KR102335651B1 - Reliability sampling plan cost-effectiveness optimization design method based on prediction result of failure rate of electronic equipment applied to weapon system - Google Patents

Abstract

The present invention provides a method for optimally designing reliability sampling cost-effectiveness, which optimizes a correlation between the number of samples and costs caused by variables of testing time according to the number of samples based on a failure rate calculated based on an electronic equipment failure rate predicting model applied to a weapon system.

Description

Reliability sampling plan cost-effectiveness optimization design method based on prediction result of failure rate of electronic equipment applied to weapon system}

The present invention relates to an optimal design method for reliability sampling cost-effectiveness based on a result of predicting failure rate of electronic equipment applied to a weapon system.

Reliability sampling test can be divided into continuous type and attribute type according to the judgment method.

First, the continuous reliability sampling inspection method is a method of determining whether to pass by sampling a certain number of samples, performing a test for a certain period of time, obtaining an estimated value of the average failure interval, and comparing this value with the acceptance decision value.

Next, the continuous reliability sampling test type can be divided into the still water interruption test, which stops the test when a predetermined number of failures occur, and the on-time interruption test, which stops the test after the test for a preset test time.

In case of applying the purified water interruption test, there are upper/lower average failure interval, producer risk, and consumer risk as necessary prior information. There is exam time.

Next, the attribute reliability sampling test method is a method of determining whether or not a pass is passed by sampling a certain number of samples and comparing the number of post-test failures with the allowable number of failures during a set test time. These include failure rate, consumer risk, test time, and allowable number of failures.

The multiple reliability sampling tests described above can be applied if you have prior information about the target device, but in the case of a weapon system, it has the characteristics of a high-cost electronic equipment complex, multi-variety, small-lot production, and intermittent process. /Lower limit The setting for the mean interval between failures is limited.

According to the characteristics of the contract being concluded according to the weapon system acquisition stage, there is a possibility that the institutions subject to R&D and mass production contracts may change and the characteristics of the enforcement process exist. Therefore, even if there is a change in weapons system research and development institutes and mass production institutes, standardization documents are established through standardization and cataloging to confirm and supplement the changes in requirements, and based on this document, the requirements for weapon systems will check In particular, since the cost required for the time-static requirement check is large compared to the time-static requirement check cost, the reliability requirement that requires a certain number of samples and test time to apply the statistical analysis Reliability sampling plan design is required to perform efficiently after development.

In order to solve the above problem, the present application optimizes the correlation between the number of sampling samples and the cost caused by the test time variable according to the number of samples based on the failure rate calculated based on the failure rate prediction model of the electronic equipment applied to the weapon system. Therefore, it is a task to solve the problem of proposing an optimal design method for reliability sampling cost-effectiveness.

However, the purpose of the present application is not limited to the above.

In order to solve the above problems,

According to one aspect of the present invention,

Based on sampling test time labor cost (C _t ), sampling test cost manufacturing cost (C _m ),

A cost-effectiveness optimal design method for cost-effectiveness sampling is provided, comprising calculating the number of samples (n) and the test time (t) according to the number of samples such that the cost-model optimal design model (C _{T ) is minimized.} .

In addition, the cost-model optimal design model (C _T ) may be determined by the following general formula (1).

[General formula 1]

In addition, the sampling test time labor cost (C _t ) may be determined by the following general formula (2).

[General formula 2]

In Formula 2, l _c is the labor cost per hour, and t is the test time according to the number of samples.

In addition, the manufacturing cost (C _m ) required for the sampling test may be determined by the following general formula (3).

[General Formula 3]

In General Formula 3, m _c represents the manufacturing cost per one electronic device, and n represents the number of samples.

In addition, the number of samples (n) may be determined by the following general formula (4).

[General formula 4]

In Formula 4, χ _β ² (2(c+1)) is ^{the 100(β)% percentile of the χ 2} distribution with c+1 degrees of freedom, c is the number of fault tolerances, λ _I is the target device failure rate, and λs is The predicted failure rate of the target device, t, represents the test time according to the number of samples.

In addition, the cost-model optimal design model (C _T ) may be determined by the following general formula (5).

[General formula 5]

In general formula 5, l _c is the labor cost per hour, t is the test time according to the number of samples, m _c is the manufacturing cost per electronic device, χ _β ² (2(c+1)) is χ with (c+1) degrees of freedom ² The 100(β)% percentile of the distribution, λs, represents the predicted failure rate of the target device.

In addition, the predicted failure rate (λs) of the target device may be determined by the following general formula (6).

[General formula 6]

In Formula 6, λs represents the failure rate per million operating hours for the target equipment, and λ _Pj represents the j-th target part failure rate.

In addition, the j-th target part failure rate (λ _Pj ) may be determined by the following general formula (7).

[General formula 7]

In Formula 7, λ _P is the failure rate per million operating hours _{for the target part, λ b} is the basic failure rate for the target part, and π _i represents the n load factors applied to the target part.

In addition, the step of calculating the number of samples (n) and the test time (t) according to the number of samples to minimize the cost-model optimal design model (C _{T ) is the following general formula 8 representing the lot acceptance rate for the target device} , and the general formula 9 representing the lot acceptance rate based on the target device failure rate considering the consumer risk.

[General formula 8]

[General formula 9]

In Formula 8 or Formula 9, c is the number of failures allowed, λ is the failure rate, T is the total test time, β is the consumer risk, and λ _I is the failure rate of the target device.

In addition, in the step of calculating the number of samples (n) and the test time (t) according to the number of samples to minimize the cost-model optimal design model (C _{T ),}

The number of samples (n) is calculated from General Expressions 10 and 11, which are converted to a chi-square distribution based on the Poisson distribution below,

If the number of failed samples among the number of samples calculated after the test (n) is equal to or smaller than the number of samples that are allowed to fail (c), the method may include determining a pass.

[General formula 10]

[General formula 11]

In Formula 10 or Formula 11, χ _β ² (2(c+1)) is ^{the 100(β)% percentile of the χ 2} distribution with c+1 degrees of freedom, c is the number of fault tolerances, and λ _I is the target device. The failure rate, t, represents the test time according to the number of samples.

According to another aspect of the present invention,

collecting weapon system-applied electronic equipment device information; calculating the target equipment failure rate based on the component load analysis method; calculating a total sampling plan test time for each number of allowable failures based on consumer risk determined according to the target equipment situation; And a sampling plan cost-effectiveness optimization result selection step according to the number of samples and test time is provided.

According to another aspect of the present invention,

Electronic equipment component configuration information, basic failure rate (λ _b ) for target part, factor (π _i ) information for target part, fault tolerance (c), consumer risk (β) information, hourly labor cost (l _c ) information, and an input unit for inputting manufacturing cost (m _{c ) information per one electronic device, respectively;} and the number of samples (n) such that the cost-model optimal design model (C _T ) is minimized based on the cost-model optimal design profile sampling test time labor cost (C _t ), the sampling test required manufacturing cost (C _{m ), and} Provided is an optimal design device for reliability sampling cost-effectiveness, including a calculator for calculating the test time t according to the number of samples.

In addition, cost-model cost based on optimal design model (C _T ), sampling test time labor cost (C _t ), sampling test required manufacturing cost (C _m ), number of samples (n), and test time (t) according to the number of samples - A profile generation unit that generates a model optimal design profile; and a display unit for displaying the generated profile.

As described above, the optimal design method and apparatus for cost-effectiveness of the environmental load screening test related to the embodiment of the present invention have the following effects.

Based on the failure rate calculated based on the failure rate prediction model of the electronic equipment applied to the weapon system, the correlation between the number of sampling samples and the cost caused by the test time variable according to the number of samples is optimized, and the reliability sampling cost-effectiveness is also optimally designed is possible

1 is a flowchart illustrating an algorithm for designing an optimal design method for reliability sampling cost versus effectiveness.
2 is a graph in which a cost model for cost-effective optimal design based on DC-DC converter information is applied for each allowable number of failures.

Since the present application may have various changes and may have various embodiments, specific embodiments will be illustrated and described in the drawings.

However, this is not intended to limit the present application to specific embodiments, and it should be understood to include all modifications, equivalents, and substitutes included in the spirit and scope of the present application. In describing the present application, if it is determined that a detailed description of a related known technology may obscure the gist of the present application, the detailed description thereof will be omitted.

Terms such as first, second, etc. may be used to describe various elements, but the elements should not be limited by the terms. The terms are used only for the purpose of distinguishing one component from another.

The terms used in the present application are used only to describe specific embodiments, and are not intended to limit the present application. The singular expression includes the plural expression unless the context clearly dictates otherwise.

In the present application, terms such as "comprises" or "have" are intended to designate that a feature, number, step, operation, component, part, or a combination thereof described in the specification exists, but one or more other features It should be understood that this does not preclude the existence or addition of numbers, steps, operations, components, parts, or combinations thereof.

Accordingly, the configuration shown in the embodiment described in the present specification is only the most preferred embodiment of the present application and does not represent all the technical spirit of the present application, so various equivalents that can be substituted for them at the time of the present application and variations.

In addition, it should be understood that the accompanying drawings in the present application are enlarged or reduced for convenience of description.

Hereinafter, an optimal design method and apparatus for reliability sampling cost-effectiveness according to an embodiment of the present invention will be described in detail with reference to the accompanying drawings.

1 is a flowchart illustrating an algorithm for designing an optimal design method for reliability sampling cost versus effectiveness.

In this application, 'Part Stress Analysis (PSA)' among the failure rate prediction methods can be applied from the stage when the design is specified in order to predict reliability in more detail, and prediction is performed based on the actual designed shape. way to do it. Mainly, it is a method of estimating the overall electronic equipment failure rate based on the failure rate for each component considering detailed information on _{various load factors (π i} ) applied to the target part as the actual electronic equipment is operated and the electronic equipment component configuration information.

The form of the failure rate model for each part for the part load analysis is as shown in General Equation 7 below.

[General formula 7]

Here, λ _P is the failure rate per million operating hours _{for the target part, λ b} is the basic failure rate for the target part, and π _i is the n load factors applied to the target part.

Next, the target device (weapon system applied electronic equipment) predicted failure rate (λs) model form based on the failure rate model form for each component is as shown in General Equation 6 below.

[General formula 6]

Here, λs is the failure rate per million operating hours for the target equipment, and λ _Pj is the j-th target part failure rate.

On the other hand, the failure rate sampling plan cost by optimizing the correlation between the number of sampling samples and the cost caused by the test time variable according to the number of samples based on the failure rate calculated based on the failure rate prediction model of the electronic equipment applied to the weapon system of the present application In order to propose the effect optimal design method, the acceptance rate based on the failure rate of the target device considering the lot acceptance rate and consumer risk must be satisfied.

That is, referring to FIG. 1 , the step of calculating the number of samples (n) and the test time (t) according to the number of samples to minimize the _{cost-model optimal design model (C T ), which will be described later, is performed in the target device below.} General Equation 8, which represents the lot acceptance rate, and General Equation 9, which represents the lot acceptance rate based on the target device failure rate considering consumer risk.

[General formula 8]

[General formula 9]

c is the number of fault tolerance, λ is the failure rate, T is the total test time, β is the consumer risk, and λ _I is the failure rate of the target device.

Referring to FIG. 1 , based on the derived target device failure rate (λ _I ) and consumer risk (β), the total test time (T) based on the number of failures allowed (c) is calculated. Then, the value of the total test time (T) and the number of samples (n) are derived through the following general formulas 10 and 11 by converting to a Chi-squared distribution based on the Poisson distribution. can do.

[General formula 10]

[General formula 11]

Here, χ _β ² (2(c+1)) is ^{the 100(β)% percentile of the χ 2} distribution with c+1 degrees of freedom, c is the number of fault tolerances, λ _I is the failure rate of the target device, and t is the number of samples. The test time is indicated.

In the step of calculating the number of samples (n) and the test time (t) according to the number of samples to minimize the cost-model optimal design model (C _{T ), which will be described later, it is converted into a chi-square distribution based on the Poisson distribution} If the number of samples (n) calculated from General Formulas 10 and 11 is equal to or smaller than the number of faulty samples among the number of samples (n) calculated after the test, it is judged as pass.

Then, the cost-model optimal design model (C _T ) is calculated by adding the hourly labor cost (l _c ) information and the manufacturing cost per electronic equipment (m _{c ) information.}

The cost-model optimal design model (C _T ) is calculated based on the sampling test time labor cost (C _t ) and the sampling test required manufacturing cost (C _m ), and the sample that minimizes the cost-model optimal design model (C _{T )} Calculate the test time (t) according to the number (n) and the number of samples.

Cost-model The optimal design model (C _T ) is determined as the minimum value of the sum of the sampling test time labor cost (C _t ) and the sampling test cost manufacturing cost (C _m ), as in General Formula 1 below.

[General formula 1]

Specifically, the sampling test time labor cost (C _t ) is determined by the following general formula (2).

[General formula 2]

Here, l _c is the labor cost per hour, and t is the test time according to the number of samples.

Specifically, the manufacturing cost (C _m ) required for the sampling test is determined by the following general formula (3).

[General Formula 3]

Here, m _c is the manufacturing cost per one electronic device, and n is the number of samples.

The number of samples (n) is determined by the following general formula (4).

[General formula 4]

where χ _β ² (2(c+1)) is ^{the 100(β)% percentile of the χ 2} distribution with c+1 degrees of freedom, c is the number of fault tolerances, λ _I is the target device failure rate, and λs is the target device prediction The failure rate, t, represents the test time according to the number of samples.

That is, finally, the general formulas 1 to 4 are summarized, _{and the cost-model optimal design model (C T} ) is expressed by applying the weapon system-applied electronic equipment predicted failure rate (λs) to the _{target device failure rate (λ I ).} Same as 5.

[General formula 5]

where l _c is the labor cost per hour, t is the test time according to the number of samples, m _c is the manufacturing cost per unit of electronic equipment, and χ _β ² (2(c+1)) is the distribution ^{of χ 2 with (c+1) degrees of freedom.} The 100(β)% percentile, λs, represents the predicted failure rate of the target device.

If the cost-model optimal design model (C _T ) derived according to Formula 5 is the minimum value, the reliability sampling cost-effectiveness is also selected as the optimal design value (C _T ), and the number of samples (n) and the number of samples at this time is Calculate the test time (t) according to

On the other hand, according to one aspect of the present application,

collecting weapon system-applied electronic equipment device information;

calculating the target equipment failure rate based on the component load analysis method;

calculating a total sampling plan test time for each number of allowable failures based on consumer risk determined according to the target equipment situation; and

It is possible to provide an optimal design method for reliability sampling cost-effectiveness, including a step of selecting a cost-effectiveness optimization result of a sampling plan according to the number of samples and test time.

In one example, an example of applying a weapon system-applied electronic equipment DC-DC Converter to the reliability sampling cost-effectiveness optimal design method is as follows.

1. Step of collecting information on the electronic equipment (DC-DC Converter) applied to the weapon system

physical properties size 61×59×13mm weight 130g electrical characteristics pressure voltage 18~36V dc output voltage 5.2V dc electric current 9.6A temperature characteristics operating temperature -55~100℃ storage temperature -55~125℃

As shown in Table 1 above, physical, electrical, or temperature information was collected for device information of a weapon system-applied electronic equipment (DC-DC converter).

2. Calculating the target equipment failure rate based on the component load analysis method

failure rate analysis classification Kinds Quantity DC-DC Converter
Applicable parts
configuration information resistance 31 51 inductor 7 7 capacitor 23 46 semiconductor 13 23 integrated circuit 4 4 etc 2 2 ※ Failure rate calculation result based on component load analysis method (temperature condition: 85℃): 31.543186 X 10 ^-6

The classification, type, and quantity of parts applied to the DC-DC Converter for performing part load analysis are shown in Table 2 above, and the result of calculating the failure rate based on the part load analysis method (temperature condition: 85℃) is calculated as ^{31.543186 X 10 -6} became

3. Calculating the total sampling plan test time by number of permissible failures based on consumer risk determined according to the target equipment situation

consumer risk Applicable failure rate Allowable number of failures total test time c=0 29048.77 hr c=1 64112.52 hr c=2 98448.48 hr c=3 132366.55 hr c=4 166014.24 hr c=5 199469.99 hr c=6 232780.77 hr c=7 265977.2 hr c=8 299080.51 hr c=9 332106.09 hr c=10 365065.55 hr

Calculation of total sampling plan test time for each allowable number of failures in the case where the consumer risk is determined to be 60% for the DC-DC converter. The component load analysis results are shown in Table 3 above.

4. Sampling plan cost-effectiveness optimization result selection stage according to the number of samples and test time

consumer
danger apply
failure rate permit
number of failures sample water test time optimal cost 60% 31.543186 X 10 ^-6 c=0 58 EA 501 hr ￦ 64,081,117 c=1 87 EA 737 hr ￦ 95,180,350 c=2 110 EA 895 hr ￦ 117,951,415 c=3 125 EA 1,059 hours ￦ 136,759,346 c=4 140 EA 1,186 hours ￦ 153,165,274 c=5 155 EA 1,287 hr ￦ 167,883,308 c=6 157 EA 1,394 hours ￦ 181,358,613 c=7 179 EA 1,486 hr ￦ 193,860,133 c=8 188 EA 1,591 hr ￦ 205,573,357 c=9 199 EA 1,669 hr ￦ 216,621,930 c=10 209 EA 1,747 hours ￦ 227,126,422 ※ Hourly labor cost: ￦64,919 won
※ Manufacturing cost: ￦ 544,081 won (calculated based on material cost, labor cost, expenses, general management cost)

Based on the DC-DC converter information, the cost-effective optimal cost for each allowable number of failures is shown in Table 4 above. When the number of allowable failures is 0, the sampling plan cost was the lowest at 64,081,117 won (t=501hr, n=58). 2 is a graph in which a cost model for cost-effective optimal design based on DC-DC converter information is applied for each allowable number of failures.

Referring to the graph on the right, which is an enlarged graph on the left of FIG. 2 , it can be seen that _{C T is the minimum when t=501hr.}

According to another aspect of the present application, there is provided an apparatus for designing an optimal reliability sampling cost-effectiveness.

The reliability sampling cost-effectiveness optimal design device includes electronic equipment component configuration information, basic failure rate (λ _b ) for target parts, factor (π _i ) information for target parts, allowable number of failures (c), consumer risk ( β) may include an input unit for inputting information, labor cost per hour (l _c ) information, and manufacturing cost (m _{c ) information per one electronic device, respectively.}

In addition, the reliability sampling cost-effectiveness optimal design device is based on the cost-model optimal design profile sampling test time labor cost (C _t ), sampling test required manufacturing cost (C _m ),

The cost-model optimal design model (C _T ) may include a calculation unit for calculating the number of samples (n) and a test time (t) according to the number of samples to be minimized.

Cost-based on the cost-model optimal design model (C _T ), sampling test time labor cost (C _t ), sampling test required manufacturing cost (C _m ), number of samples (n), and test time (t) according to the number of samples- a profile generator for generating a model optimal design profile; and a display unit for displaying the generated profile, providing an optimal design device for reliability sampling cost-effectiveness.

The preferred embodiments of the present invention described above are disclosed for the purpose of illustration, and various modifications, changes, and additions may be made by those skilled in the art having ordinary knowledge of the present invention within the spirit and scope of the present invention, and such modifications, changes and additions shall be considered to fall within the scope of the following claims.

Claims (13)

Based on sampling test time labor cost (C _t ), sampling test cost manufacturing cost (C _m ),
Comprising the step of calculating the number of samples (n) and the test time (t) according to the number of samples such that the cost-model optimal design model (C _{T ) is minimized,}
The cost-model optimal design model (C _T ) is determined by the following general formula (1),
The sampling test time labor cost (C _t ) is determined by the following general formula 2,
Sampling test required manufacturing cost (C _m ) is determined by the following general formula 3,
The number of samples (n) is determined by the following general formula (4), an optimal design method for reliability sampling cost-effectiveness.:
[General formula 1]

[General Formula 2]

[General Formula 3]

[General formula 4]

In general formula 2, l _c is the labor cost per hour, t is the test time according to the number of samples,
In general formula 3, m _c represents the manufacturing cost per one electronic device, n represents the number of samples,
In Formula 4, χ _β ² (2(c+1)) is ^{the 100(β)% percentile of the χ 2} distribution with c+1 degrees of freedom, c is the number of fault tolerances, λ _I is the target device failure rate, and λs is The predicted failure rate of the target device, t, represents the test time according to the number of samples.
delete delete delete delete The method of claim 1,
The cost-model optimal design model (C _T ) is the optimal design method for reliability sampling cost-effectiveness, which is determined by the following general formula (5):
[General formula 5]

In general formula 5, l _c is the labor cost per hour, t is the test time according to the number of samples, m _c is the manufacturing cost per electronic device, χ _β ² (2(c+1)) is χ with (c+1) degrees of freedom ² The 100(β)% percentile of the distribution, λs, represents the predicted failure rate of the target device.
7. The method of claim 6,
The target device predicted failure rate (λs) is determined by the following general formula (6), reliability sampling cost-effectiveness optimal design method:
[General formula 6]

In Formula 6, λs represents the failure rate per million operating hours for the target equipment, and λ _Pj represents the j-th target part failure rate.
8. The method of claim 7,
The j-th target part failure rate (λ _Pj ) is determined by the following general formula 7, the optimal design method for reliability sampling cost effectiveness:
[General formula 7]

In Formula 7, λ _P is the failure rate per million operating hours _{for the target part, λ b} is the basic failure rate for the target part, and π _i represents the n load factors applied to the target part.
The method of claim 1,
The step of calculating the number of samples (n) and the test time (t) according to the number of samples such that the cost-model optimal design model (C _{T ) is minimized is,} And, including the general formula 9 representing the lot acceptance rate based on the target device failure rate considering consumer risk, the optimal design method for reliability sampling cost effectiveness.
[General formula 8]

[General formula 9]

In Formula 8 or Formula 9, c is the number of failures allowed, λ is the failure rate, T is the total test time, β is the consumer risk, and λ _I is the failure rate of the target device.
The method of claim 1,
In the step of calculating the number of samples (n) and the test time (t) according to the number of samples to minimize the cost-model optimal design model (C _{T ),}
The number of samples (n) is calculated from formulas 10 and 11, which are converted to a chi-square distribution based on the Poisson distribution below,
An optimal design method for reliability sampling cost-effectiveness, including determining that the number of failed samples among the number of samples (n) calculated after the test is equal to or smaller than the number of failures (c).
[General formula 10]

[General formula 11]

In Formula 10 or Formula 11, χ _β ² (2(c+1)) is ^{the 100(β)% percentile of the χ 2} distribution with c+1 degrees of freedom, c is the number of fault tolerances, and λ _I is the target device. The failure rate, t, represents the test time according to the number of samples.
delete In the reliability sampling cost-effectiveness optimal design apparatus using the reliability sampling cost-effectiveness optimal design method of claim 1,
Electronic equipment component configuration information, basic failure rate (λ _b ) for target part, factor (π _i ) information for target part, fault tolerance (c), consumer risk (β) information, hourly labor cost (l _c ) information, and an input unit for inputting manufacturing cost (m _{c ) information per one electronic device, respectively;} and
Based on the cost-model optimal design profile sampling test time labor cost (C _t ), sampling test cost manufacturing cost (C _m ),
Cost-model optimal design model (C _T ), including a calculation unit for calculating the number of samples (n) and a test time (t) according to the number of samples to minimize the reliability sampling cost effectiveness design apparatus.
13. The method of claim 12,
Cost-model Cost-model based on optimal design model (C _T ), sampling test time labor cost (C _t ), sampling test required manufacturing cost (C _m ), number of samples (n) and test time (t) according to the number of samples a profile generator for generating an optimal design profile; and
An optimal design device for reliability sampling cost-effectiveness, including a display unit for displaying the generated profile.

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