CN110717265A - Method and device for approximately calculating spare part demand of lognormal unit - Google Patents
Method and device for approximately calculating spare part demand of lognormal unit Download PDFInfo
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Abstract
The invention relates to a method for approximately calculating the spare part demand of a lognormal type unit, wherein lognormal distribution is approximately gamma distribution, a gamma distribution parameter is calculated according to the lognormal distribution parameter, and the spare part satisfaction rate is calculated according to the convolution additivity characteristic of the gamma distribution. The invention converts the multiple convolution problem related to the computation of the spare part demand of the log-normal type unit into the fast convolution computation problem of gamma distribution, thereby realizing the approximate computation of the spare part demand of the log-normal type unit. The calculation complexity does not increase exponentially due to the increase of the number of spare parts, and the requirement of the spare parts of the log-normal type unit can be calculated quickly.
Description
Technical Field
The invention relates to the technical field of equipment maintenance support, in particular to a method and a device for approximately calculating spare part demand of a lognormal unit.
Background
A log normal distribution is a common lifetime distribution, often used to describe the lifetime distribution of helicopter rotating blades, aircraft structures, metal fatigue, motor winding insulation, semiconductor devices, silicon transistors, germanium transistors, and the like. The lognormal type unit refers to a unit whose lifetime follows lognormal distribution, and the lifetime X follows lognormal distribution and is recorded as X-Ln (mu, sigma)2) Where μ > 0 is a log mean parameter, σ > 0 is a log root variance parameter, and the density function of X is
In theory, the spare part satisfaction rate when calculating the number of spare parts as k involves a k-deconvolution calculation of the unit life distribution function. The k-deconvolution analytic expression of the lognormal distribution is very complex and is difficult to derive. Furthermore, if a computer numerical calculation is adopted, the calculation amount increases exponentially with the increase of k, and thus the calculation is difficult to be completed quickly in a limited time. At present, no quick and accurate spare part demand calculation method exists for the lognormal type unit.
Disclosure of Invention
Aiming at the technical problems in the prior art, the invention provides a method for quickly and accurately calculating the requirement of a lognormal unit spare part.
The technical scheme for solving the technical problems is as follows:
in a first aspect, the present invention provides a method for approximately calculating a spare part demand of a lognormal type unit, comprising the following steps:
s1, initializing the spare part number j, making j equal to 0, and distributing Ln (μ, σ) in log-normal mode2) Approximate to a gamma distribution G (a, b), and
s2, calculating the spare part satisfaction rate PSAccording to the additive character of convolution of gamma distribution, let
Where Γ () is a gamma function,
t is guarantee task time;
s3, judging PSWhether the requirement of spare part guarantee is met or not is judged, namely P is judgedSWhether it is less than the lowest spare part satisfaction rate P1, if PSIf P1 is less than the threshold, j is made j +1, and the process proceeds to step S2, otherwise, the calculation is terminated and S is output as the final spare part demand.
The invention has the beneficial effects that: we find that in some cases, the lognormal distribution and the gamma distribution are relatively approximate, after research, a calculation method of gamma distribution parameters a and b is further given, and then the multiple convolution problem (difficult to quickly complete calculation within a limited time) involved in the lognormal unit spare part demand calculation is converted into the quick convolution calculation problem of the gamma distribution by utilizing the convolution additivity characteristic of the gamma distribution, so that the approximate calculation of the lognormal unit spare part demand is realized. The method converts the lognormal distribution into the gamma distribution, the calculation complexity cannot increase exponentially due to the increase of the number of spare parts, and the requirement quantity of the spare parts of the lognormal unit can be calculated quickly.
In a second aspect, the present invention provides an apparatus for approximating a spare part requirement of a lognormal type unit, comprising:
the input module is used for setting guarantee task time T and the lowest spare part satisfaction rate P1;
the calculating module is used for calculating the demand of spare parts of the universal parts; the specific calculation method is as follows:
s1, initializing the spare part number j, making j equal to 0, and distributing Ln (μ, σ) in log-normal mode2) Approximate to a gamma distribution G (a, b), and
s2, calculating the spare part satisfaction rate PSAccording to the additive character of convolution of gamma distribution, let
Where Γ () is a gamma function,
t is guarantee task time;
s3, judging PSWhether the requirement of spare part guarantee is met or not is judged, namely P is judgedSWhether it is less than the lowest spare part satisfaction rate P1, if PSIf the value is less than P1, j is made to be j +1, and the step is jumped to step S2, otherwise, the calculation is terminated, and S is made to be j and output as the final spare part demand;
and the output display module is used for outputting and displaying the final spare part demand calculated by the calculation module.
In a third aspect, the present invention provides an approximate calculating apparatus for spare part demand of a lognormal type unit, including:
a memory for storing a computer software program;
and the processor is used for reading and executing the computer software program stored in the memory, and realizing the approximate calculation method for the spare part demand of the lognormal type unit in the first aspect.
In a fourth aspect, the present invention provides a non-transitory computer-readable storage medium, in which a computer software program for implementing the method for approximating a spare part requirement of a lognormal-type unit according to the first aspect is stored.
Drawings
Fig. 1 is a flowchart of a method for approximately calculating a spare part demand of a lognormal unit according to an embodiment of the present invention;
FIG. 2 is a diagram illustrating exemplary simulation results according to a first embodiment of the present invention;
fig. 3 is a structural diagram of a device for approximating a demand of a spare part of a lognormal unit according to a second embodiment of the present invention.
Detailed Description
The principles and features of this invention are described below in conjunction with the following drawings, which are set forth by way of illustration only and are not intended to limit the scope of the invention.
Calculating the spare part satisfaction rate when the number of spare parts is k involves k-deconvolution calculation of the unit life distribution function. The k-deconvolution analytic expression of the lognormal distribution is very complex and is difficult to derive. Furthermore, if a computer numerical calculation is adopted, the calculation amount increases exponentially with the increase of k, and thus the calculation is difficult to be completed quickly in a limited time.
According to research, the lognormal distribution and the gamma distribution are approximate under certain conditions, after research, a calculation method of gamma distribution parameters a and b is further provided, and then the multiple convolution problem (difficult to quickly complete calculation within a limited time) related to the lognormal unit spare part demand calculation is converted into the quick convolution calculation problem of the gamma distribution by utilizing the convolution additive characteristic of the gamma distribution, so that the approximate calculation of the lognormal unit spare part demand is realized. The method converts the lognormal distribution into the gamma distribution, the calculation complexity cannot increase exponentially due to the increase of the number of spare parts, and the requirement quantity of the spare parts of the lognormal unit can be calculated quickly.
In the invention, the following is agreed: when the unit breaks down, the unit is repaired in a mode of replacing and repairing (the time for replacing and repairing is ignored). And recording the guarantee task time as T and the spare part demand as S, wherein the spare part satisfaction rate is required to be not lower than P1.
Example one
The embodiment of the invention provides an approximate calculation method for spare part demand of a lognormal type unit, which comprises the following steps as shown in figure 1:
s1, initializing the spare part number j, making j equal to 0, and distributing Ln (μ, σ) in log-normal mode2) Approximate to a gamma distribution G (a, b), and
(Note that when a is less than 0.3, the error of the result obtained by the method of the invention is large, so when the method of the invention is used for calculating the spare part demand of the lognormal type unit, the value of a is used for judging whether to continue to execute the next step or not.)
S2, calculating the spare part fullnessFoot rate PSAccording to the additive character of convolution of gamma distribution, letWhere Γ () is a gamma function,
t is guarantee task time;
s3, judging PSWhether the requirement of spare part guarantee is met or not is judged, namely P is judgedSWhether it is less than the lowest spare part satisfaction rate P1, if PSIf P1 is less than the threshold, j is made j +1, and the process proceeds to step S2, otherwise, the calculation is terminated and S is output as the final spare part demand.
The method adopts the following simulation model to simulate the spare part guarantee process.
1) According to the distribution rule of unit life, 1+ S random numbers simT are generatediI is more than or equal to 1 and less than or equal to 1+ S, and is used for simulating the respective service lives of the unit and the S spare parts;
2) order to
3) If the simT1 is not less than T, ensuring success, and recording flag as 1; otherwise, the guarantee fails, and the flag is equal to 0.
After the model is operated for many times, a large number of simulation results of the flag are counted, and the mean value of the simulation results is the simulation result of the spare part meeting the probability.
Examples of the design
The lifetime of a certain cell follows a log-normal distribution Ln (6.6, 0.9)2) And the task time is guaranteed to be 5000 hours. The spare part demand of the unit is calculated by adopting the method, so that the spare part satisfaction rate is not lower than 0.85.
Solution: 1) initializing the number of spare parts, and enabling j to be 0; let a be 0.8013 and b be 1375.4.
2) Calculating spare part satisfaction rate PS。
Table 1 lists the corresponding spare part satisfaction rates when the number of spare parts takes various values.
TABLE 1
3) When j is 7, the spare part satisfaction rate PSAnd the number is 0.880, and the spare part guarantee requirement that the spare part satisfaction rate is not lower than 0.85 is met.
4) The calculation is terminated and the spare part requirement for the unit is 7.
FIG. 2 shows the result of the satisfaction rate of the spare parts obtained by the method and the simulation method of the present invention when the number of the spare parts of the above calculation examples is from 0 to 11. A large number of simulation results show that: the error of the two is within the range of engineering application.
Example two
An embodiment of the present invention provides an approximate computing apparatus for spare part demand of a lognormal unit, as shown in fig. 3, including:
the input module is used for setting guarantee task time T and the lowest spare part satisfaction rate P1;
the calculating module is used for calculating the demand of spare parts of the universal parts; the specific calculation method is as follows:
s1, initializing the spare part number j, making j equal to 0, and distributing Ln (μ, σ) in log-normal mode2) Approximate to a gamma distribution G (a, b), and
s2, calculating the spare part satisfaction rate PSAccording to the additive character of convolution of gamma distribution, let
Where Γ () is a gamma function,
t is guarantee task time;
s3, judging PSWhether the requirement of spare part guarantee is met or not is judged, namely P is judgedSWhether it is less than the lowest spare part satisfaction rate P1, if PSIf the value is less than P1, j is made to be j +1, and the step is jumped to step S2, otherwise, the calculation is terminated, and S is made to be j and output as the final spare part demand;
and the output display module is used for outputting and displaying the final spare part demand calculated by the calculation module.
EXAMPLE III
The embodiment of the invention provides a device for approximately calculating the spare part demand of a lognormal type unit, which comprises:
a memory for storing a computer software program;
and the processor is used for reading and executing the computer software program stored in the memory, and realizing the approximate calculation method for the spare part demand of the lognormal type unit in the embodiment of the invention.
Example four
The embodiment of the invention provides a non-transitory computer readable storage medium, wherein a computer software program for realizing the approximate calculation method for the spare part demand of the lognormal type unit is stored in the storage medium.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above-described technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods described in the embodiments or some parts of the embodiments.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (4)
1. A method for approximately calculating the spare part demand of a lognormal unit is characterized by comprising the following steps:
s1, initializing the spare part number j, making j equal to 0, and distributing Ln (μ, σ) in log-normal mode2) Approximate to a gamma distribution G (a, b), and
s2, calculating the spare part satisfaction rate PSAccording to the additive character of convolution of gamma distribution, let
Where Γ () is a gamma function,
t is guarantee task time;
s3, judging PSWhether the requirement of spare part guarantee is met or not is judged, namely P is judgedSWhether it is less than the lowest spare part satisfaction rate P1, if PSIf P1 is less than the threshold, j is made j +1, and the process proceeds to step S2, otherwise, the calculation is terminated and S is output as the final spare part demand.
2. An apparatus for approximating a demand for spare parts of a lognormal-type unit, comprising:
the input module is used for setting guarantee task time T and the lowest spare part satisfaction rate P1;
the calculating module is used for calculating the demand of spare parts of the universal parts; the specific calculation method is as follows:
s1, initializing the spare part number j, making j equal to 0, and distributing Ln (μ, σ) in log-normal mode2) Approximate to a gamma distribution G (a, b), and
s2, calculating the spare part satisfaction rate PSAccording to the additive character of convolution of gamma distribution, letWhere Γ () is a gamma function,
s3, judging PSWhether the requirement of spare part guarantee is met or not is judged, namely P is judgedSWhether it is less than the lowest spare part satisfaction rate P1, if PSIf the value is less than P1, j is made to be j +1, and the step is jumped to step S2, otherwise, the calculation is terminated, and S is made to be j and output as the final spare part demand;
and the output display module is used for outputting and displaying the final spare part demand calculated by the calculation module.
3. An apparatus for approximating a demand for spare parts of a lognormal-type unit, comprising:
a memory for storing a computer software program;
a processor for reading and executing the computer software program stored in the memory to implement the method for approximating a spare part requirement of a lognormal unit as claimed in claim 1.
4. A non-transitory computer readable storage medium having stored therein a computer software program for implementing a spare part demand approximation calculation for a lognormal type unit as claimed in claim 1.
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| US20170177756A1 (en) * | 2015-12-22 | 2017-06-22 | Bwxt Mpower, Inc. | Apparatus and method for safety analysis evaluation with data-driven workflow |
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