METHOD FOR OPERATING A SYSTEM WITH OPTIMAL AVAILABILITY AND SYSTEM WITH OPTIMAL AVAILABILITY

Description

[0001] The invention relates to a method for operating a system with optimal availability and a system with optimal availability.

[0002] An operating device, which may be, for example, a production plant for producing products, a plant for providing operating resources such as water under high pressure, or even the provision of a service such as the operation of public transport by means of corresponding operating devices, usually comprises several components.

[0003] The components are each subject to wear and aging processes, which are usually modeled using the stochastic parameter MTBF (mean time between failures).

[0004] If the operating device has been in operation or maintained for 20 years or more, the availability of spare parts for individual components on the market may be limited.

[0005] Proactive inventory management is intended to ensure the availability of components for the operation of the operating device in order to keep possible downtime as short as possible.

[0006] Furthermore, the procurement of new spare parts can result in very long delivery times, especially for custom-made products, which must be taken into account to ensure high availability of the operating device.

[0007] Patent DE10010494 A1 discloses a method for supporting the maintenance of technical systems, in which at least two spare parts warehouses are available. If demand exceeds the inventory of a spare parts warehouse, a procurement-oriented process contacts a neighboring spare parts warehouse, a central warehouse, or a supplier's spare parts warehouse.

[0008] However, systemic warehousing, where the storage of spare parts for the operating device is directly linked to the operating device, for example, through a warehouse belonging to or connected to a maintenance unit of the operating device, can lead to problems if the spare parts for the components of the operating device have already reached their expected service life or MTBF before or prematurely after commissioning as a spare part, for example due to corrosion, deterioration, material fatigue, or desaturation of flash memory cards. This can lead to unwanted failures, i.e., reduced availability of the operating device, which reduces its efficiency.

[0009] It is an object of the invention to overcome the disadvantages of the prior art and to provide an improved method for efficient and highly available operation of an operating device.

[0010] The object of the invention is achieved according to claim 1.

[0011] The invention takes into account not only the expected service life of the active components of the operating device, but also the expected service life of the spare parts in stock. This allows the expected service life of a replaced component of the operating device to be determined more precisely, improving the availability of the operating device.

[0012] A lot of identical components C = { c 1 , c 1 , ..., c n } represent the current quantity of components of this type installed on the operating device.

[0013] For example, these identical components can be hardware assemblies, rails, motors, etc.

[0014] In order to take into account different components, i.e. components of different design, a set of all componentsA (each of different design) into unconnected subsets A j with components of the type j be divided into j = 1 ...Anzahl unterschiedlicher Bauarten. Each type is then tested separately for each type j determined, whereby C as A j is set.

[0015] Each of these components C = { c 1 , c 1 , ... , c n } has the same failure probability (MTBF), the same installation time t install ( c i ) and an associated service end t eos ( c i ) (English "end-of-service").

[0016] The end of service or the service end time t eos ( c i ) describes a point in time until which error-free operation of the system, which includes the components CThis can be agreed, for example, through a maintenance contract with a service provider.

[0017] A probability distribution function (PDF) h inst ( t ) represents the failure probability of an installed component, i.e. the probability of a time interval from the installation of a component to its replacement in the event of a failure.

[0018] A probability distribution function h stock ( t ) represents the failure probability of a component in stock, i.e. the probability of a time interval from the storage of a component until its replacement due to aging.

[0019] For the probability distribution functions h inse ( t ) and h stock ( t) general distributions can be assumed, but exponential or Weibull distributions are particularly suitable for realizing a bathtub failure curve or for preventive maintenance, where a component is replaced after a given time, regardless of whether a failure has occurred or not.

[0020] The probability distribution functions h inse ( t ) and h stock ( t ) can also be derived from the two corresponding MTBF values.

[0021] A point in time t stock represents the point in time at which a supplier announces the availability of a replacement component, meaning that the replacement component is no longer available. t stock A reasonable number of spare components should be kept in stock.

[0022] A random variable S with the probability distribution function f s which describes the number of components that are in stock at the time t stock should be available so that all necessary replacement components are available according to the probability distribution functions h inse ( t ) and h stock ( t ) can be guaranteed.

[0023] A renewal process or an exchange is a stochastic model of renewals or component exchanges that occur randomly over time.

[0024] A random variable X 1 describes the time between 0 and the first necessary component exchange. Random variables X 2 , X 3 ,... each describe a subsequent component exchange. These random variables X i are called inter-arrival times.

[0025] The distribution of random variables X i can be determined by the probability distribution functions h inst ( t ) and h stock ( t ) can be determined.

[0026] The random variables ( X 1 ,X 2 ,X 3 , ... ) form a sequence of independent random variables that describe the periods between renewals, i.e. a respective component exchange. X i = 0 ∞ Pr X i > 0 > 0

[0027] The variable X i can be calculated using a probability distribution function h Xi ( t ) and an associated distribution function F Xi ( t ) are described.

[0028] A random variable T [ n ] for a number n ∈ ℕ describes the so-called arrival time.

[0029] F T [ n ] ( t ) describes the probability of n Renewals untilt . F T n t = Pr T n ≤ t

[0030] The random variable T [ n ] is the sum of the interarrival times X i . T n = ∑ i = 1 n X i

[0031] The probability distribution function of T[n] is therefore the folding of its components. f T n = f * X n = f X ∗ f X ∗ … ∗ f X

[0032] To add two random variables, the convolution operator must be applied to their probability distribution function. The convolution operator * of two functions f and g is defined for a continuous case as f ∗ g t = ∫ f t ′ g t − t ′ dt ′ and for a discrete case as f ∗ g n = ∑ m = − ∞ ∞ f m g n − m

[0033] The expression f * stands for the n-times application of the convolution operator to a function f .

[0034] Accordingly, in a further development of the invention, it is provided that when determining the optimal storage size, the respective arrival time is taken into account using a probability distribution function.

[0035] This makes it possible to create a model for the system in a simple manner, which allows an efficient determination of the optimal storage size and ensures an optimal material flow for the operation of the system's operating device with optimal availability.

[0036] For many families of probability distribution functions, the addition of two random variables and therefore the calculation of the probability distribution functions is possible in a simple way.

[0037] For example, the sum of two Poisson-distributed variables with the parameters λ 1 and λ 2 : POI λ 1 + POI λ 1 = POI λ 1 + λ 2

[0038] In the renewal process, the variables for the arrival time T [ n ] is used to create a random variable or counting variable N [ t ] which represents the number of expected renewals in the period [0, t ] counts. N t = n ∈ ℕ : T n ≤ t with t ≥ 0

[0039] The process for determining the arrival time T [ n ] and the counting process to determine the random variable N [ t ] are inverse to each other, where the probability function of the random variable N [ t ] from the probability function of the arrival time T [ n ] can be obtained.

[0040] For t ≥ 0 and n ∈ ℕ applies: 1. T [ n ] ≤ t, if and only if N [ t ] ≥ n 2. N [ t ] = n, if and only if T [ n ] ≤ t <T [ n + 1]

[0041] Therefore, the counting variable N [ t ] from a known error distribution X a component can be obtained.

[0042] For more complex distributions of X The implementation can be used to determine N using numerical methods. The most important case is the Poisson process, where X an exponential distribution with the parameter λ The n -th arrival time T [ n ] a gamma distribution with a shape parameter n and an inverse scale parameter λ The counting variable N [ t ] has a Poisson distribution with one parameter λ t on.

[0043] A random variable N inst [ c ] indicates the number of renewals, i.e. component replacement of installed components until the end of service t eos ( c ), where c ∈ C applies. N inst c = N t eos c − t install c

[0044] The interarrival variables X i have probability distribution functions h inst ( t ), except for the first variable X 1 , which is a probability distribution function h inst 1 t has. h inst 1 t = 0 t < t stock h inst t ∫ t stock ∞ h inst t dt t ≥ t stock

[0045] The reason for using h inst 1 t is that the component c at the time t stock is actually still in operation, otherwise it would have already been replaced. Therefore, the first part of the probability distribution function h inst 1 t until the time t stock be set to zero, and the remaining remainder scaled to the area of ​​one to obtain a valid probability distribution function.

[0046] A random variable N stock [ c] indicates the number of renewals, i.e., component replacements of in-stock components. Such renewals are necessary, for example, due to aging of the in-stock components. N stock c = N t eos c − t stock c

[0047] Associated interarrival variable X i have a probability distribution function h stock on.

[0048] To simplify the notation, an ⊕-operator for two random variables A and B with respective probability distribution functions f A and f B be introduced.

[0049] The probability distribution function of the new discrete random variable C = A ⊕ B is defined by f C n : = ∑ k = 0 ∞ f A k f B ∗ k n

[0050] Where the notation f* k< stands for the convolution operator, which k -fold on f is applied: f : f * f * f * ... ( k -academic subject)

[0051] The warehouse size S [ c ] of components c , that is, the number of components included in the inventory, is a random variable for the component c ∈ C with a probability Pr ( S [ c ] = n ), that n parts in stock as replacement components for the component c required to carry out necessary renewals of installed and stored components until the end of service t eos ( c ) without adversely affecting the availability of the operating device. S c = ∑ r = 0 ∞ S r c where S 0 c = N inst c ⊕ N stock c S i c = S i − 1 c ⊕ N stock c , i = 1 , 2,3 , …

[0052] Usually, only a few iteration steps, for example five iterations, are required, since later iteration steps are S ( i )< [ c ] can be neglected.

[0053] Accordingly, a further development of the invention provides for the optimal bearing size to be determined iteratively. This allows the optimal bearing size to be determined in a simple and efficient manner.

[0054] However, a degenerate case can occur, where the failure rate of in-stock components and the resulting need for replacement is too high and cannot be compensated by additional in-stock components. In this case, the theoretical inventory size is infinite.

[0055] This theoretical case can be prevented in practice by the design of the components. Components should have a correspondingly low bearing failure rate h stock ( t ) so that their stock failures can be compensated by additional stored components.

[0056] Accordingly, in a further development of the invention, it is provided that the second service end time t eos 2 of the second component is longer than the storage time of the second component in the second warehouse, preferably by a factor of 10, particularly preferably by a factor of 100, and in particular by a factor of 1000. This can avoid the degenerate case or keep the warehouse size limited to a reasonable level. Since the first and second components are identical in design, the first and second service end times t eos 1 , t eos 2 equal length.

[0057] The storage time of the second component in the second warehouse is the difference between the inter-arrival time of the second component in the second warehouse and the arrival time of the second component in the operating device. During the storage time, the second service end time t eos 2, however, may not yet be achieved, as the first component is not being replaced by an outdated, no longer usable second component. Exceeding the storage time can occur in a case where the storage size is not optimal and a second component is stored in the second warehouse for too long. However, this should be avoided.

[0058] A maintenance period for a component replacement, such as the installation of the second component in place of a defective first component, is included in the storage time for the sake of simplicity.

[0059] A total storage size S is a random variable with a probability Pr ( S = n ), that n parts in stock as replacement components for all components C required to carry out necessary renewals of installed and stored components until the end of service t eos ( c) without adversely affecting the availability of the operating device. S = ∑ c ∈ C S c

[0060] The total inventory size S is a known probability function that can be used to determine the number of components stored in a corresponding warehouse and thus to control the material flow during the operation of a system.

[0061] For example, a risky decision can be based on a value for the 50% quantile of the total stock size S is reached.

[0062] A cautious decision can, for example, be based on a value for the 98% quantile of the total stock size S is reached.

[0063] The object according to the invention is also achieved by a system with optimal availability, comprising an operating device with a first component, a first warehouse with a first number of copies of a second component and a second warehouse with a second number of copies of the second component, and a control device which is configured to carry out the method according to the invention.

[0064] The invention is explained in more detail below using an exemplary embodiment shown in the accompanying drawings. In the drawings: Fig. 1 shows an embodiment of a method and a system according to the invention, Fig. 2 shows an example of durations and times of installed components of the same type of operating device from the Fig. 1 , Fig. 3a first example of probability distribution functions h inse ( t ) and h inst 1 t , Fig. 4 a second example of probability distribution functions h inst ( t ) and h inst 1 t .

[0065] Fig. 1 shows an embodiment of a method according to the invention.

[0066] It is clear that further devices are required to carry out the method, which are not shown for the sake of clarity, such as transport devices between storage areas and an operating device, as well as computing devices for calculating parameters and further control devices for controlling the processes and method steps according to the invention.

[0067] A system 1 comprises an operating device 10 with a first component 11.

[0068] The operating device 10 can, for example, be a production plant for producing products or a plant for providing operating resources.

[0069] In a broader sense, the operating device 10 may also be the provision of a service in which one or more devices are used to provide the service, such as the operation of a public transport means by corresponding operating devices.

[0070] The operating device 10 comprises one or more components 11, such as vehicles, parts of the vehicles, but also rails or a power supply for the operation of the vehicles.

[0071] A first bearing 21 comprises a first number 31 of second components 12, which are identical in construction to the first component 11.

[0072] The component 11, 12 could, for example, be a wagon or a switch of a railway system.

[0073] Storing a number 32 of such a second component 12 in the second warehouse 22 beyond what is necessary to maintain optimal availability may be undesirable, for example due to corrosion or damage during storage of the second component 12.

[0074] For example, it may be provided that storage in the second warehouse 22 takes place in the open field without special safety or preservation measures for the second component 12.

[0075] Of course, an undesirably high space requirement for the storage of second components 12 in the second warehouse 22 can also be an aspect that speaks in favor of determining an optimal stock level and corresponding storage.

[0076] The first warehouse 21 may, for example, be a warehouse at a manufacturer or a wholesaler and is not in direct contact with the operating device 10.

[0077] A correspondingly long period of time may be required for the provision from the first warehouse 21 to the second warehouse 22, for example due to long production times, long transport routes or administrative regulations.

[0078] The first warehouse 21 can, for example, also be a logistical goods receipt of system 1 and not a physical storage location.

[0079] A second bearing 22 comprises a second number 31 of second components 22. The second bearing 22 is a bearing which is in direct contact with the operating device 10 and is, for example, part of a maintenance unit for the operating device 10.

[0080] The second component 12 is thus provided to the operating device 10 in the system 1 in the order from the first warehouse 21 to the second warehouse 22 to the operating device 10.

[0081] The first component 11 has a first arrival time T 1 and a first service end time t eos 1 on.

[0082] The second component 12 has a second arrival time T 2 and a second service end time t eos 2 on.

[0083] The second service end time t eos 2 of the second component 12 is longer than the storage time of the second component 12 in the second warehouse 22.

[0084] The first and second service end time t eos 1 , t eos 2 are derived in this example from the MTBF of the corresponding component.

[0085] The first or second arrival time T 1 , T 2 each indicate the point in time at which the respective component 11 or 12 is included in system 1.

[0086] At least one copy of the second component 12 is provided from the first warehouse 21 to the second warehouse 22 as soon as the second number 32 falls below an optimal storage size.

[0087] Consequently, as many copies of the second component 12 are provided until the optimal storage size is reached.

[0088] This applies to initial and ongoing operation of System 1.

[0089] In this example, the optimal storage size corresponds to the previously defined storage size S [ c ].

[0090] By adding at least one copy to the second warehouse 32, the second number 32 with the optimal warehouse size is thus achieved again.

[0091] The optimal storage size is determined using the first and second arrival times T 1 , T 2 and the first and second service end time t eos 1 , t eos 2 determined.

[0092] When the operating device 10 is operated, when the first service end time is reached t eos 1 of the first component 11 a provision of a copy of the second component 12 from the second warehouse 22 to the operating device 10.

[0093] In the operating device 10, the first component 11 is replaced by the second component 12.

[0094] In this example, the arrival time T 1 , T 2 is taken into account using a probability distribution function.

[0095] In Fig. 1 a system 1 according to the invention with optimal availability can also be seen.

[0096] The system 1 further comprises a control device 2 which is configured to carry out the method according to the invention.

[0097] Fig. 2 shows an example of installation times t install ( c 1 ), t install (c 2 ) and t install ( c 3 ) and associated service end time t eos ( c 1 ), t eos ( c 2 ) and t eos ( c 3 ) of three installed components C = { c 1 , c 1 , c 3} same type of operating device 10.

[0098] For this example, it is assumed that all components C still work and at the time of observation t stock are in use. If a component is already in use before the date of t stock has been replaced, the replacement component is part of the components C and no longer the originally installed component.

[0099] Fig. 3 shows a first example of probability distribution functions h inst ( t ) and h inst 1 t .

[0100] The probability distribution function h inst 1 t is based here on the probability distribution function h inst ( t ) with an exponential distribution.

[0101] For an exponentially distributed probability distribution function, a horizontal shift of the curve from time zero to time t stock in the same function h inst 1 t .

[0102] Fig. 4 shows another example of probability distribution functions h inst ( t ) and h inst 1 t .

[0103] The probability distribution function h inst 1 t is based here on the probability distribution function h inst ( t ) with a uniform distribution between a function value 0 and 5.

[0104] The probability distribution function h inst 1 t is uniformly distributed between a function value of 2 and 5. Bezugszeichenliste:

[0105] 1System 2Control device 10Operating device 11, 12Component 21, 22Warehouse 31, 32Stock level, number of components in stock h inst ( t ), h inse ( t )Probability distribution function t Time t eos , t eos 1 , t eos 2 Service end (time), ie end time of a service obligation t install Time of installation of a component in the operating device t stock Time of observation

Claims

1. Method comprising computing apparatuses, required for its execution, for calculating parameters for operation of a system (1) with optimal availability, comprising an operating apparatus (10) comprising a production installation for generating products, or comprising an operating apparatus (10) comprising one or more vehicles, parts of vehicles, rails or power supply for the operation of the vehicles, a carriage or a switch of a railway system, in each case with a first component (11), a first warehouse (21) with a first number (31) of examples of a second component (12) and a second warehouse (22) with a second number (32) of examples of the second component (12), wherein the second component (12) is identical in construction to the first component (11), and the first and the second component (11, 12) have a first or second arrival time and a first or second service end time (teos1, teos2), wherein the first and second arrival time identify that point in time in each case at which the respective component (11, 12) is received in the system (1), and at least one example of the second component (12) is provided from the first warehouse (21) to the second warehouse (22) as soon as the second number (32) drops below an optimal warehouse size and the second number (32) therefore once again reaches the optimal warehouse size, wherein the optimal warehouse size is determined using the first and second arrival time and the first and second service end time (teos1, teos2), and during operation of the operating apparatus (10), when the first service end time (teos1) of the first component (11) is reached, an example of the second component (12) is provided from the second warehouse (22) to the operating apparatus (10) and in the operating apparatus (10) the first component (11) is replaced with the second component (12).

2. Method according to the preceding claim, wherein when the optimal warehouse size is determined, the respective arrival time is taken into account with the aid of a probability distribution function.

3. Method according to one of the preceding claims, wherein the optimal warehouse size is determined iteratively.

4. System (1) with optimal availability, comprising an operating apparatus (10) with a first component (11), a first warehouse (21) with a first number (31) of examples of a second component (12) and a second warehouse (22) with a second number (32) of examples of the second component (12), and a control apparatus (2), which is designed to execute the method according to one of the preceding claims.