CN109376380B - Method for determining subsequent spare part demand of gamma type unit - Google Patents
Method for determining subsequent spare part demand of gamma type unit Download PDFInfo
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- CN109376380B CN109376380B CN201811051393.3A CN201811051393A CN109376380B CN 109376380 B CN109376380 B CN 109376380B CN 201811051393 A CN201811051393 A CN 201811051393A CN 109376380 B CN109376380 B CN 109376380B
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Abstract
A method for determining the demand of subsequent spare parts of a gamma-type unit belongs to a design method of equipment guarantee performance, and solves the problem that the demand of the subsequent spare parts under the condition that (old) unit + (new) spare parts cannot be accurately calculated in the conventional gamma-type unit subsequent spare part demand method. The method comprises the steps of setting an initial value, calculating the residual life failure degree, calculating the guarantee probability and judging. The method considers the influence of the 'old product unit' which works for a period of time on the demand of the subsequent spare parts, can accurately calculate the demand of the subsequent spare parts and the guarantee probability corresponding to the quantity of the spare parts, and lays a foundation for realizing the accurate guarantee of the equipment.
Description
Technical Field
The invention belongs to a design method for guaranteeing performance of equipment, and particularly relates to a method for determining the demand of subsequent spare parts of a gamma-type unit.
Background
The premise assumption that the unit and the spare parts are new products is that most of spare part demand calculation methods, the spare part demand result obtained by calculation at the moment is called an initial spare part scheme, and the initial meaning is that the unit is at the initial zero time and is just started to be used. If the unit which has been working for a period of time is regarded as a new product and is used for calculating the demand quantity of subsequent spare parts, the risk of less spare parts and insufficient guarantee can be caused; if the unit which has been working for a period of time is treated as a fault part by suggestive means for calculating the demand of the subsequent spare parts, the situation of excessive quantity and over-guarantee of the spare parts can be caused.
In fact, in most cases, a unit has been in operation for a period of time and has not failed, and can continue to be used during the next task, which may be referred to as a "legacy unit". Therefore, how to calculate the demand of the subsequent spare parts in the case of "old spare part unit + new spare part" is a more general problem than the calculation problem of the initial spare part. Theoretically, only the units whose life span is subject to exponential distribution, and the subsequent spare parts thereof can adopt the initial spare part demand calculation method.
The gamma distribution is a common distribution type and is suitable for describing the process of gradual and continuous performance degradation in engineering practice, for example, the wear of a cutter is a typical continuous-time and continuous-state performance degradation process, and the service life of the cutter can be represented by the gamma distribution. For the units with the service life subject to gamma distribution, the invention is called gamma type units for short. In the existing method for determining the subsequent spare part demand of a gamma-type unit, a common idea is to regard a unit which has been operated for a period of time as a new product, and determine the subsequent spare part demand by a method for calculating the initial spare part demand under the assumption of a new product unit and a new spare part, which can cause the risks of less spare part quantity and insufficient guarantee; another common idea is to treat a unit that has been working for a certain period of time as a faulty component, and calculate the demand of subsequent spare parts under the assumption of "faulty unit + new spare part", which may result in a situation of excessive quantity of spare parts and over-provisioning.
Noting that the lifetime z of a gamma-type cell obeys a gamma distribution Ga (α, λ), where α > 0 is a shape parameter and λ > 0 is a scale parameter, these two parameters are determined for a specific gamma-type cell, the density function f (z) of the gamma distribution:
wherein Γ (α) is a gamma function, and
suppose the unit has been operating normally for time t 1 And no fault occurs, the residual service life is recorded as T 1 I.e. unit life t 1 +T 1 The remaining life refers to the time that the unit can normally work again after working for a period of time without failure.
Disclosure of Invention
The invention provides a method for determining the subsequent spare part demand of a gamma-type unit, which solves the problem that the subsequent spare part demand can not be accurately calculated under the condition of (old) unit + (new) spare part) in the conventional gamma-type unit subsequent spare part demand method.
The invention provides a method for determining the demand of subsequent spare parts of a gamma type unit, which comprises the steps of setting an initial value, calculating the residual life failure degree, calculating the guarantee probability and judging, and is characterized in that:
(1) Setting an initial value:
setting guarantee probability target values P0, 0-P1, and setting a spare part demand variable j =0;
(2) Calculating the residual service life failure degree:
calculating residual life failure F (x | t) 1 )：
Wherein x is a time variable, and x>0，t 1 For the cell has been in working order, λ > 0 is a scale parameter, α > 0 is a shape parameter, Γ (α) is a gamma function, and
y is an independent variable;
(3) Calculating guarantee probability:
calculating guarantee probability P when the number of spare parts is j:
in the above formula, F (x | t) 1 ) Residual lifetime failure in step (2), T w Planned work time, T, for the next task of a unit w ＞0；
(4) A judging step:
and (4) judging whether P is larger than or equal to P0, if so, obtaining a j value which is the spare part demand, otherwise, giving j to the j +1 value, and turning to the step (3).
In step (3), the remaining lifetime failure degree F (x | t) 1 ) Embodies the working of' old product unitAs time t 1 Influence on the subsequent spare part demand, and step (3) reduces the original complex j +1 reintegration problem in the spare part demand calculation into a double integration problem.
The invention can eliminate the risks of over-guarantee and under-guarantee, and the calculation by utilizing the sum of the residual service life of the old product and the service life of the new spare part is actually the executed convolution operation. The method considers the influence of the 'old product unit' which works for a period of time on the demand of the subsequent spare parts, can accurately calculate the demand of the subsequent spare parts and the guarantee probability corresponding to the quantity of the spare parts, and lays a foundation for realizing the accurate guarantee of equipment.
Detailed Description
The present invention is further illustrated by the following examples.
Example (b): the lifetime of a cell, which has accumulated a normal operating time t, follows a gamma distribution Ga (2.1, 0.002) 1 The projected operating time T of the unit for the next task is predicted to be 650h w The task is 1500h, the spare part guarantee probability is required to be more than or equal to 0.85, and the subsequent spare part demand prepared for the task is calculated, and the task comprises the following steps:
(1) Setting an initial value:
setting a guarantee probability target value P0=0.85, and setting a spare part demand variable j =0;
(2) Calculating the residual service life failure degree:
calculating the remaining life failure degree F (x | 650):
(3) Calculating guarantee probability:
calculating guarantee probability P when the number of spare parts is j:
in the above formula, T w Is under the unitA scheduled work time for a task;
(4) A judging step:
and (4) judging whether P is larger than or equal to P0, if so, obtaining a j value which is the spare part demand, otherwise, giving j to the j +1 value, and turning to the step (3).
The calculation results of step (3) are shown in table 1:
TABLE 1 results of calculation
The simulation results in table 1 were obtained by simulation using a simulation method.
It can be known from table 1 that, when the spare part demand is 2, the guarantee probability can satisfy the guarantee probability requirement of not less than 0.85, and the guarantee probability calculated in step (3) is extremely consistent with the simulation result.
When the number of spare parts is j, the simulation method for simulating the primary guarantee process is as follows:
(1) Generating 1 random number simT1 for simulating normal operation t 1 Unit life of (1), simT1 obeys the gamma distribution Ga (alpha, lambda), and simT1 > t 1 ；
(2) Judging whether j is larger than 0, if so, performing the step (3), and otherwise, turning to the step (4);
(3) Generating j random numbers simT k (k is more than or equal to 1 and less than or equal to j) for simulating the service life of j spare parts, simT k Obeying a gamma distribution Ga (alpha, lambda), such that
Turning to the step (5);
(4) Let simT = simT1-t if j =0 1 (ii) a Turning to the step (5);
(5) Judging whether SimT is more than or equal to T w If yes, making flag =1, the spare part guarantee task is successful, otherwise, making flag =0, and the spare part guarantee task is failed.
And simulating the guarantee process for multiple times to obtain a large number of flag values, wherein the statistical mean value of the flag values of the multiple times is the corresponding guarantee probability when the number of the simulated spare parts is j.
Claims (1)
1. A method for determining the demand of subsequent spare parts of a gamma type unit comprises the steps of setting an initial value, calculating the residual life failure degree, calculating the guarantee probability and judging, and is characterized in that:
(1) Setting an initial value:
setting guarantee probability target values P0, 0-P0-1, and setting a device demand variable j =0;
(2) Calculating the residual service life failure degree:
calculating residual life failure F (x | t) 1 )：
Wherein x is a time variable, and x>0，t 1 For the cell has been in working order, λ > 0 is a scale parameter, α > 0 is a shape parameter, Γ (α) is a gamma function, and
y is an independent variable;
(3) Calculating guarantee probability:
calculating guarantee probability P when the number of spare parts is j:
in the above formula, F (x | t) 1 ) Residual lifetime failure in step (2), T w Planned work time, T, for the next task of a unit w ＞0；
(4) A judging step:
and (4) judging whether P is larger than or equal to P0, if so, obtaining a j value which is the spare part demand, otherwise, giving j to the j +1 value, and turning to the step (3).
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| RU2014116761A (en) * | 2014-04-24 | 2015-10-27 | Открытое акционерное общество "Системы и технологии обеспечения безопасности. Техдиагностика" | METHOD OF OPERATION OF TECHNOLOGICAL EQUIPMENT |
| CN106874238A (en) * | 2017-01-20 | 2017-06-20 | 中国人民解放军海军工程大学 | A kind of computational methods of Weibull type unit spare parts demand amount |
| CN107784374A (en) * | 2016-08-25 | 2018-03-09 | 新疆金风科技股份有限公司 | Forecasting Methodology, device and the equipment of Wind turbines spare parts demand |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| RU2014116761A (en) * | 2014-04-24 | 2015-10-27 | Открытое акционерное общество "Системы и технологии обеспечения безопасности. Техдиагностика" | METHOD OF OPERATION OF TECHNOLOGICAL EQUIPMENT |
| CN107784374A (en) * | 2016-08-25 | 2018-03-09 | 新疆金风科技股份有限公司 | Forecasting Methodology, device and the equipment of Wind turbines spare parts demand |
| CN106874238A (en) * | 2017-01-20 | 2017-06-20 | 中国人民解放军海军工程大学 | A kind of computational methods of Weibull type unit spare parts demand amount |
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