RU2782634C1 - Method for determining the number of failing objects using the data on the runtime of the operated technical objects - Google Patents

Abstract

FIELD: measuring equipment.

SUBSTANCE: invention relates to measuring equipment, namely, to methods for determining the number of failing objects using the data on the runtime of the operated technical objects. Proposed is a method for determining the number of failing objects using the data on the runtime of the operated technical objects while recording the time of the first failure event and calculating the residual lives thereof. All work units are put into operation simultaneously. A failure of the first technical object is expected, and the runtime until the failure of said object is recorded. The time of non-failing objects of the test series is recorded. With each new failing object, the failure of only one object is recorded, while data on the runtime of all objects is recorded for the other objects. The accumulated failure intensity is calculated, the estimated runtime values of each i ^th unit of the technical object at the beginning and at the end of the regulated current period is determined, the probability of failure of each i ^th technical object is calculated in the current supply period, and the number of failing objects is determined.

EFFECT: higher accuracy of determining the number of failing objects in the absence of statistical data.

1 cl, 8 dwg, 1 tbl

Description

The invention relates to the field of measuring technology, namely to methods for determining the number of out-of-service objects using data on the operating time of operated technical objects and can be used in industries where a continuous technological process is required.

A known method of information support for decision-making on the use of mobile repair and diagnostic complexes, which consists in continuous monitoring of the technical condition of weapons, military and special equipment and sets of operational spare tools and accessories, the completeness of the types of repair and diagnostic complexes, the availability, technical condition and location of replacement kits technological equipment of repair and diagnostic complexes and a repair kit of spare tools and accessories, development of a comprehensive task and operational situational management of repair and diagnostic complexes, carrying out repairs at the locations of weapons, military and special equipment. At the planning stage, based on the results of technical diagnostics, many types of work are determined for various types of repair and diagnostic complexes for each type of weapons, military and special equipment (RU 2016136045, publ. 03/07/2018)

A significant disadvantage of the known method is the need to monitor and analyze a large amount of data, which entails increased complexity when implemented under normal conditions, and also requires additional systems for assessing the technical condition of these objects.

Closest to the claimed method is a method for determining the residual resource of technical objects (RU2502974, published on December 27, 2013).

In the prototype method, based on a sample of tested objects with their corresponding failure times or operating time, a statistical series is formed, sorted by increasing operating time. Based on the generated statistical series, the accumulated failure rates are determined, then the distribution function is selected, the values of its parameters are determined, and the gamma-percentage indicators of the resource are calculated, on the basis of which the residual resource is determined. In addition, the residual resource is determined in case of failure of each subsequent object to improve the accuracy of determining the residual resource .

The method is based on determining the residual resource of newly developed and operated technical objects with a limited scope of their testing.

The disadvantage of the known prototype method is the impossibility of determining the number of failing objects, the lack of replacement of which in the shortest possible time will lead to equipment downtime and financial losses.

The problem that the claimed technical solution solves is to determine the number of out-of-service objects by multiple samples with a variable operating time of units of technical objects, without having sufficient statistical data.

The technical result is expressed in increased accuracy in determining the number of failing objects in the absence of statistical data.

The technical result is achieved by the fact that when implementing the method for determining the number of failing objects using data on the operating time of operated technical objects, when fixing the time of the first failure event T ₁ and using the generated statistical series, the probability of reaching the i -th object of the limit state is determined.

,

, соответственно, по формулам:The features of the proposed technical solution, which are different from the prototype, determine the estimated operating time of each i -th unit of the technical object at the beginning and end of the current period

,

, respectively, according to the formulas:

where

t _i - operating time by the i -th technical object at the current moment of the first failure event T ₁ ,h;

m _i - the number of days of operation of the i -th technical object;

r is the number of days between scheduled deliveries of objects;

j is the number of the forecasting period.

Based on the estimated operating time, the probability g _i of failure of each i -th technical object is calculated for the current delivery period

,

,

where

S _1, S ₂ - the desired distribution parameters, depending on the choice of the distribution function (for normal and lognormal distributions S ₁ =μ, S ₂ =σ; for the Weibull distribution S ₁ =α, S ₂ =β);

t is the operating time of the object.

Using the probability values, the number of failing objects is determined using the data on the operating time of the operated technical objects N according to the formula:

,

,

where n is the number of operated units of technical facilities.

In the period between deliveries, with each subsequent failure of the i -th technical object, the number of failing objects N is recalculated.

The claimed method allows, when determining the number of failing objects, to use the operating time to failure of a failed instance (s) of a technical object, as well as the operating time of object instances that continue to be operated. At the same time, to improve the accuracy, the determination of the number of failing objects is carried out with the failure of each subsequent instance, taking into account the fact that at each moment of time different instances have different operating time.

The inventive method allows to increase the accuracy in determining the number of failing objects.

The invention is illustrated by the following figures.

Figure 1 presents Table 1. Statistics of operating time and failures of mud pumps.

Figure 2 - Table 2. The failure time vector and the vector of censoring operating time for the failure of the 1st pump.

Figure 3 - Table 3. The failure time vector and the vector of censoring operating time for the failure of the 2nd pump.

Figure 4 - Table 4. The vector of the failure time and the vector of censoring operating time for the failure of the 7th pump.

Figure 5 - Table 5. Calculation of the accumulated failure rate.

In Fig.6. shows the calculation of distribution parameters in the Mathcad package.

Figure 7 - Table 6. Calculation of an approximate estimate of the operating time at the end of the first delivery period

Figure 8 - Table 7. Calculation of the probability of failure of each of their drilling pumps.

The method is carried out as follows.

1. Form a spare batch of technical objectsN based on the period of time for which the corresponding spare lot is purchased, for example, one delivery per year. To do this, at the beginning, a series of new technical objects is purchased, the total number of which consists of units of objects intended for work and units of spare objects.N. All objects intended for the operation of the series are put into operation simultaneously.

It is assumed that there are no failure statistics for this type of object, and therefore these objects will be replaced by the first spare objects while the initial statistics are being collected.

2. Waiting for the failure of the first technical object.

3. Fix the operating time to failure of the first object at time T ₁ , which is defined as the total operating time from the start of operation to the moment it is impossible to continue the operation of this object.

4. Record the operating time of non-failed objects of the tested series at time T ₁ .

5. A statistical series is formed based on a selection of technical objects with their corresponding failure times and operating times, on the basis of which two adjacent vectors are obtained, sorted by increasing operating time:

- one-dimensional vector of operating times for failed objects;

- an additional vector with censoring developments for developments that did not fail objects.

The position of the object in the vectors of developments is characterized by the quantile q _i .

6. The search for operating time parameters is carried out simultaneously by several quantiles corresponding to the current operating time of individual technical objects. Failure is fixed only for one object. With each calculation of the number of out-of-operation objects, data on the operating times of all objects are recorded and statistical series are formed corresponding to a given time point T ₁ .

7. Determine the accumulated failure rates, assuming that each element of the sample corresponds to one quantile. The i -th object can be taken as an object with a time between failures and an object with a censoring time. Accumulated failure rates are determined by the formula:

,

,

where

p _i is the cumulative failure rate (the proportion of objects that failed during the operating time, less than the operating time of the i -th object relative to the total number of objects that failed during the operating time less than and equal to q _i , and worked more than q _i );

t _i ^otk - the number of objects failed when operating time is less than q _i ;

t _i ^prices* - the number of objects that have worked more than q _i ;

q _i - quantile of the i -th product.

8. The form of the distribution function (DF) is selected, for example, from three types most often used for complex technical objects: normal, lognormal and Weibull distribution. In case of failures of the first objects, it is not possible to unambiguously choose one of the forms, so several FDs can be used simultaneously. In case of failures of subsequent objects, the form of the distribution function can be chosen unambiguously.

9. Determine the values of the parameters of the FR. The shape of the curve of each distribution function is determined by the values of the corresponding operating time parameters.

DF formulas and the corresponding desired parameters for the recommended distributions (Kobzar A. I. Applied mathematical statistics. For engineers and scientists. - M .: FIZMATLIT, 2006. - 816 p.) are listed below:

Distribution distribution function The desired distribution parameters (s ₁ , s ₂ ) Normal

µ, σ lognormal

µ, σ Weibulla

α, β

10. Solve a system of equations to search for parameters using the least squares method:

where f ( t ,μ, σ) - distribution function;

μ, σ - distribution parameters;

p _i ( i =1: n ) - accumulated failure rate;

a _i - difference (error value) between theoretical and actual accumulated failure rates;

q _i ( i =1: n ) - quantile of the i -th product;

t - running time.

11. Get the values of the parameters μ and σ (for a lognormal distribution) to search for parameters and build a curve of dependence of the probability of failure on the number of days of operation.

12. Based on the obtained curve, the number of failing objects N is determined at the end of the regulated period for the supply of spare parts. To do this, determine the estimated values of the operating time at the beginning and end of the current delivery period for each object based on the known, previously recorded values of the operating time using one of the known methods, for example, the linear trend method:

,

- приближенная оценка наработки i-ой единицы объекта на начало и конец периода поставки;where

,

- an approximate estimate of the operating time of the i -th unit of the object at the beginning and end of the delivery period;

t _i - operating time (in hours) of the i -th unit of the object at the current time;

m _i - the number of days of operation of the i -th piece of equipment;

r is the number of days between scheduled deliveries;

j - delivery period number.

13. Calculate the probability g _i of failure of each i -th technical object for the current delivery period

,

,

where S _1, S ₂ are the desired distribution parameters, depending on the choice of the distribution function (for normal and lognormal distributions S ₁ =μ, S ₂ =σ; for the Weibull distribution S ₁ =α, S ₂ =β).

14. Determine the number of failing objects using data on the operating time of operated technical objects N :

,

,

where n is the number of operated units of technical facilities.

The number of failing objects N is recalculated in the period between deliveries with each subsequent failure of the i -th technical object.

Similarly, it is possible to predict the number of failing objects N - not only for the current period, but also for several subsequent ones.

Thus, a qualitative and reliable determination of the number of failing objects N is carried out, which can be used when planning the required volume of supply of spare parts.

An example of the proposed method.

For calculations, data on the operation of a series of mud pumps of the NB-32 brand in the amount of 10 pieces (BN_1 - BN_10) were taken.

All ten mud pumps were put into operation at the same time.

In figure 1, table 1 shows the statistics of operating time and failures of a series of pumps, on the basis of which a statistical series was formed. Based on a sample of mud pump failures with their corresponding failure times, a one-dimensional vector of failure times and an additional vector with censoring operating times were obtained.

In tables 2,3,4 in figures 2,3,4 vectors are presented for the 1st, 2nd and 7th failures.

The accumulated failure rate is determined by the formula:

,

,

p _i is the cumulative failure rate (the proportion of objects that failed during the operating time, less than the operating time of the i -th object relative to the total number of objects that failed during the operating time less than and equal to q _i , and worked more than q _i );

t _i ^otk - the number of objects failed when operating time is less than q _i ;

t _i ^prices* - the number of objects that have worked more than q _i ;

q _i - quantile of the i -th product.

For example, for the pump of the ninth quantile of vectors in case of failure of the first pump BN_1:

.

.

For the pumps of the remaining quantiles in case of failure of the first pump BN_1, the calculations are summarized in table 5 in Fig.5.

Select the distribution function after determining the accumulated failure rate of mud pumps, by which to determine the distribution parameters based on the solution of the system of equations. A logarithmically normal distribution was chosen, the desired distribution parameters of which are μ, σ. The distribution function has the form:

.

.

The system of equations to be solved takes the form:

Solving the system of equations using the Mathcad package by the least squares method (Fig.6), the values of the distribution parameters at the first failure of the object were obtained: μ=6.228, σ=0.173.

In the event of subsequent pump failures, these parameters must be clarified.

The estimated values of the operating time at the beginning and end of the current delivery period for each pump are determined by the formulas:

where t _i is the operating time of the i -th technical object at the current moment of the first failure event T ₁ ,h;

m _i - the number of days of operation of the i -th technical object;

r is the number of days between scheduled deliveries of objects;

j - forecasting period number,

For example, it is assumed that the number of days between scheduled deliveries is 365 (1 year). The first failure event occurred on day 450, therefore, the calculation will refer to the second forecast period, i.e. j =2.

An approximate estimate of the operating time of the pump of the first quantile at the beginning and end of the second period is made, based on the first failure event that occurred on the 450th day of operation:

дней;

days;

дней.

days.

For the remaining pumps, the calculation results are summarized in table 6 (Fig.7).

The probability of failure is calculated for each mud pump for the current delivery period using the formula:

where g _i is the probability of reaching the limit state by the i -th pump.

For the first quantile pump:

. g _i =

.

For the pumps of the remaining quantiles, the calculations are summarized in Table 7 (Fig. 8).

The number of failing objects for the current period is determined by the formula:

,

,

where N is the number of failing objects; n is the number of pumps in operation.

At the end of the second period, N deliveries were 5,709.

The resulting value is rounded up, i.e. N =6.

In the event of another failure, it is necessary to update the forecast for the number of failing objects.

Claims (23)

A method for determining the number of failing objects using data on the operating time of operated technical objects when fixing the time of the first failure event T ₁ and calculating their residual resources, characterized in that a series of new technical objects is purchased, consisting of units intended for work and spare units objects, put all working units into operation simultaneously, expect the failure of the first technical object, fix the operating time to failure of the first object at time T ₁ , which is defined as the total operating time from the moment the operation begins to the moment it is impossible to continue the operation of this object, fix the operating time of non-failed objects of the tested series at time T ₁ , with each new failure of the object, the failure of only one object is recorded, for the rest, data on the operating time of all objects is recorded corresponding to the moment of failure of the current object, the accumulated intensive failure rate, assuming that each element of the sample corresponds to one quantile q _i - operating time of the i -th product, for which both the time to failure and the censoring time can be taken, according to the formula:

, where p _i is the cumulative failure rate (the proportion of objects that failed when the operating time was less than the i -th object relative to the number of all objects that either failed when the operating time was less than q _i , or worked more than q _i ); t _i ^failure - the number of objects that failed when operating time less than q _i ; t _i ^prices* - the number of objects that have worked more than q _i ; q _i - quantile (operating time) of the i -th product, determine the estimated values of the operating time of each i -th unit of a technical object at the beginning and end of the regulated current period

,

, respectively, according to the formulas:

where t _i - operating time by the i -th technical object at the current moment of the first failure event T ₁ , h; m _i - the number of days of operation of the i -th technical object; r is the number of days between scheduled deliveries of objects; j - forecasting period number, then calculate the probability g _i of failure of each i -th technical object for the current delivery period

where S _1, S ₂ - the desired distribution parameters, depending on the choice of the distribution function; for normal and lognormal distributions S ₁ =μ, S ₂ =σ; for the Weibull distribution S ₁ =α, S ₂ =β; t - operating time of the object, and determine the number of failing objects N by the formula:

, where n is the number of operated units of technical facilities, moreover, the number of failing objects N is recalculated for each subsequent failure of the i -th technical object in the period between deliveries.

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