTo representThe success probability of the element represented by the operator, and the output signal strength are expressed as:
R(t)＝S(t)·Pg (12)
(2) type 22 operator-OR gate
The type 22 operator is a logic gate used to represent the logical relationship of a plurality of signals, and the output signal strength is expressed as:
Figure BDA0002964515810000051
(3) type 23 operator-NOT gate
The type 23 operator is a logic gate which is in the logical relationship of an input signal and an output signal NOT gate, and the expression of the strength of the output signal is as follows:
R(t)＝1-S(t) (14)
(4) type 30 operator-AND gate
Representing the logical relationship of a plurality of signals, and assuming that M input signals are independent of each other, the output signal strength is expressed as:
Figure BDA0002964515810000052
(5) type 35 operator-a working element that fails over time
A type 35 operator, γ represents the failure probability of the element represented by the operator in unit time, i.e. failure rate, assuming γ is constant, and for the type 35 operator, the second input signal strength represents a time interval, the output signal strength r (t) decreases due to the effect of failure rate, r (t) is influenced by the main input signal S (t) before the time point tk) The effect, expressed as:
Figure BDA0002964515810000053
step 33: the high-speed railway traction substation has various component elements, so that the simplification is realized by adopting an equivalent unit method, and each equivalent unit is represented by an operator;
step 34: based on the GO-FLOW method principle, the GO-FLOW diagram of the main wiring of the high-speed railway traction substation is established by considering that the electrical equipment of the traction substation has a certain service life, namely the failure probability of elements changes along with the change of time.
Further, in the step 5: assuming that N shutdown-related serial parts correspond to one operator, when I is 1, the equivalent failure rate of the serial structure is lambdaRMean time to repair τRThe method comprises the following specific steps:
step 51: failure rate λRThe expression of (a) is:
Figure BDA0002964515810000054
Figure BDA0002964515810000061
Figure BDA0002964515810000062
the tape (18) is brought with the formula (19) to give (20):
Figure BDA0002964515810000063
wherein λ isSiIs the failure rate of the ith series equivalent cell, τSiMean time to repair, μ, of the ith series equivalent cellSiThe variation range of the value of i is [1, N ] for the average maintenance rate of the ith series equivalent unit]；
Step 52: probability value P of successful state of output signal of series equivalent unitR(1) The expression is as follows:
Figure BDA0002964515810000064
i.e. probability value P of fault state of output signal of series equivalent unitR(2) The expression is as follows:
Figure BDA0002964515810000065
due to the adoption of the technical scheme, compared with the prior art, the invention has the following advantages and positive effects:
1. the invention relates to a reliability analysis method of a high-speed railway traction substation system, which is mainly based on a GO-FLOW method, and is a system probability analysis technology which takes success as guidance;
2. the high-speed railway traction substation conforms to the GO-FLOW basic modeling rule, the model structure is clear, the significance of internal parameters of each component of the model is clear, and the internal parameters are easy to obtain;
3. the invention is suitable for modeling analysis of large complex systems, especially for reliability and safety analysis of complex systems with multiple states and time sequence function conversion, and has short modeling time, low cost and strong practicability.
4. The invention proves the correctness and the applicability of the GO-FLOW method based on the GO method, and embodies the superiority of the GO-FLOW method. The reliability and the safety of the train in the running process can be improved, meanwhile, corresponding theoretical reference is provided for avoiding the rail transit traction power supply system fault, and a basis and a premise are provided for the overhaul and the health management of the traction power supply system.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort. In the drawings:
FIG. 1 is an overall flow chart of the reliability research method of the high-speed railway traction substation system of the invention;
FIG. 2 is a schematic diagram of the electrical main wiring of the high speed railway traction substation;
FIG. 3 is a diagram of the GO-FLOW method defining 14 types of standard operators and their type names and symbols;
FIG. 4 is a GO-FLOW diagram of the main wiring of a high-speed railway traction substation.
Detailed Description
While the embodiments of the present invention will be described and illustrated in detail with reference to the accompanying drawings, it is to be understood that the invention is not limited to the specific embodiments disclosed, but is intended to cover various modifications, equivalents, and alternatives falling within the scope of the invention as defined by the appended claims.
As shown in fig. 1-2, the present embodiment discloses a reliability analysis method for a high-speed railway traction substation system, which includes the following steps:
step 1: defining an evaluation system of a high-speed railway traction substation system, namely, specifying a system range and determining a system reliability index;
step 2: determining a successful guide criterion and a reliability index of reliability modeling of a high-speed railway traction substation system;
and step 3: taking the main electrical wiring of the high-speed railway traction substation as a research object, determining the signal FLOW direction of GO-FLOW and selecting a proper operator, and establishing a GO-FLOW diagram of the main electrical wiring of the traction substation;
and 4, step 4: inputting reliability parameters of the operational characters;
and 5: obtaining steady-state and dynamic reliability indexes of the GO-FLOW through quantitative calculation and analysis of each operational character;
step 6: and completing the reliability evaluation of the high-speed railway traction substation system.
Further, in the step 1: from the aspect of reliability, the traction substation is an engineering redundancy repairable system, all primary partial equipment, subsystems and systems of the traction substation are assumed to be subjected to exponential distribution and have the system average characteristic in a stable operation stage, main component equipment of the high-speed railway traction substation comprises a bus, a traction transformer, a circuit breaker, an isolating switch, a voltage transformer, a current transformer and the like, in order to meet continuous power supply requirements, two groups of traction transformers (T1, T2) and (T3 and T4) which are mutually hot standby are adopted, and an external power supply is a 220 kv-grade power supply.
Further, in the step 2: the method is characterized in that normal power supply of an uplink and downlink contact network by a high-speed railway traction substation is used as a successful guidance criterion for reliability modeling, and reliability indexes related to the research of the embodiment mainly comprise fault rate lambda, maintenance rate, reliability, mean time to failure (MTBF), mean maintenance time (MTTR), mean life cycle, steady-state mean working probability, mean shutdown probability and mean failure times.
Further, the step 2 specifically includes the following steps:
step 21: the reliability R (t) and the unreliability F (t) are respectively expressed as:
R(t)＝P(T＞t)(0＜t＜∞) (1)
F(t)＝1-R(t) (2)
wherein T is the lifetime of the system component;
step 22: the fault rate lambda (t) is expressed as:
Figure BDA0002964515810000081
this gives a relation to the reliability:
Figure BDA0002964515810000082
step 23: the maintenance rate is a probability index for measuring the maintenance performance of the product, and is expressed by mu (t), and the formula is as follows:
Figure BDA0002964515810000091
in the formula, TDRepairing time for the product;
step 24: mean Time Between Failures (MTBF), MTBF is an average value of the operating Time Between two adjacent failures of a repairable element when the element fails, and the expression of MTBF is:
Figure BDA0002964515810000092
step 25: mean Time To Repair (MTTR) which is the average of component repair times and is the ratio of the total repair Time To the number of repairs, and the expression of MTTR is:
Figure BDA0002964515810000093
step 26: the steady-state availability A (availability), which is also called the average working probability, is the availability of the element when the time approaches infinity, and the expression is as follows:
Figure BDA0002964515810000094
i.e. unavailability
Figure BDA0002964515810000095
Expressed, its expression is:
Figure BDA0002964515810000096
step 27: the average life Cycle MCT (mean Cycle time) is expressed as:
MCT＝MTBF+MTTR (10)
step 28: the average failure frequency f is expressed as:
Figure BDA0002964515810000097
further, in the step 3: in the GO-FLOW method, a connection line representing an input/output relationship between operators is referred to as a signal line, and the signal FLOW strength in this embodiment represents the reliability of the system, i.e., the probability of successful operation of the system. The present embodiment introduces several operational rules in detail, and other simple expressions, the specific steps are as follows:
step 31: the GO-FLOW method defines 14 types of standard operators, the type names and symbols of which are shown in fig. 3, and in general, at time t, the strength of the output signal is represented by r (t), the strength of the main input signal is represented by s (t), and the number of time points is represented by n;
step 32: the functions and characteristics of operators in the GO-FLOW method are generally distinguished by type numbers, and each specific type number corresponds to a specific operation rule:
(1) type 21 operator-two-state element
Type 21 operators are used to represent two state elements, PgRepresenting the success probability of the element represented by the operator, the output signal strength is expressed as:
R(t)＝S(t)·Pg (12)
(2) type 22 operator-OR gate
The type 22 operator is a logic gate used to represent the logical relationship of a plurality of signals, and the output signal strength is expressed as:
Figure BDA0002964515810000101
(3) type 23 operator-NOT gate
The type 23 operator is a logic gate which is in the logical relationship of an input signal and an output signal NOT gate, and the expression of the strength of the output signal is as follows:
R(t)＝1-S(t) (14)
(4) type 30 operator-AND gate
As shown, it represents the logical relationship of a plurality of signals, and assuming that M input signals are independent of each other, the output signal strength is expressed as:
Figure BDA0002964515810000102
(5) type 35 operator-a working element that fails over time
The type 35 operator is shown in the figure, gamma represents the failure probability of the element represented by the operator in unit time, namely failure rate, and assuming that gamma is constant, for the type 35 operator, the input signal strength represents a time interval, the output signal strength R (t) is reduced due to the influence of failure rate, and R (t) is influenced by the main input signal S (t) before the time point tk) The effect, expressed as:
Figure BDA0002964515810000111
step 33: the high-speed railway traction substation has various component elements, so that the simplification is realized by adopting an equivalent unit method, each equivalent unit is represented by an operator, and the specific operator meaning is shown in table 1;
Figure BDA0002964515810000112
Figure BDA0002964515810000121
TABLE 1 operational character meaning in GO-FLOW diagram of main connection wire of high-speed railway traction substation
Step 34: based on the GO-FLOW method principle, considering that the electrical equipment of the traction substation has a certain service life, namely the failure probability of elements changes along with the change of time, a GO-FLOW diagram of the main wiring of the traction substation of the high-speed railway is established, as shown in FIG. 4.
Further, in the step 4: the reliability parameters of the main electrical equipment of the traction substation are shown in table 2:
Figure BDA0002964515810000122
TABLE 2 reliability parameters of main electrical equipments of traction substation
Further, in the step 5: assuming that N shutdown-related serial parts correspond to one operator, when I is 1, the equivalent failure rate of the serial structure is lambdaRMean time to repair τRThe method comprises the following specific steps:
step 51: failure rate λRThe expression of (a) is:
Figure BDA0002964515810000131
Figure BDA0002964515810000132
Figure BDA0002964515810000133
the tape (18) is brought with the formula (19) to give (20):
Figure BDA0002964515810000134
wherein λ isSiIs the failure rate of the ith series equivalent cell, τSiMean time to repair, μ, of the ith series equivalent cellSiThe variation range of the value of i is [1, N ] for the average maintenance rate of the ith series equivalent unit]；
Step 52: series equivalent unit output signalProbability value P of number success stateR(1) The expression is as follows:
Figure BDA0002964515810000135
i.e. probability value P of fault state of output signal of series equivalent unitR(2) The expression is as follows:
Figure BDA0002964515810000136
the above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (6)

1. A reliability analysis method for a high-speed railway traction substation system is characterized by comprising the following steps:
step 1: defining an evaluation system of a high-speed railway traction substation system, namely, specifying a system range and determining a system reliability index;
step 2: determining a successful guide criterion and a reliability index of reliability modeling of a high-speed railway traction substation system;
and step 3: taking the main electrical wiring of the high-speed railway traction substation as a research object, determining the signal FLOW direction of GO-FLOW and selecting a proper operator, and establishing a GO-FLOW diagram of the main electrical wiring of the traction substation;
and 4, step 4: inputting reliability parameters of the operational characters;
and 5: obtaining steady-state and dynamic reliability indexes of the GO-FLOW through quantitative calculation and analysis of each operational character;
step 6: and completing the reliability evaluation of the high-speed railway traction substation system.
2. The reliability analysis method for the high-speed railway traction substation system according to claim 1, wherein in the step 1: from the aspect of reliability, the traction substation is an engineering redundancy repairable system, all primary partial equipment, subsystems and systems of the traction substation are assumed to be subjected to exponential distribution and have the system average characteristic in a stable operation stage, main component equipment of the high-speed railway traction substation comprises a bus, a traction transformer, a circuit breaker, an isolating switch, a voltage transformer and a current transformer, two groups of traction transformers (T1, T2) and (T3 and T4) which are mutually hot standby are adopted to meet the continuous power supply requirement, and an external power supply is a 220 kv-grade power supply.
3. The reliability analysis method for the high-speed railway traction substation system according to claim 1, wherein in the step 2: the method is characterized in that normal power supply of an uplink and downlink contact network of a high-speed railway traction substation is used as a successful guidance criterion for reliability modeling, and reliability indexes mainly comprise fault rate lambda, maintenance rate, reliability, mean time to failure, mean maintenance time, mean life cycle, steady-state mean working probability, mean shutdown probability and mean failure times.
4. The reliability analysis method of the high-speed railway traction substation system according to claim 3, wherein the step 2 specifically comprises the following steps:
step 21: the reliability R (t) and the unreliability F (t) are respectively expressed as:
R(t)＝P(T＞t)(0＜t＜∞) (1)
F(t)＝1-R(t) (2)
wherein T is the lifetime of the system component;
step 22: the fault rate lambda (t) is expressed as:
Figure FDA0002964515800000021
this gives a relation to the reliability:
Figure FDA0002964515800000022
step 23: the maintenance rate is a probability index for measuring the maintenance performance of the product, and is expressed by mu (t), and the formula is as follows:
Figure FDA0002964515800000023
in the formula, TDRepairing time for the product;
step 24: the mean time between failure MTBF,
the MTBF is an average value of the operating time of a component between two adjacent failures when the component fails, and the expression of the MTBF is as follows:
Figure FDA0002964515800000024
step 25: mean time to repair MTTR, MTTR is the average number of component repair times and is the ratio of total repair time to the number of repairs, and the MTTR is expressed as:
Figure FDA0002964515800000025
step 26: the steady-state availability A, also called the average working probability, is the availability of the element when the time tends to infinity, and the expression is as follows:
Figure FDA0002964515800000026
i.e. unavailability
Figure FDA0002964515800000027
Expressed, its expression is:
Figure FDA0002964515800000031
step 27: the average life-cycle MCT is expressed as:
MCT＝MTBF+MTTR (10)
step 28: the average failure frequency f is expressed as:
Figure FDA0002964515800000032
5. the reliability analysis method for the high-speed railway traction substation system according to claim 1, wherein in the step 3: in the GO-FLOW method, a connection line representing an input-output relationship between operators is called a signal line, and the signal FLOW strength represents the reliability of a system, namely the probability of successful operation of the system, and the specific steps are as follows:
step 31: the GO-FLOW method defines 14 types of standard operators, wherein at a time point t, the strength of an output signal is represented by R (t), the strength of a main input signal is represented by S (t), and the number of time points is represented by n;
step 32: the functions and characteristics of operators in the GO-FLOW method are generally distinguished by type numbers, and each specific type number corresponds to a specific operation rule:
(1) type 21 operator-two-state element
Type 21 operators are used to represent two state elements, PgRepresenting the success probability of the element represented by the operator, the output signal strength is expressed as:
R(t)＝S(t)·Pg (12)
(2) type 22 operator-OR gate
The type 22 operator is a logic gate used to represent the logical relationship of a plurality of signals, and the output signal strength is expressed as:
Figure FDA0002964515800000033
(3) type 23 operator-NOT gate
The type 23 operator is a logic gate which is in the logical relationship of an input signal and an output signal NOT gate, and the expression of the strength of the output signal is as follows:
R(t)＝1-S(t) (14)
(4) type 30 operator-AND gate
Representing the logical relationship of a plurality of signals, and assuming that M input signals are independent of each other, the output signal strength is expressed as:
Figure FDA0002964515800000041
(5) type 35 operator-a working element that fails over time
A type 35 operator, γ represents the failure probability of the element represented by the operator in unit time, i.e. failure rate, assuming γ is constant, and for the type 35 operator, the second input signal strength represents a time interval, the output signal strength r (t) decreases due to the effect of failure rate, r (t) is influenced by the main input signal S (t) before the time point tk) The effect, expressed as:
Figure FDA0002964515800000042
step 33: the high-speed railway traction substation has various component elements, so that the simplification is realized by adopting an equivalent unit method, and each equivalent unit is represented by an operator;
step 34: based on the GO-FLOW method principle, the GO-FLOW diagram of the main wiring of the high-speed railway traction substation is established by considering that the electrical equipment of the traction substation has a certain service life, namely the failure probability of elements changes along with the change of time.
6. The reliability analysis method for the high-speed railway traction substation system according to claim 1, wherein in the step 5: assuming that N shutdown-related serial parts correspond to one operator, when I is 1, the equivalent failure rate of the serial structure is lambdaRMean time to repair τRThe method comprises the following specific steps:
step 51: failure rate λRThe expression of (a) is:
Figure FDA0002964515800000043
Figure FDA0002964515800000044
Figure FDA0002964515800000051
the tape (18) is brought with the formula (19) to give (20):
Figure FDA0002964515800000052
wherein λ isSiIs the failure rate of the ith series equivalent cell, τSiMean time to repair, μ, of the ith series equivalent cellSiThe variation range of the value of i is [1, N ] for the average maintenance rate of the ith series equivalent unit]；
Step 52: probability value P of successful state of output signal of series equivalent unitR(1) The expression is as follows:
Figure FDA0002964515800000053
i.e. probability value P of fault state of output signal of series equivalent unitR(2) The expression is as follows:
Figure FDA0002964515800000054
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