EP0867841A2 - Procédé pour estimer le taux de défaillance de composants d'équipements techniques - Google Patents

Procédé pour estimer le taux de défaillance de composants d'équipements techniques Download PDF

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Publication number
EP0867841A2
EP0867841A2 EP98105443A EP98105443A EP0867841A2 EP 0867841 A2 EP0867841 A2 EP 0867841A2 EP 98105443 A EP98105443 A EP 98105443A EP 98105443 A EP98105443 A EP 98105443A EP 0867841 A2 EP0867841 A2 EP 0867841A2
Authority
EP
European Patent Office
Prior art keywords
lifetime
lifetime distribution
distribution
components
component
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
EP98105443A
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German (de)
English (en)
Other versions
EP0867841A3 (fr
Inventor
Ulrich Dr. Leuthäusser
Jürgen Dr. Sellen
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
ESG Elektroniksystem und Logistik GmbH
Original Assignee
ESG Elektroniksystem und Logistik GmbH
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
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Publication date
Application filed by ESG Elektroniksystem und Logistik GmbH filed Critical ESG Elektroniksystem und Logistik GmbH
Publication of EP0867841A2 publication Critical patent/EP0867841A2/fr
Publication of EP0867841A3 publication Critical patent/EP0867841A3/fr
Withdrawn legal-status Critical Current

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    • G—PHYSICS
    • G07—CHECKING-DEVICES
    • G07C—TIME OR ATTENDANCE REGISTERS; REGISTERING OR INDICATING THE WORKING OF MACHINES; GENERATING RANDOM NUMBERS; VOTING OR LOTTERY APPARATUS; ARRANGEMENTS, SYSTEMS OR APPARATUS FOR CHECKING NOT PROVIDED FOR ELSEWHERE
    • G07C5/00—Registering or indicating the working of vehicles
    • G—PHYSICS
    • G07—CHECKING-DEVICES
    • G07C—TIME OR ATTENDANCE REGISTERS; REGISTERING OR INDICATING THE WORKING OF MACHINES; GENERATING RANDOM NUMBERS; VOTING OR LOTTERY APPARATUS; ARRANGEMENTS, SYSTEMS OR APPARATUS FOR CHECKING NOT PROVIDED FOR ELSEWHERE
    • G07C3/00—Registering or indicating the condition or the working of machines or other apparatus, other than vehicles

Definitions

  • the invention relates to a method for estimating the failure rate ⁇ (t) of corresponding components in one Inventory of technical facilities, such as B. vehicles of all kinds, one continuously counting the number of each Failing time interval and therefore by repair or Exchange of components to be replaced and from them determines a lifetime distribution f (t) of these components.
  • the components in question can be used directly or via the cumulative lifetime distribution F (t) the failure rate Calculate ⁇ (t).
  • the lifetime distribution of the respective component is therefore ongoing during the use of the technical Establishments to determine the failure rate for calculate a forecast of future needs for this component.
  • the failure rate can be derived directly from the data obtained in this way ⁇ (t) from the quotient of the number of failed Determine components and the relevant observation period.
  • ⁇ (t) the system noise caused by statistical fluctuations the lifetimes of the individual components are not taken into account.
  • a reliable failure forecast based on a failure rate ⁇ (t) calculated directly from the data obtained is not possible.
  • lifetime data f (t) are determined from the data obtained, in the following the lifetime distribution of the components that failed for the first time in the maintenance period with f 1 (t) and the lifetime distribution of the components f 2 (t) which fail for the second time, etc.
  • the failure rate ⁇ (t) can then be determined in principle from the lifetime distributions thus determined, for example by summing up the Laplace transforms of the lifetime distributions and the sum back-transformed (see e.g. Cox, DR; Miller, H .: The Theory of Stochastic Processes, Methun & Co. LTD, London).
  • a simple relationship for the Laplace-transformed failure rate ⁇ (s) can be derived from the classical renewal theory, namely as the quotient of the Laplace transform f 1 (s) of the first lifetime distribution f 1 (t) divided by the difference between 1 and the Laplace - Transformed f (s) into one of the other lifetime distributions f (t).
  • the prerequisite here is that the other lifetime distributions are all the same. It is also a prerequisite that the inventory of technical equipment does not change. However, these requirements are often not met.
  • the number of fighter jets is changing over time according to given retirement plans.
  • further inventory reductions may occur, e.g. B. due of accidents or repairs that are no longer worthwhile.
  • the invention is based on the consideration that, for. Legs Reduction of inventory leads to fewer failures, d. H. to changed lifetime distributions. If you lay these life distributions then the calculation of the failure rate ⁇ (t) of the based on the respective component, this usually results values for the failure rate ⁇ (t) too low; higher reliability the respective component is faked. A Demand forecast for the component based on the so Failure rate ⁇ (t) determined therefore gives incorrect results.
  • the invention has for its object a method of Specify the type mentioned at the beginning, which one is temporally changing total inventory of technical facilities taken into account.
  • This object is achieved in that one according to a predefined or continuously determined inventory function G (t) temporally changing total inventory the lifetime distribution f (t) or the cumulative lifetime distribution F (t) corrected by taking into account the inventory function G (t).
  • the failure rate ⁇ (t) results the measured lifetime distribution f (t), namely, accordingly the chosen mathematical formalism, immediately from the lifetime distribution f (t) or from the accumulated lifetime distribution F (t).
  • the invention Correction to take into account the inventory function G (t) can with the lifetime distribution f (t) or the cumulative lifetime distribution F (t) can be made.
  • the corrected lifetime distribution f 0 (t) can be determined by time differentiation of the corrected cumulative lifetime distribution F 0 (t).
  • the invention is concerned with a method for estimating the failure rate ⁇ (t) of corresponding components in an inventory technical facilities such.
  • the failure rate ⁇ (t) can be directly calculated simply by approximating the failure rate ⁇ (t) according to the following relationship: ⁇ (t) ⁇ 1 ⁇ + ⁇ ⁇ 3rd ⁇ T - ⁇ ⁇ 2nd ⁇ 1 ⁇ - 3rd 2nd 1 + ⁇ 2nd ⁇ 2nd + ⁇ 2nd 2 ⁇ 3rd , where ⁇ 1 the first moment of the first life distribution f 1 (t), ⁇ the first moment of a further, preferably the second life distribution f 2 (t), ⁇ the difference between the first moments ⁇ 2 and ⁇ 3 of two successive, preferably the second and third lifetime distributions f 2 (t) and f 3 (t), ⁇ the
  • Fig. 1 is an inventory of technical equipment schematically represented in the form of six vehicles a to f that consist of a large number of schematically represented components 12, 14, 16, 18 put together, such as. B. an engine, a brake system, a battery, a steering or the like.
  • Each vehicle in the inventory is constructed the same and thus consists of the same components as each other vehicles of the stock together.
  • the individual components are in turn composed of component parts, which in the event of failure of one of the components 12, 14, 16, 18 can be replaced individually for repair.
  • the vehicles a to f of the stock are in terms of their Failure behavior, d. H. with regard to failures individual components and repairs or new installation of the same, monitored and any failures that occur are documented.
  • an inventory function shown in Fig. 2a can G (t) are taken into account.
  • This inventory function G (t) gives the stock of vehicles (i.e. the number of the vehicles in operation) related to the Opening balance depending on the operating time t der Vehicles.
  • the course of the inventory function G (t) can on the one hand be determined by vehicles due to a predetermined retraction curve are put out of operation and thus a further observation of the failure behavior of the Components in such a vehicle are no longer possible or that, on the other hand, the vehicle is in an accident or the like fails and is no longer repaired. Also in this second case the observation of the individual breaks System components.
  • a first failure a 1 of the component S a has occurred
  • the failure data of component S in vehicles b to f are shown according to the same principle, with particular attention being paid to components S c and S d of vehicles c, d.
  • the last observation period t c3 'and t d3 ' does not end with component S c or S d failure.
  • the observed component S c or S d is still functional at the end of the observation (decommissioning for vehicle d, end of observation period B E for vehicle c), ie it has not failed, and must therefore not be used without a corresponding correction when estimating a failure rate ⁇ (t) (see below) are treated as component failure, as this would falsify the result.
  • the failure data of component S of vehicles a to f shown in FIG. 2b for illustration can now be used to determine the lifetime distributions f i (t) for the ith failure of component S, as in FIGS. 3 to 5 for the first, second and third component failures.
  • Fig. 3 the first failures (index 1) of component S in vehicles a to f are plotted as a histogram, which forms the lifetime distribution f 1 (t).
  • Each failure is marked with a point and the associated time interval from the start of the observation to the failure is indicated using a dimension arrow (in FIG. 3 above).
  • the failures that occur in each time step of the t-axis are added up; the sum gives the step height.
  • the lifetime distribution f 1 (t) until the first failure the case may occur that the start of the observation does not coincide with the time when the component S was first started up. So even "brand new" delivered vehicles already have a certain operating time (e.g. test run time) behind them.
  • the lifetime distribution f 1 (t) thus obtained does not have the course of the desired lifetime distribution with the start of observation from the first start-up.
  • the service life distribution f 1 (t) is also taken into account in the method described below.
  • the measured lifetime distribution f 2 (t) from the first failure to the second failure of the components S a to S f (see FIG. 4) is therefore the first complete lifetime distribution.
  • FIG. 3 shows, in addition to f 1 (t), a cumulative lifetime distribution F 1 (t) up to the first failure. This describes the probability that a component S of vehicles a to f will fail until time t.
  • FIG. 4 shows a graph corresponding to FIG. 3 for the failures a 2 to f 2 , ie in each case for the second failure of component S in vehicles a to f since the vehicle was restarted after the first failure of component S.
  • the respective lifetimes t a2 to t f2 are the operating times of the respective vehicles a to f from the restart after the first failure of component S to the second failure of component S.
  • the service life distribution is f 2 (t) until the second failure and a cumulative lifetime distribution F 2 (t) obtained according to equation (2) is plotted over time.
  • all vehicles a to f are in operation until the second failure of component S, ie component S has failed twice in each vehicle before one of vehicles a to f has been shut down.
  • FIG. 5 shows a lifetime distribution f 3 (t) (dashed line) and a cumulative lifetime distribution F 3 (t) (dash-and-dot line) obtained therefrom for the failures of component S in vehicles a, b and f.
  • Vehicle c is in operation after the second failure of component S and the corresponding repair beyond the observation period without further failure of component S.
  • Vehicle d is decommissioned with component S intact during the observation period. Vehicle d is shut down immediately after the second failure of component S.
  • the cumulative lifetime distribution F 3 (t) is to be understood here as the lifetime distribution that is obtained when the number of facilities remains unchanged over the observation period.
  • the cumulative lifetime distribution F 3 (t) forms the lower limit for the actual lifetime distribution F 3 0 (t), since it only takes into account the failures that occurred with decreasing inventory.
  • a determination of the failure rate ⁇ (t) on the basis of the cumulative lifetime distribution F 3 (t) would result in a failure rate ⁇ (t) which is too low, since the failures to be expected are not taken into account in the shutdown components.
  • An upper limit for the actual cumulative lifetime distribution F 3 0 (t) is then obtained when the non-failed during the observation period, however, disused components (S c, S d, S e) are in each case taken into account in determining the lifetime distribution as if at the time of their decommissioning according to the retirement curve f end (t) or at the end of the observation period B E (points marked with crosses).
  • the actual cumulative lifetime distribution F 3 0 (t) thus runs between the lower limit F 3 (t) and the upper limit F 3 '(t), as indicated by way of example in FIG. 5.
  • a (t) is the number of all failures up to time t Components.
  • B (t) is a first correction factor, which includes the determined number b (i) of the components which are put out of operation in the time interval i and a first term ⁇ (i).
  • C (t) is a second correction factor, which also includes the number b (i) of the components which are put out of operation in the time interval i and a second term ⁇ (i).
  • Equation 2 The above-mentioned relationship (equation 2) between f i (t) and F i (t) applies to the calculation of f 0 (t) from F 0 (t).
  • the lifetime distributions of the observed component have essentially the same course with increasing operating time of the technical device, ie they are invariant. If one takes up the example of component S in vehicles a to f mentioned at the beginning, this case can be explained in that component S, for example an engine, after a failure each time by a brand new component S, that is, by a brand new engine. In this case, it can be expected that the average life of the new component S corresponds to that of the failed component S.
  • a failure rate ⁇ (t) for the observed component e.g. B. S, in a stock of technical facilities such. B. in vehicles a to f, taking into account the falling inventory function G (t).
  • the failure rates ⁇ (t) expected in the future can be estimated.
  • expected failures which can serve as a basis for determining future spare parts.
  • the lifetime distributions change observed component S with increasing operating time of the technical Facilities.
  • Such a variant of lifetime distributions can occur if, for example, the observed Component S after a failure is not a brand new one same component is replaced, but only one or several defective component parts are replaced and the component S thus overhauled with the replacement parts again is put into operation. This means that the Component S from brand new component parts and already used components. Such Refurbished component S often has one of a brand new one Component has a very different lifetime distribution.
  • the average life of the component may decrease, since the component parts "age”, ie the number of brand new component parts decreases with increasing operating time.
  • the mean life of the components can also increase over time if components that are prone to failure are gradually replaced by more robust component parts after their failure.
  • FIG. 6 Such an increase in the average service life and thus a change in two successive service life distributions f i (t) and f i + 1 (t) is shown in FIG. 6.
  • the first moments ⁇ i and ⁇ i + 1 of the two distributions shown are entered on the t-axis.
  • the difference ⁇ between the two moments ⁇ i and ⁇ i + 1 is shown with the aid of a dimension arrow.
  • the second moments ⁇ i and ⁇ i + 1 are also approximately entered.
  • the first service life distribution f 1 (t) which may be falsified by the start of the observation, is used Lifetime distribution of the observed component until the first failure, and at least one second lifetime distribution, preferably the lifetime distribution of the observed component until the second failure f 2 (t), are determined.
  • the first lifetime distribution f 1 (t) is then transformed into the Laplace space so that it is obtained as a function of the Laplace variable s.
  • the first moment and the second moment of the existing lifetime distribution f 2 (t) and possibly further lifetime distributions f 3 (t), etc. are determined in each case.
  • the failure rate ⁇ (t) is obtained by Laplace inverse transformation.
  • this failure rate asymptotically approaches a limit value, which in this example is approximately 0.75, and which is indicated by a dashed straight line to which the following relationship applies:
  • This straight line can be described by the following equation: ⁇ (t) ⁇ 1 ⁇ + ⁇ ⁇ 3rd ⁇ T - ⁇ ⁇ 2nd ⁇ 1 ⁇ - 3rd 2nd 1 + ⁇ 2nd ⁇ 2nd + ⁇ 2nd 2 ⁇ 3rd
  • ⁇ 1 the first moment of the first life distribution f 1 (t)
  • ⁇ the first moment of a further preferably the second life distribution f 2 (t)
  • ⁇ the (constant) difference of the first moments ⁇ i and ⁇ i + 1 of two successive ones preferably the second and third lifetime distributions f 2 (t) and f 3 (t)
  • ⁇ the second moment of the further preferably second lifetime distribution f 2 (t) and ⁇ 2 the (constant) difference of the squares of two second moments, preferably ⁇ 2 and ⁇ 3 of the two successive lifetime distributions mean f 2 (t) and f 3 (t).
  • This approximation formula means that the failure rate ⁇ (t) can be easily determined for big times.
  • the inventory can be optimize for necessary spare parts, d. H. Stock shortages or inventory surplus with a sufficiently large inventory almost exclude.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)
  • Testing Electric Properties And Detecting Electric Faults (AREA)
EP98105443A 1997-03-26 1998-03-25 Procédé pour estimer le taux de défaillance de composants d'équipements techniques Withdrawn EP0867841A3 (fr)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
DE19712767A DE19712767A1 (de) 1997-03-26 1997-03-26 Verfahren zum Abschätzen der Ausfallsrate von Komponenten technischer Einrichtungen
DE19712767 1997-03-26

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EP0867841A2 true EP0867841A2 (fr) 1998-09-30
EP0867841A3 EP0867841A3 (fr) 2002-03-13

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EP (1) EP0867841A3 (fr)
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Cited By (5)

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EP1146468A3 (fr) * 2000-04-13 2004-01-21 General Electric Company Système et méthode de prédiction des interventions et de leurs côuts dans la durée de vie d'un produit
EP1160712A3 (fr) * 2000-05-25 2004-01-21 General Electric Company Système et méthode de prédiction du temps de réalisation d'un service futur pour un produit
US6832205B1 (en) 2000-06-30 2004-12-14 General Electric Company System and method for automatically predicting the timing and costs of service events in a life cycle of a product
EP2228493A3 (fr) * 2000-03-31 2012-06-27 Hitachi Construction Machinery Co., Ltd. Procede et systeme de gestion de machines de construction et dispositif de traitement arithmetique
CN103258245B (zh) * 2013-05-10 2016-03-30 北京航空航天大学 一种新的电子产品失效率预计修正方法

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Cited By (6)

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Publication number Priority date Publication date Assignee Title
EP2228493A3 (fr) * 2000-03-31 2012-06-27 Hitachi Construction Machinery Co., Ltd. Procede et systeme de gestion de machines de construction et dispositif de traitement arithmetique
EP1146468A3 (fr) * 2000-04-13 2004-01-21 General Electric Company Système et méthode de prédiction des interventions et de leurs côuts dans la durée de vie d'un produit
EP1160712A3 (fr) * 2000-05-25 2004-01-21 General Electric Company Système et méthode de prédiction du temps de réalisation d'un service futur pour un produit
US6799154B1 (en) 2000-05-25 2004-09-28 General Electric Comapny System and method for predicting the timing of future service events of a product
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CN103258245B (zh) * 2013-05-10 2016-03-30 北京航空航天大学 一种新的电子产品失效率预计修正方法

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EP0867841A3 (fr) 2002-03-13
DE19712767A1 (de) 1998-10-01
US6085154A (en) 2000-07-04

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