CN107798149A - A kind of aircraft maintainability appraisal procedure - Google Patents

A kind of aircraft maintainability appraisal procedure Download PDF

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CN107798149A
CN107798149A CN201610780874.2A CN201610780874A CN107798149A CN 107798149 A CN107798149 A CN 107798149A CN 201610780874 A CN201610780874 A CN 201610780874A CN 107798149 A CN107798149 A CN 107798149A
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CN107798149B (en
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刘宣
鞠成玉
王守敏
陈星星
苏明
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Chinese Flight Test Establishment
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Abstract

The invention belongs to aircraft testing field, and in particular to a kind of aircraft maintainability appraisal procedure, mean repair time (MTTR) be assessed.Currently take a flight test the stage, traditional the point estimation method is not fully appropriate for the maintainability distribution work in the stage of taking a flight test, it is impossible to it is accurate, objectively respond take a flight test at the end of real maintainability it is horizontal.The present invention provides a kind of suitable for Aircraft Flight Test stage maintainability data characteristicses, reasonably, accurately, the high mean repair time appraisal procedure of Evaluation accuracy, it is proposed that stage maintainability of taking a flight test is established using dark function increases data assessment models, appraisal procedure is reasonable, assessment result is accurate, can truly reflect the real process for stage aircraft maintainability growth of taking a flight test, and this method can be good at being applied to the engineering reality that stage maintainability distribution works of taking a flight test.Assessment result can equip the maintenance sex work after army for aircraft and provide decision support.

Description

Aircraft maintainability assessment method
Technical Field
The invention belongs to the field of airplane testing, and particularly relates to an airplane maintainability assessment method, which is used for assessing the Mean Time To Repair (MTTR).
Background
Currently, the domestic Mean Time To Repair (MTTR) evaluation is mainly based on the provisions of the "maintainability test and assessment" of GJB2072, and a point estimation method of the ratio of the cumulative maintenance time to the maintenance frequency is adopted. The method is mainly suitable for maintainability assessment under the condition that the factors such as equipment technical state, maintainer technical level and the like are stable, but in the current test flight stage, the maintainability design, maintenance scheme, maintainer proficiency and other maintenance factors of the airplane are in improved or improved dynamic change, so that the application of the point estimation method in the maintainability assessment work in the test flight stage is limited to a certain extent, the actual process of airplane maintainability increase in the test flight stage cannot be accurately reflected, and the method is mainly shown in the following aspects:
a) Aiming at the maintainability problem found in the test flight, the maintainability level of the airplane can be increased by carrying out corresponding maintainability design improvement;
b) With the progress of test flight, the maintenance skills and proficiency of maintenance personnel can be slowly improved, the maintenance flow, the maintenance plan and the maintenance guarantee resources can be continuously optimized and perfected, and the maintenance performance level of the airplane is further improved by the factors;
c) The maintenance data collected in the test flight stage come from various maintenance technical states, and the point estimation method cannot accurately reflect the maintainability level under the current technical state condition.
Therefore, the conventional point estimation method cannot be completely applied to the maintainability assessment work in the test flight stage, and cannot accurately and objectively reflect the real maintainability level at the end of the test flight.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method is suitable for the characteristic of maintainability data in the test flight stage of the airplane, and is reasonable and accurate, and the average repair time evaluation method with high evaluation precision is provided.
The invention relates to an aircraft maintainability assessment method, which is used for assessing the mean repair time MTTR and adopts a power function as a model structure of growth trend analysis, so that the relationship between the accumulated repair time CT and the repair times x is established as follows:
CT=ax b
a and b are constants, wherein a represents initial accumulated maintenance time, and b controls the change trend of the CT;
whereby the mean repair time MTTR is
When the MTTR is evaluated, firstly, the maintainability data in the test flight stage is sorted and analyzed, and abnormal values influencing the evaluation result are removed; estimating parameters a and b of the growth model by using sample data; and secondly, carrying out goodness-of-fit inspection, calculating the goodness-of-fit when the inspection data conform to the model, and proving that the obtained model is true when the goodness-of-fit is within a specified range, namely the goodness-of-fit inspection can be used for evaluating the MTTR (mean time to repair).
In the step of arranging and analyzing the data, the steps are as follows:
taking logarithm of the collected single repair time;
the samples after taking the logarithm are sequentially arranged as follows:
fx (1) <fx (2) <…<fx (n)
calculating the mean and standard deviation:
if it is usedOrThen fx (n) Removing abnormal values;
the above steps are repeated for the remaining samples until all outliers are eliminated.
When parameters a and b are estimated, nonlinear least square regression is adopted to process data, and a confidence domain method based on an internal mapping Newton method is used for solving a nonlinear least square equation.
And the goodness-of-fit inspection step judges whether the growth of the product conforms to the growth model according to the sample test data, and inspects the fitting significance of the model and the sample data by adopting F distribution.
The test statistics of the F distribution are:
wherein, ESS is regression sum of squares, its degree of freedom is k, k is the number of regression parameters, k =2:
RSS is the sum of squared residuals with degrees of freedom n-k-1, n is the number of samples:
where y is the value of the sample,is the average value of the samples and is,is an estimate of the corresponding point or points,
for the selected significance level alpha, looking up an F distribution table according to the numerator degree of freedom k and the denominator degree of freedom n-k-1 to find a theoretical critical value F α When F > F α When it is time, the model is considered to be available, otherwise the model is not available.
The significance level was taken to be 0.1.
The calculated fit is:
the minimum sample size is 30.
The invention has the beneficial effects that: aiming at the characteristic that the maintenance operation time is shortened due to factors such as improvement of maintainability in the trial flight stage, improvement of technical proficiency of maintenance personnel and the like, the method for evaluating the maintainability growth data of the trial flight stage is provided and established by utilizing the meditation function, is reasonable in evaluation method and accurate in evaluation result, can truly reflect the actual process of the maintainability growth of the airplane in the trial flight stage, and can be well suitable for engineering practice of maintainability evaluation work in the trial flight stage. The evaluation result can provide decision support for maintenance work after the airplane is arranged in a troop.
Drawings
FIG. 1 is a maintainability growth assessment flow diagram;
FIG. 2 is a graph of random data accumulation;
FIG. 3 is a graph of cumulative maintenance time for a particular type of aircraft;
FIG. 4 is a graph of accumulated maintenance time for an avionics system of an aircraft;
fig. 5 shows the regression result of the belief domain method based on the intra-mapping newton method.
Detailed Description
Maintainability data preprocessing
Due to the influence of factors such as a data collection method and technical level, a certain deviation is generated on part of maintainability data collected by a test flight work site, and an abnormal value is generated, so that an evaluation result is obviously influenced. This may be caused by carelessness of the person responsible for collecting the repair data, inaccurate filling, or the time of multiple repairs combined into one record, and other unpredictable reasons that affect the repair process. Also, there may be multiple such outliers in the collected data at the same time.
Therefore, the data should first be analyzed to verify authenticity and reliability, and if necessary, corrected or restored. According to the state military standard, the repair time generally follows a lognormal distribution. Therefore, after the repair time at the same stage is logarithmized, statistical analysis is performed in accordance with normal distribution, and sample values whose residual errors are outside ± 3 times the standard deviation (± 3 σ) are regarded as abnormal values. After an abnormal value is removed, the mean value and the standard deviation need to be recalculated, and whether the abnormal value exists is checked, wherein the steps are as follows:
a) Taking logarithm of the collected repairing time;
b) The samples after taking the logarithm are sequentially arranged as follows:
fx (1) <fx (2) <…<fx (n)
c) Calculating the mean and standard deviation:
d) If it is usedThen x (n) Is an abnormal value, ifThen x (1) Is an abnormal value; otherwise, consider it to beAnd if no abnormal value exists, completing the abnormal value test process.
e) The outliers removed are recorded and the remaining samples are repeated in steps b) -d).
After the abnormal data are found, the data are abandoned according to the investigation of the actual maintenance condition, if the data belong to the error data; if the correction can be restored by the correction, the analysis is carried out again.
Growth trend model
The main idea of the maintenance growth analysis is to establish a functional relationship between the accumulated maintenance time and the maintenance frequency by analyzing the relationship between the accumulated maintenance time and the maintenance frequency, and further to obtain the corresponding average repair time. And accumulating the maintenance time of each time, drawing a growth curve of the accumulated maintenance time, and searching for a growth rule. If the accumulated maintenance time is CT and the maintenance frequency is x, the relationship between the accumulated maintenance time and the maintenance frequency is:
CT=F(x)
then the MTTR is:
the transient MTTR was:
obviously, as the number of repairs increases, the cumulative repair time increases, i.e., as the number of repairs tends to be infinite, the cumulative repair time tends to be infinite. Therefore, the relationship between the accumulated maintenance time and the number of maintenance cannot be regressed using a model structure having a saturated state.
In order to select a suitable model structure, the maintainability growth situation can be analyzed by means of computer simulation. And randomly generating three groups of random numbers by using a computer, wherein the first group is 100 random numbers obeying the same normal distribution, the second group is normal random numbers with the average value increasing progressively, and the third group is normal random numbers with the average value decreasing progressively. The three sets of data are accumulated to obtain the graph shown in fig. 2. The middle part of the graph is approximately a straight line and is a graph drawn by the first group of data, the concave curve corresponds to the second group of data, and the convex curve corresponds to the third group of data.
We performed the analysis with the third set of data. The slope is larger in the former stage and smaller in the latter stage, which indicates that the random number change is larger in the former stage and smaller in the latter stage from the general trend. This is similar to the law of increased serviceability. If the maintainability is increased during the test flight, the single maintenance time is gradually reduced with the increase of the maintenance times, at this time, although the accumulated maintenance time is increased, the increase amplitude is reduced, and the accumulated time curve is in a convex form, as shown in fig. 3. Conversely, if the serviceability is negatively increased, the cumulative time curve is in a concave form, as shown in FIG. 4. Similar situations exist for analyzing collected maintenance data of a plurality of models of airplanes and maintenance data of different systems.
According to the rule that the influence effect of the unit change of the independent variable x on the dependent variable y is continuously decreased (increased) along with the increase of the independent variable x, a power function can be selected as a model structure for growth trend analysis, and the relationship between the accumulated maintenance time and the maintenance frequency is as follows:
CT=ax b
wherein, the parameter a represents the initial accumulation time, and the parameter b controls the variation trend of the CT. According to different values of b, the following conditions can be divided:
CT varies linearly with x when b =1, when there is no increase;
when 0-b-n (1) are covered, the CT curves are raised upwards, and the maintainability is in a positive growth state;
when b is greater than 1, the CT curve is concave, and the maintainability is in a negative growth state;
when b =0, CT is a straight line parallel to the horizontal axis, which is because the following maintenance time is zero, and such a situation does not occur when we reject data with zero maintenance time;
when b <0, the CT curve tends to fall, which does not occur because the dependent variable is the accumulated maintenance time.
Thus, the MTTR is:
the transient MTTR was:
growth parameter estimation method
The parameter estimation of the growth model adopts a least square method (LS), which means a mathematical method for solving unknown parameters by calculating partial derivatives of the unknown parameters and making them equal to zero, in order to obtain ideal estimated values of regression parameters, and is a commonly used optimal fitting method. Although the power function can be linearized into a linear function, the parameters are estimated using least squares. However, the conventional least square method has some limitations, and when the collected data is small and abnormal points are included in the data, the result obtained by the least square method becomes unreliable, and in this case, the accuracy of prediction or fitting is rather low or even not available by applying the obtained regression equation or model to prediction, fitting, and the like.
Therefore, the data are processed by using a more robust nonlinear least square regression, and the nonlinear least square equation is solved by using a confidence domain method based on an internal mapping Newton method, so that the robustness of parameter estimation is further ensured.
Fig. 5 shows the regression result of the confidence domain method of the interior mapping newton method, and it can be seen from the figure that the method can better fit the actual data, eliminate the influence of individual abnormal data, and can give the corresponding confidence interval.
Goodness of fit test
After obtaining the growth model and estimating the parameters of the model, goodness-of-fit testing is required to check whether the data conforms to the model. An F-test is used here to test the significance of the fit of the candidate model to the sample data. The null hypothesis for the F-test is that each regression parameter is equal to zero, i.e., the model cannot be used to fit the sample. The test statistics are:
wherein, ESS is regression sum of squares, its degree of freedom is k, k is the number of regression parameters:
RSS is the sum of squared residuals with degrees of freedom n-k-1, n is the number of samples:
the value of F calculated from the sample obeys F k,n-k-1 And (4) distribution. For the selected significance level alpha, searching an F distribution table according to the numerator degree of freedom k and the denominator degree of freedom n-k-1, and finding out a theoretical critical value F α . When F > F α And (4) rejecting the original hypothesis, namely, considering that the regression relationship between the independent variable and the dependent variable in the overall regression function is obvious. When F is less than or equal to F α When the original assumption is accepted, namely the regression relation between the independent variable and the dependent variable in the overall regression function is not considered to be obvious, the established regression model has no meaning, namely the model cannot be used for evaluating the maintainability growth trend. Significance levels were typically taken to be 0.1.
If the model fails the test, there may be several cases: 1) Data is inaccurate, and whether the data has abnormal values needs to be reexamined; 2) When the model parameter estimation is not appropriate, the parameter needs to be estimated again; 3) The selection of the confidence coefficient is too harsh, and the requirement of the confidence coefficient can be properly relaxed under the condition allowed by the actual condition; 4) The number of samples is not sufficient.
Fitness calculation
The fitting degree is a number between 0 and 1, the larger the value is, the better the fitting degree is, when the value is 0.5, only 50% of samples conform to the model, and the fitting degree is defined as:
where y is the value of the sample,is the average value of the samples and is,is an estimate of the corresponding point.
Conditions for model adaptation
When the sample data is larger than 3, the model can be used for evaluation. It should be noted, however, that the minimum sample size required in evaluating the average repair time is 30 per the provisions in GJB2072 "serviceability tests and assessments". When the number of samples is less than 30, the samples cannot traverse the whole sample space, and the result obtained by directly averaging the repair time cannot represent the true average repair time level, and the fluctuation is large. At this time, the accumulated average repair time obtained by analyzing the maintainability growth trend by using the model is probably hard to be matched with the result obtained by directly sampling the average value of the sample, and when the sample data is more than 30-50, the accumulated MTTR obtained by analyzing the maintainability growth trend is better matched with the result obtained by directly sampling the average value of the sample.

Claims (8)

1. An aircraft maintainability assessment method for assessing the mean repair time MTTR, characterized in that the method uses a power function as a model structure for growth trend analysis, thereby establishing the relationship between the cumulative repair time CT and the number of repairs x as follows:
CT=ax b
a and b are constants, wherein a represents initial accumulated maintenance time, and b controls the change trend of the CT;
so that the mean repair time MTTR is
When the MTTR is evaluated, firstly, the maintainability data in the test flight stage is sorted and analyzed, and abnormal values influencing the evaluation result are removed; estimating parameters a and b of the growth model by using sample data; and secondly, carrying out goodness-of-fit inspection, calculating the goodness-of-fit when the inspection data conform to the model, and proving that the obtained model is true when the goodness-of-fit is within a specified range, namely the goodness-of-fit inspection can be used for evaluating the MTTR (mean time to repair).
2. The aircraft serviceability assessment method according to claim 1, wherein: in the step of sorting and analyzing the data, the steps are as follows:
taking logarithm of the collected single repair time;
the samples after taking the logarithm are sequentially arranged as follows:
fx (1) <fx (2) <…<fx (n)
calculating the mean and standard deviation:
if it is notOrThen fx (n) Removing abnormal values;
the above steps are repeated for the remaining samples until all outliers are rejected.
3. The aircraft serviceability assessment method according to claim 1, wherein: when parameters a and b are estimated, data are processed by adopting nonlinear least square regression, and a confidence domain method based on an internal mapping Newton method is used for solving a nonlinear least square equation.
4. The aircraft serviceability evaluation method as recited in claim 1, wherein: and the goodness-of-fit inspection step judges whether the growth of the product conforms to the growth model according to the sample test data, and inspects the fitting significance of the model and the sample data by adopting F distribution.
5. The aircraft serviceability assessment method according to claim 4, wherein: the test statistics of the F distribution are:
wherein, ESS is regression sum of squares, its degree of freedom is k, k is the number of regression parameters, k =2:
RSS is the sum of squared residuals with degrees of freedom n-k-1, n is the number of samples:
where y is the value of the sample,is the average value of the samples and is,is an estimate of the corresponding point or points,
for the selected significance level alpha, looking up an F distribution table according to the numerator degree of freedom k and the denominator degree of freedom n-k-1 to find a theoretical critical value F α When F > F α When it is time, the model is considered to be available, otherwise the model is not available.
6. The aircraft serviceability evaluation method of claim 5, wherein: the significance level was taken to be 0.1.
7. The aircraft serviceability assessment method according to claim 1, wherein: the calculated fit is:
8. the aircraft serviceability evaluation method according to any one of claims 1 to 7, wherein: the minimum sample size is 30.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113536460A (en) * 2021-07-15 2021-10-22 北京航空航天大学 Aircraft multi-stage maintenance time verification data supplementing method and system
US11568292B2 (en) * 2020-06-25 2023-01-31 Textron Innovations Inc. Absolute and relative importance trend detection
CN118037135A (en) * 2024-04-11 2024-05-14 生态环境部卫星环境应用中心 Qualitative analysis method for influence of vegetation coverage change on ecosystem service

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CN102043839A (en) * 2010-12-13 2011-05-04 北京航空航天大学 Template method for multidimensional integrated balancing of property and reliability, maintainability and supportability
CN103559555A (en) * 2013-10-29 2014-02-05 中航沈飞民用飞机有限责任公司 Method for optimizing product planned maintenance interval by civil airplane manufacturer
CN105787139A (en) * 2014-12-25 2016-07-20 北京电子工程总体研究所 Maintenance support simulation and optimization method of complex system based on failure synthesis

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Publication number Priority date Publication date Assignee Title
US20100241400A1 (en) * 2009-03-20 2010-09-23 International Business Machines Corporation Determining Component Failure Rates Using Accelerated Life Data
CN102043839A (en) * 2010-12-13 2011-05-04 北京航空航天大学 Template method for multidimensional integrated balancing of property and reliability, maintainability and supportability
CN103559555A (en) * 2013-10-29 2014-02-05 中航沈飞民用飞机有限责任公司 Method for optimizing product planned maintenance interval by civil airplane manufacturer
CN105787139A (en) * 2014-12-25 2016-07-20 北京电子工程总体研究所 Maintenance support simulation and optimization method of complex system based on failure synthesis

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US11568292B2 (en) * 2020-06-25 2023-01-31 Textron Innovations Inc. Absolute and relative importance trend detection
CN113536460A (en) * 2021-07-15 2021-10-22 北京航空航天大学 Aircraft multi-stage maintenance time verification data supplementing method and system
CN118037135A (en) * 2024-04-11 2024-05-14 生态环境部卫星环境应用中心 Qualitative analysis method for influence of vegetation coverage change on ecosystem service

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