A method for allocating reliability indicators of an electromechanical system based on characteristic life

Abstract

The application discloses a kind of based on feature life electromechanical system reliability index distribution method, belong to reliability design technical field.The technical scheme is: the life of electromechanical system obeys Weibull distribution, the reliability index of electromechanical system is converted into the feature life of Weibull distribution, according to use profile and duty cycle determines the duty cycle of each unit, establishes the relationship between certain parameter to be solved and the feature life of each unit, unknown parameter is solved using the feature life relationship equation of system and unit, to calculate the reliability index distribution value of each unit.The application overcomes the defect that the reliability index distribution method of electronic product is distributed to the reliability index of electromechanical system, leading to unreasonable distribution value.

Description

Technical Field

[0001] This invention relates to the field of reliability design technology, and specifically to a method for allocating reliability indicators for electromechanical systems based on characteristic lifetime. Background Technology

[0002] Reliability allocation is the process of quantitatively decomposing the reliability requirements of a product, from the overall structure to its components, according to given criteria. Its purpose is to clarify the reliability design requirements for each component. Reliability allocation is primarily conducted during the design and prototype stages of product development.

[0003] For complex electromechanical equipment, the reliability allocation process often follows the principle that lifespan follows an exponential distribution. This results in some electromechanical equipment having excessively high reliability index allocation values ​​that do not conform to reality, thus creating difficulties for reliability design and testing. Summary of the Invention

[0004] In view of this, the present invention provides a method for allocating reliability indicators of electromechanical systems based on characteristic lifetime, which can overcome the defect of unreasonable allocation values ​​caused by using the reliability indicator allocation method of electronic products to allocate reliability indicators of electromechanical systems.

[0005] A method for allocating reliability indicators for electromechanical systems based on characteristic lifetimes, wherein the electromechanical system S consists of N devices connected in series, and the implementation of the method includes the following steps:

[0006] Step 1: Convert the system's reliability metrics into the system's characteristic lifetime;

[0007] Step 2: Based on the system's usage profile and the duty cycle of each device during system operation, determine the relationship between the task time of each unit and the system's task time, and calculate the task time of each unit;

[0008] Step 3: Establish the relationship between the characteristic lifetime of a unit and a certain parameter to be determined;

[0009] Step 4: Using the characteristic lifetime relationship equations of the system and its components, calculate the parameters through numerical calculations;

[0010] Step 5: Based on the parameter values, the functional relationship between the parameters and the unit characteristic lifetime in Step 3, and the relationship between the characteristic lifetime of each unit and the reliability index in Step 1, calculate the reliability index allocation value for each unit.

[0011] Furthermore, in step one, the system reliability index is converted into the system's characteristic lifetime η using the parameter relationship of the Weibull distribution. S ;

[0012] When allocating reliability, the conversion formula is:

[0013]

[0014] In the formula, t S Let S be the task time of system S, which is an input parameter for system design and is a known value;

[0015] m S Let be the shape parameter of the Weibull distribution of system S, selected based on information about similar products, and take values ​​in [1.5, 4].

[0016] R S The reliability requirement of system S is a known value and is an input parameter for system design.

[0017] When allocating average lifespan, the conversion formula is as follows:

[0018]

[0019] In the formula, θ S The average lifetime requirement of system S is a known value and is an input parameter for system design.

[0020] m S Let be the shape parameter of the Weibull distribution of system S, selected based on information about similar products, and take values ​​in [1.5, 4].

[0021] Γ(·) is the gamma function.

[0022] When allocating reliable lifetime, the conversion formula is as follows:

[0023]

[0024] In the formula, t S (R S ) represents the reliable life requirement value of system S, which is an input parameter for system design and is a known value;

[0025] R S The minimum reliability requirement value for system S is a known value and is an input parameter for system design.

[0026] m S Let be the shape parameter of the Weibull distribution of system S, selected based on information about similar products, and take values ​​in [1.5, 4].

[0027] When allocating median lifetime, the conversion formula is as follows:

[0028]

[0029] In the formula, t S(0.5) is the median lifetime requirement of system S, which is an input parameter for system design and is a known value;

[0030] m S Let be the shape parameter of the Weibull distribution of system S, selected based on information about similar products, and take values ​​in the range [1.5, 4]. Further, in step two, let the task time t of unit i (i = 1, 2, ..., N) be... i It is a function of system task time, that is

[0031] t i =f i (t S (5)

[0032] In the formula, t S This refers to the system's task time.

[0033] Furthermore, in step three, the unit characteristic lifetime η is established using an equal allocation method or a scoring allocation method. i The relationship with a certain parameter p to be determined:

[0034] η i =g i (p) (6)

[0035] In the formula, p is the parameter to be determined.

[0036] When using the equal distribution method, it is generally assumed that the average lifespan is equal, g i (p) represents the relationship between characteristic lifetime and mean lifetime, where p is the mean lifetime θ.

[0037]

[0038] When using the scoring and allocation method, the scoring coefficient c for the average lifespan of each unit is calculated based on the experts' scores for the complexity, technical level, working time, and environmental conditions of each unit. i Let c = min{c i ;i=1, 2,...,N}, then

[0039]

[0040] Furthermore, in step four, the characteristic lifetime relationship equation between the system and the unit is as follows:

[0041]

[0042] In the formula, N is the number of units contained in the system;

[0043] m i(i = 1, 2, ..., N) represents the shape parameter of the Weibull distribution of the unit, which is selected based on information about similar products and takes values ​​in [1.5, 4].

[0044] t i (i = 1, 2, ..., N) represents the task time of the unit, which is determined through step two;

[0045] η i (i = 1, 2, ..., N) represents the characteristic lifetime of the cell, which is substituted from step three;

[0046] t S m S η S The meaning is the same as in step one;

[0047] When m i =m S , t i =t S When (i=1,2,…,N), the characteristic lifetime relationship equation between the system and the unit is:

[0048]

[0049] When m i =m S , t i =t S η1=η2=…=η N At that time, the characteristic lifetime relationship equation between the system and the unit is:

[0050]

[0051] In the above formula, m S When η = 1, the mean time between failures (MTBF) θ is used instead of the characteristic life (η), i.e.

[0052] θ i =Nθ S (12) is a commonly used formula for allocating reliability indicators for electronic products.

[0053] Furthermore, the formula for calculating the reliability index allocation value of each unit in step five is as follows:

[0054] The reliability is:

[0055]

[0056] The average lifespan is:

[0057]

[0058] Reliable lifespan is:

[0059]

[0060] The median lifetime is:

[0061]

[0062] Beneficial effects:

[0063] 1. This invention proposes a reliability allocation method for electromechanical systems, which effectively solves the problem that when using the allocation method for electronic products to allocate the reliability of electromechanical systems, the important characteristic that the lifetime follows the Weibull distribution and the lifetime is determined by the weak link is ignored. This leads to the reliability index allocation value of the electromechanical unit being the product of the number of units and the system reliability index value. The reliability index allocation value of the electromechanical unit increases exponentially, resulting in the unit's reliability index allocation value being too high or even infeasible.

[0064] 2. In step four of this invention, the shape parameters of the units and the system are the same, the task time of each unit is equal to the task time of the system, and the characteristic lifetime is divided equally, which is a common usage scenario, i.e., m i =m S , t i =t S η1=η2=…=η N Since the shape parameters of electromechanical systems generally satisfy m S >1, at this time, Therefore, the present invention can significantly reduce the allocated value of the unit reliability index, for example, m S When η = 3.25 and N = 10, i =2.03η S <10η S It can be seen that the allocation value of the unit reliability index (2.03 times) is much smaller than the allocation value (10 times) when it is treated as an electronic product, and the more complex the electromechanical system, the more obvious the effect.

[0065] 3. This invention allocates reliability based on the lifespan distribution of electromechanical systems, which avoids the situation where traditional allocation methods, due to the lack of reliability allocation methods for electromechanical products, treat them as electronic products, resulting in excessively high or even infeasible allocation values ​​for unit reliability indicators. Attached Figure Description

[0066] Figure 1 This is a flowchart illustrating the steps of the method for allocating reliability indicators of electromechanical systems based on characteristic lifetime according to the present invention. Detailed Implementation

[0067] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0068] Example 1:

[0069] The principle of the method of this invention:

[0070] The lifespan of electromechanical products generally follows a Weibull distribution. That is:

[0071]

[0072] In the formula, m is the shape parameter and η is the characteristic lifetime.

[0073] The task time of system S is t S The shape parameter is m S At that time, its reliability is

[0074]

[0075] When system S consists of N electromechanical units connected in series, let the lifetime distribution parameter of a certain unit i be F(t). i m i η i ), i = 1, 2, ..., N. The reliability of the series system at this time is

[0076]

[0077] The reliability of system S is equal to the reliability of the system composed of series-connected units, R(t) S ) = R S (t S From equations (17) and (18), we get

[0078]

[0079] That is

[0080]

[0081] In the formula, t S It is the system's task time, which is determined during system design and is a known value;

[0082] m S These are the shape parameters of the system. During the system development process, the values ​​of similar products can be referenced, as they are known values.

[0083] η S It is the characteristic lifetime of the system;

[0084] t i It is the task time of unit i;

[0085] m i The shape parameter of element i can be obtained by referring to the values ​​of similar elements of the same type, and is a known value.

[0086] It can be seen that equation (19) is a functional relationship between the system's reliability parameters and the unit's reliability parameters, and can be used to assign the system's reliability index to the unit. In equation (19), since the unit's characteristic lifetime η i and task time t i If there are N elements, it is very difficult to directly assign the characteristic lifetime of the system to the elements, and there can be infinitely many solutions.

[0087] In practice, problems can often be simplified based on existing data. According to the system's operating mode and the duty cycle of each unit, the task time of unit i is a function of the system's task time, i.e.

[0088] t i =f i (t S (20)

[0089] In extreme cases, the task time of the unit is equal to the task time of the system, i.e., t i =t S .

[0090] Similarly, establishing the relationship between the characteristic lifetimes of each unit can simplify the allocation process. For example, using existing techniques such as equal allocation and scoring allocation, combined with the relationships between the parameters of the Weibull distribution, the characteristic lifetime η can be established. i The relationship with a certain parameter p to be determined, i.e.

[0091] η i =g i (p) (21)

[0092] When using the equal distribution method, it is assumed that the average lifespan is equal, g i (p) represents the relationship between characteristic lifetime and mean lifetime, where p is the mean lifetime θ.

[0093]

[0094] When using the scoring allocation method, the scoring coefficient c of the average lifespan of each unit can be calculated based on the experts' scores for factors such as the complexity, technical level, working time, and environmental conditions of each unit. i Let c = min{c i ;i=1, 2,...,N}, then

[0095]

[0096] The rating coefficient c of the average lifetime of each unit i The scores are calculated through expert evaluation. For example, when evaluating four factors—complexity, technical level, working hours, and environmental conditions—the calculation process is shown in Table 1.

[0097] Table 1. Calculation process of expert scoring method

[0098]

[0099] Substituting equations (20) and (21) into equation (19) yields...

[0100]

[0101] From equation (22), we can determine the task time t of system S. S Shape parameter m S Characteristic lifetime η S and the shape parameter m of each unit i (i = 1, 2, ..., N), calculate the parameter p, and then obtain the characteristic lifetime η of each unit through equation (21). i (i = 1, 2, ..., N), the reliability index is allocated by utilizing the relationship between reliability parameters and characteristic lifetime.

[0102] In particular, when m S =m i , t S =t i When (i=1,2,…,N), (19) becomes

[0103]

[0104] η1=η2=…=η N At that time, we can obtain from the above formula

[0105]

[0106] Furthermore, when m S When η = 1, the mean time between failures (MTBF) θ is used to replace the characteristic life η, i.e.

[0107] θ i =Nθ S

[0108] This is a commonly used formula for allocating reliability indicators for electronic products.

[0109] The specific implementation steps of this embodiment are as follows:

[0110] The electromechanical system S on a certain missile is a single-use product, consisting of four units, U1, U2, U3, and U4, connected in series. Based on historical data from similar products, the lifetimes of all four units in this electromechanical system follow a Weibull distribution, with shape parameters m... S =1.5, Based on the usage profile and operating mode of the electromechanical system, the duty cycle (the ratio of working time to total time within one cycle) of each unit is as follows: Given that the task time of electromechanical system S is t S =2.5h, the reliability index requirement is mission reliability R S Not less than 0.996. The system reliability index is assigned to each unit, and for ease of use and management, the average lifespan of each unit must be consistent.

[0111] Step 1 utilizes the parameter relationships of the Weibull distribution to convert the system's reliability index into the system's characteristic lifetime η. S :

[0112]

[0113] Step 2: Based on the system's usage profile and the duty cycle of each device during system operation, determine the relationship between the task time of each unit and the system's task time, and calculate the task time of each unit:

[0114]

[0115]

[0116]

[0117]

[0118] Step 3 employs methods such as equal allocation, scoring allocation, and proportional combination to establish the unit characteristic lifetime η. i The relationship with a certain parameter p to be determined. For this case, to ensure that the average lifetime of all elements is equal, the equal distribution method can be used to determine the characteristic lifetime η of the elements. i The relationship with a certain parameter p to be determined. Let the average lifetime be θ. U At this point, the parameter p to be determined is the average lifetime θ. U By utilizing the functional relationship between characteristic lifetime and mean lifetime, the characteristic lifetime η of each unit can be obtained. i With average lifespan θ U The relationships are as follows:

[0119]

[0120]

[0121]

[0122]

[0123] Step 4 uses the characteristic lifetime relationship equation between the system and the unit to calculate the parameter p numerically. Substituting the numerical values ​​or relationships obtained in Steps 1, 2, and 3, along with the known conditions, into the characteristic lifetime relationship equation between the system and the unit, we get:

[0124]

[0125] The average lifetime of each unit is calculated to be θ. U =73.58.

[0126] Step 5: Based on the value of p and the relationship between the characteristic lifetime and reliability index of each unit, calculate the reliability index allocation value for each unit. The characteristic lifetime of each unit is calculated using the relationship between characteristic lifetime and average lifetime. Then, based on the relationship between reliability and characteristic lifetime, the reliability index allocation value for each unit can be calculated as follows:

[0127] U1: Characteristic lifetime η1 = 73.58 ÷ 0.887 = 82.95, reliability

[0128] U2: Characteristic lifetime η2 = 73.58 ÷ 0.893 = 82.40, reliability

[0129] U3: Characteristic lifetime η3 = 73.58 ÷ 0.896 = 82.12, reliability

[0130] U4: Characteristic lifetime η4 = 73.58 ÷ 0.886 = 83.05, reliability

[0131] Clearly, the reliability of the series connection of the units is R1×R2×R3×R4=0.996, which is consistent with the reliability of the system, indicating that the allocation result is correct.

[0132] This example illustrates that the system consists of four units connected in series. Following traditional methods, it can be considered an electronic product with a lifespan following an exponential distribution. Using an average distribution method, the system's average lifespan is... The average lifetime allocation value of the unit is 50 × 4 = 202.8. However, according to the method provided by this invention, the average lifetime allocation value of the unit is 83.66, which avoids the situation where the traditional allocation method, due to the lack of a reliability allocation method for electromechanical products, treats them as electronic products, resulting in excessively high or even infeasible reliability index allocation values ​​for the units.

[0133] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for allocating reliability indicators for electromechanical systems based on characteristic lifetime, characterized in that, The electromechanical system S in this method consists of N The method consists of several devices connected in series, and its implementation includes the following steps: Step 1: Convert the system's reliability metrics into the system's characteristic lifetime; Step 2: Based on the system's usage profile and the duty cycle of each device during system operation, determine the relationship between the task time of each unit and the system's task time, and calculate the task time of each unit; Step 3: Establish the relationship between the characteristic lifetime of a unit and a certain parameter to be determined; Step 4: Using the characteristic lifetime relationship equations of the system and its components, calculate the parameters through numerical calculations; Step 5: Based on the parameter values, the functional relationship between the parameters and the unit characteristic lifetime in Step 3, and the relationship between the characteristic lifetime of each unit and the reliability index in Step 1, calculate the reliability index allocation value for each unit. In step one, the system reliability index is converted into the system's characteristic lifetime using the parameter relationships of the Weibull distribution. ; When allocating reliability, the conversion formula is: （1） In the formula, Let S be the task time of system S, which is an input parameter for system design and is a known value; Let be the shape parameter of the Weibull distribution of system S, selected based on information about similar products, and take values ​​in [1.5, 4]. The reliability requirement of system S is a known value and is an input parameter for system design. When allocating average lifespan, the conversion formula is as follows: （2） In the formula, S The average lifetime requirement of system S is a known value and is an input parameter for system design. Let be the shape parameter of the Weibull distribution of system S, selected based on information about similar products, and take values ​​in [1.5, 4]. For gamma function; When allocating reliable lifetime, the conversion formula is as follows: （3） In the formula, Let S be the reliable life requirement value of system S, which is an input parameter for system design and is a known value; The minimum reliability requirement value for system S is a known value and is an input parameter for system design. Let be the shape parameter of the Weibull distribution of system S, selected based on information about similar products, and take values ​​in [1.5, 4]. When allocating median lifetime, the conversion formula is as follows: （4） In the formula, The median lifetime requirement of system S is a known value and is an input parameter for system design. Let be the shape parameter of the Weibull distribution of system S, selected based on information about similar products, and take values ​​in [1.5, 4]. In step two, let the unit i ( i =1,2,…, N ) task time It is a function of system task time, that is （5） In the formula, For the system's task time; In step three, the unit characteristic lifetime is established using either the equal allocation method or the scoring allocation method. With a certain parameter to be determined p Relationship: （6） In the formula, These are the parameters to be determined; When using the equal distribution method, it is assumed that the average lifespan is equal. This describes the relationship between characteristic lifetime and average lifetime. p This is the average lifespan. θ ,Right now （7） When using the scoring and allocation method, the scoring coefficient for the average lifespan of each unit is calculated based on the experts' scores for the complexity, technical level, working time, and environmental conditions of each unit. c i ,remember ,but （8）； In step four, the characteristic lifetime relationship equation between the system and the unit is as follows: （9） In the formula, N This represents the number of units contained in the system. ( i =1,2,…, N The shape parameter of the Weibull distribution for each unit is selected based on information about similar products and takes values ​​in the range of [1.5, 4]. ( i =1,2,…, N The task time for the unit is determined through step two; ( i =1,2,…, N The characteristic lifetime of the unit is denoted by ) and substituted from step three. , , The meaning is the same as in step one; when , ( i =1,2,…, N When ), the characteristic lifetime relationship equation between the system and the unit is: （10） when , At that time, the characteristic lifetime relationship equation between the system and the unit is: （11）。 2. The method for allocating reliability indicators of electromechanical systems based on characteristic lifetime as described in claim 1, characterized in that, The formula for calculating the reliability index allocation values ​​of each unit in step five is as follows: The reliability is: （13） The average lifespan is: （14） Reliable lifespan is: （15） The median lifetime is: （16）。

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