Reliability Analysis of Life Testing --（加速）寿命试验可靠性分析hnthinkertest.com/uploads/files/201811/1541031923931597.pdf · 2018-11-01 · reliability analyses have

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Reliability Analysis of（Accelerated）Life Testing--（加速）寿命试验可靠性分析

Design For Six Sigma六西格玛设计系列课程

研究院-RAMS工程中心: 陈慧军

2018年10月26日


执着创新托起思维的明天目录

• What’s Life Test? ………………………………… P3

• Where Are We in DFR? …………….…………….. P8

• Reliability Functions………………………………. P11

• How to Analysis Life Test Data?................................ P11

• What’s ALT?.............................................................. P43

• Testing Sample of ALT……………………………. P52


执着创新托起思维的明天Foreword引言：讲在专业之前

0

10

20

30

40

50

0-4岁 10-14岁 20-24岁 30-34岁 40-44岁 50-54岁 60-64岁 70-74岁 80-84岁 90+

死亡率‰/可靠性

时间/年龄

人口死亡率与年龄曲线图(1988-1999)

--据中国人寿报告

婴幼期青壮期老年期

MTBF=1佰年？50-60岁、矿工 1仟年?35-35岁、码农 1萬年？20-40岁、家庭主妇

MTTR=4小时?

妇幼保健院安养院/社区学校/家庭/工作

PMT/B-I MTBF/RQT/ORT/ALT MTTF/MTTR


执着创新托起思维的明天Foreword引言：讲在专业之前

A Paper Clip’s Life…

Key point

Bend

0°----->45/60°

End life in your hand!

What’s it mean?


执着创新托起思维的明天

The table Right:

Published by the Reliability Analysis

Center (RAC), is based on a survey of

reliability tasks.

右图是美国可靠度分析中心发布的常用的可靠度活动内容。

Reliability Tasks：可靠度活动



Life Testing寿命试验？

What’s Life to a product:

产品生存时间-产品从投运至失效所经历的总时间,寿命是产

品最主要的一个可靠性特征量。

What’s Life Testing:

研究产品寿命特征的方法,在制程比较稳定的条件下,剔除早

期失效产品后进行的试验,通过试验了解产品寿命分布的统

计规律(失效率、平均寿命、失效模式等), 其寿命分布依产

品而别有多种模型。



Life Testing寿命试验？

寿

命

试

验

按产品状态分类

按施加应力水平分类

按试验目的分类

按试验场地分类

工作寿命试验

贮存寿命试验

加速应力寿命试验

正常应力寿命试验

寿命测定试验

寿命验证试验

厂内(实验室)寿命试验

外场使用寿命试验

恒定应力加速寿命试验

步进应力加速寿命试验

序进应力加速寿命试验

定型阶段寿命试验

验收阶段寿命试验

《可靠性工程师手册》中国人民大学出版社李良巧



Reliability Challenge可靠度挑战

• Based on the six devices tested at 200 C. What is

the probability that a product will survive one year

of service given that 2080 hours = 1 year of life? 以6个在200°C环境中测试的元件寿命举例。估算在使用1年

（2080小时）后的正常工作概率。



Reliability Challenge学完课程后要学会解决的问题？

如何从累积分布寿命曲线上找到B5 & B10 寿命？



Objectives of Life Testing寿命试验的意义

No matter how advanced or sophisticated the design and

reliability analyses have been, there is no substitute for

hardware testing.无论设计多么成熟或先进，可靠性分析结果多么好，

硬件验证测试都不可缺少。

Reliability tests are performed with one or both of the following

objectives: 执行可靠度试验有以下两个方面的目的

• to uncover latent modes of failure揭示潜在失效模式,以确定影响

产品寿命的根本原因和可能采取的纠正措施

• to measure or verify the level of reliability actually achieved

量测或验证实际的可靠度状况（使用寿命、贮存寿命）达到要求



Where Are We in DFR Process?处于可靠度设计的哪个阶段？

寿命试验适用于产品设计定型阶段(&试用阶段和使用阶段)


执着创新托起思维的明天Verify/Validate Reliability Requirements

重要器件(E-cap, Fan, Bat)、系统的可靠性鉴定：建议先进行寿命试验,收集数据进行分析。



Reliability Measures可靠度度量指标

Reliability (R(t)): The reliability of a product over a specified period of time 。是指产品在规定条件下规定时间内完成规定功能的能力。

ex.: R(2000 hrs)=0.85

Mean-Time-Between Failure (MTBF): Mean time between failures for

repairable systems. /MTBF，平均故障间隔时间（可维修系统）。

ex.: MTBF=200 hrs

Mean-Time-to-Failure (MTTF): Mean time to failures for non-repairable

systems./MTTF, 平均故障时间（不可维修系统）。

ex.: MTTF=200 hrs

Percentiles of Life (Bx Life): Defines x percentile of the cumulative failure

rate. It means life of a product at which x % failed。某百分点故障率时的累计时间。

ex.: B10, B5 life



• Probability Density Function 概率密度函数

Plot of “amount "of failures vs. time (or cycles, miles etc.)

某时间段（周期、里程）内的失效数量。

• Cumulative Distribution Function 累积分布函数

For any given time what is the probability that the part is not working

到任一时间点（0~t）产品失效的概率。

• Reliability Function 可靠性函数

For any given time what is the probability that the part is still working

任一时间点后（t~∞）产品正常工作的概率。

• Hazard Function 危险函数

Instantaneous failure rate –This is the failure rate that is represented in the bathtub curve!

瞬时失效率-描述浴缸曲线…

Types of Reliability Functions可靠度函数类型



Reliability Function 可靠性函数

Time

f(t)

R(t)F(t)

f(t)

F(t), R(t), f(t) Relation

F(t)+R(t)=1

)(/)()( tRtfthtionHazardFunc



Hazard Function、Bathtub、MTBF、Useful Life危险函数、浴缸曲线、MTBF和服务期限

Useful Life服务期限MTBF

平均故障间隔时间



Procedure for Life Testing寿命试验程序

Developing a model of our life test data includes the

following steps: 要进行寿命数据分析，遵从以下步骤

1) Prepare test plan准备试验计划

2) Obtain life test data 收集试验数据

3) Fit the data to a probability distribution数据拟合分析

4) Use statistical functions to express reliability

用统计函数表达可靠度

5) Make predictions about the design’s reliability

对可靠度预估



1. Prepare Test Plan准备试验计划

The enormous cost of Reliability testing makes it crucial to do careful test

planning.由于可靠度试验花费较多，需要谨慎进行试验计划。

Test planning seeks to determine the sample size and testing time needed to

demonstrate that you have met specified reliability requirements.根据要验证的可靠度指标确定试验样品数量及测试时间。

A test plan include:

The number of units you need to test

试验样机需求数量（需要综合考虑试验时间与成本支出后确定）。

A stopping rule –the amount of time you must test each unit or the number

of failures that must occur

制定停止试验标准：每台机达到需要测试的时间或失效数达到某值时停止。

Success criterion –the number of failures allowed while the test still passes

(for example, every unit runs for the specified amount of time and there are

no failures) Pass标准，在测试时间内失效数量在标准以下或无失效



1. Prepare Test Plan准备试验计划

Minitab covers three kinds of test plans:

Minitab包含三种试验计划

Demonstration Test Plans

实证试验计划

Estimation Test Plans

预估试验计划

Accelerated Test Plans

加速实验计划



Demonstration Test Plans实证试验计划

• Use demonstration test plans to determine the sample size or

testing time needed to demonstrate, with some level of

confidence, that the reliability exceeds a given requirement.

在一定的置信水平注释1下，使用实证试验计划注释2确定试验样品数

量和时间，验证可靠度达到规格要求。

• In a demonstration test, you verify that only a certain

number of failures occur in a set of amount of test time .

设定出允许的最大失效机数量n（需要先定义清楚失效）。实证试

验计划，在设定的试验时间内，验证失效数少于一定数量n 。


执着创新托起思维的明天Demonstration Test Plans (continued)



To create a test plan, you need information about the data you

expect to collect. You can obtain planning information from:

制定一个试验计划，先要明确需要收集的数据，再结合以下内容制定试验计划：

• Design specifications

设计规格书

• Expert opinions

专家意见

• Prior studies or small pilot studies

预先的研究或小批样机的试验数据分析做支撑。

Characteristics of a Demonstration Test Plan (continued)



Example: Creating a Demonstration Test Plan举例：创建一个实证试验计划

The reliability goal for a turbine engine combustor is a 1

percentile of at least 2000 cycles. The number of cycles to

failure tends to follow a Weibull distribution with shape = 3.

You can accumulate up to 8000 test cycles on each ombustor.

You must determine the number of combustors needed to

demonstrate the reliability goal using a 1-failure test plan at

95% confidence level?

一个涡轮发动机的可靠度目标为：1%, ≥2000cycles. 转数-失

效分布关系符合Weibull分布，形状参数为3.

制定试验计划: 每个涡轮发动机进行8000cycles的测试，允许1个失效，置信水平为95%, 确定需要试验样品数？



Example: Creating a Demonstration Test Plan举例：创建一个实证试验计划

在允许1个失效的前提下，需要8台涡轮发动机，各试验8000小时。

才可以证明在95.2%的置信水平下，运行2000小时，失效率小于1%。


执着创新托起思维的明天Class Exercise: 课堂练习

How many power module must be tested on a 1440 hour test if zero

failures are allowed to demonstrate a MTTF value of 43800 hrs

using a confidence level of 90%?

Assume exponential distribution.

练习：

CF: 90%, MTTF=43800hrs, 每台测试时间=1440hrs，0 失效.

假设为指数分布，求要多少台电源插件？


执着创新托起思维的明天Class Exercise:课堂练习


执着创新托起思维的明天2. Obtain life test data收集寿命试验数据

• 未删失数据

• 删失数据（censored data）

• 右删失数据

• 区间删失数据

• 左删失数据

只收集和分析未删失和右删失的数据。



3. Probability Distributions Commonly Used to Fit Data 常用拟合寿命模型

• Exponential指数分布

Constant failure rate恒定失效率

• Normal正态分布

Increasing failure rate渐增失效率

• Log-Normal对数正态分布increasing, decreasing asymptotically to zero渐增，在渐进线处降到0

• Wei bull威布尔分布• Can be increasing, decreasing or constant failure rate增、降、稳定

• Monotonic单调的



Exponential Distribution –Definition指数分布-定义

• This distribution was historically the first distribution used

as a model of time-to-failure distribution and it is still one of

the most widely used ones in parametric modeling.指数模型

是历史上最早的TOF失效分布模型，至今仍最常用模型之一。

• It is often used to describe failure process of electronic

components.常用在描述电子器件失效推移

• The exponential distribution is also widely used for

modeling failure phenomena at the system level since the

overall effect of the random occurrences of individual

components is modeled as a constant failure rate processes.因为假设零件的失效是随机的，并且失效率是恒定的，在此情况下，整机的失效状况也常用指数分布来分析。


执着创新托起思维的明天Exponential Distributions –Properties

• Probability Density Function, f(t)概率密度

Where λis the failure rate

• Cumulative Distribution Function, F(t) 累积分布

• Reliability Function, R(t)可靠性

tetf )(

tetF 1)(

tetFtR )(1)(



Exponential Distribution指数分布



Weibull Distribution威布尔分布

• The Weibull distribution is often used for product life, because it models

either increasing or decreasing failure rates easily. It is also used as the

distribution for product properties such as strength (electrical or

mechanical), elongation, resistance, etc., in accelerated tests.

• It is used to describe the life of roller bearings, electronic components,

ceramics capacitors, and dielectrics in accelerated tests.它被用来描述在加速试验中滚珠轴承、电子零件、陶瓷电容器、电绝缘介质的寿命。

• It is commonly used for practical applications because an appropriate choice

of its parameters allows one to use it to describe various physical

phenomena.如果参数选择适当，可以描述各种物理现象，因此它也经常被用于实际生活。

• It becomes Exponential distribution when its shape parameter is equal to 1

and it approximates to a Normal Distribution when its shape parameter is

around 3.5.当其形状参数=1时，它就变成指数分布；其形状参数=3.5时，近似于正态分布。




• Probability Density Function, f(t) 概率密度

where,

αis the characteristic life of a product.特征寿命

βis the shape parameter.形状参数

t is the elapsed time to failure.失效时间

/

1

)( tet

tf




• Cumulative Probability Density Function, F(t)

累积概率密度函数

• Reliability Function, R(t) 可靠度函数

)/(1)( tetF

)/()(1)( tetFtR




失效率：可增加、可降低或稳定。



How to Fit a Distribution to a Given Life data?如何对给定的寿命数据进行拟合？


执着创新托起思维的明天Analyze “Goodness of Fit” Results from Minitab



Exercise: Parametric Analysis of Time-to-Failure Data数据分析练习

Time-to-failure data for 10 electrical

components are given in the Table.

Use MINITAB to:

• Enter the data in ‘Minitab’

• Fit the best distribution?

Sample Time-to-Failure (hrs)

1 200

2 370

3 500

4 620

5 730

6 840

7 950

8 1050

9 1160

10 1400



4. Use Statistical Functions to Express Reliability使用统计函数来描述可靠度。

• Reliability can be calculated by using either F(t) or R(t) of the best fitted distribution to the life data。可靠度可以用对寿命数据拟合最优的函数F(t) or R(t)来计算。

• F(t), R(t) can be generated and plotted in Minitab using “Distribution Overview Plot”。可以用Mintab软件里面的“Distribution Overview Plot（分布概要图）”来产生F(t), R(t) 图。

• F(t), R(t) is a graphical representation of the reliability of the Life data F(t), R(t)。是用图像法来表示可靠度状况（寿命数据）。

• Plots also indicate some statistics like distribution Parameters, descriptive statistics and goodness of fit measures。那些图能够显示出统计分布参数、描述统计和拟合优度参数。



Example: Parametric Analysis of Time-to-Failure Data 举例：TOF数据参数分析



For the best fitted distribution do the

following:

右表是10个电子器件的TOF数据，请拟合其寿命/失效率分布。

在白板上画…?

• Generate and Plot f (t)=?

• Generate and Plot F (t)=?

• Generate and Plot R (t) =?


1 200

2 370

3 500

4 620

5 730

6 840

7 950

8 1050

9 1160

10 1400数据拟合结果为最符合3参威布尔分布。



Solution: Parametric Analysis of Time-to-Failure Data 答案：TOF数据参数分析

•



5. Make Predictions About the Design’s Reliability预计设计可靠度

Can be done in two ways:两条路来实现。

1. Use of Reliability Function of the best fitted

distribution

使用最优拟合函数来计算。

2. Use of “Estimate” option of the Parametric

Distribution Analysis in Minitab

使用minitab工具里面的“预计”选项来进行，下面举一例。



Example: Parametric Analysis of Time-to-Failure Data 举例：TOF数据参数分析



For the best fitted distribution do the

followings using MINITAB :

• What is the reliability at 1,000 hrs

of operation?

• What is the B5 and B10 life?


1 200

2 370

3 500

4 620

5 730

6 840

7 950

8 1050

9 1160

10 1400





Reliability Analysis of ALT Data加速寿命试验可靠度数据分析

What is ALT?

• Accelerated Life Test is defined as a design

verification method which involves increasing

operating or environmental stress levels to increase

the failure rate of a component when testing that

component to failure under normal operating stress is

not practical. ALT是通过增加包括操作和环境等应力的方法去激

发失效（常态测试下失效率较低）的设计验证方法。

• Accelerated Life Test allows designers to make

predictions about the life of a product by developing a

model that correlates reliability under accelerated

conditions to reliability under normal conditions. 根据加

速寿命试验结果与加速模型（失效率与加速系数），设计者可以预计产品的可靠度。



Accelerated Life Test: Benefits加速寿命试验优点

• Better understanding of the effects of various stresses on

product life 更好了解产品寿命周期内的各种应力影响

• Provides an estimation of life in relation to stress(es)

induced for decision making on design通过应力关系得到预估

寿命，为产品设计决策参考

• Improve product reliability through identification and

elimination of design and process deficiencies通过发现和改

善设计问题等提高产品可靠性

• Shorter Design Verification & Production Verification test

times which ends in less time, resource and cost in product

development. 缩短开发验证周期，减少资源成本支出等



Understanding ALT如何理解加速寿命试验？

• In typical life data analysis one determines, through the use of statistical distributions, a life distribution that describes the times-to-failure of a product. Statistically speaking, one wishes to determine the use level probability density function, or pdf, of the times-to-failure. 寿命数据分析结果从统计学上反映产品真实的可靠度状况。

• Once the pdf is obtained, all other desired reliability results can be easily determined including but not limited to:一旦获得失效概率，可得出但不限于以下其它可靠度结果

• % failing under warranty 质量成本

• Risk assessment 风险评估

• Design Comparison 设计比较

• Wear-out period 损耗期


执着创新托起思维的明天Understanding ALT 如何理解ALT？

• In accelerated life data analysis, however, we face the

challenge of determining this use level pdf from accelerated

life test data rather than from times-to-failure data obtained

under use conditions as shown in Figure 1.在加速寿命数据的

分析中，我们面临着加速条件与正常使用条件下失效几率不一致的

挑战。

Figure 1.pdf@ different stress levels



Accelerated Life Test Planning加速寿命试验计划

Planning for a good ALT must include the following steps:

一个好的ALT计划必须包含以下几个步骤：

1.Define objective and scope of the test

定义实验目标与范围

2.Collect required information about the product

收集产品必需的信息

3.Identify the stress(es) 鉴别应力（应用环境会遭受到的应力）

4.Determine level of stress(es) 确定试验应力

5.Conduct the ALT test and analyze the ALT data.

执行试验、收集数据和进行分析



Failure Mechanism Failure Mechanism Failure Mechanism & Acceleration Stress失效机制和加速应力

Failure Mechanism Possible Acceleration Stresses 加速应力

Corrosion

腐蚀1. Temperature 温度2. Humidity 湿度3. Voltage 电压

Creep

蠕变1. Mechanical Stress 机械应力2. Temperature 温度

Diffusion

扩散1. Temperature 温度2. Temperature Gradient 温度梯度

Electro migration

电迁移1. Current Density 电流密度2. Temperature 温度3. Temperature Gradient 温度梯度

Fatigue

疲劳1. Frequency(usage rate) 频率（使用率）2. Cyclic Temperature Range 循环温度范围3. Cyclic mechanical stress/strain amplitude or range

Wear out

损耗1. Contact force 接触力2. Relative Sliding velocity 相对滑动速度3. Temperature 温度4. Lubrication 润滑



Identify the Stress识别应力



Determining a Life-Stress Relationship确定寿命应力关系

Common Life-Stress Models are:常用模型

Arrhenius Model 阿伦纽斯模型

Temperature-Humidity Model温-湿度模型

Eyring Model 循环模型

Inverse Power Law Model 逆幂模型

Temperature Non-Thermal Model温度非热能模型

Table in next slide provides listing of available Life-Stress

Modules in terms of description and application.下页表单提

供几个常用的应力模型清单。


执着创新托起思维的明天Life-stress Model寿命-应力模型


执着创新托起思维的明天Example 1: LKJ15S Power Module ALT Plan


执着创新托起思维的明天Reference: 参考文献免费大放送

1. GBT 29309-2012 电工电子产品加速应力试验规程高加速寿命试验导则

2. GB-T34986-2017 产品加速试验方法

3. TB/T-2468-2018 铁路信号产品可靠性要求评定方法


执着创新托起思维的明天Q&A

• Any advice or comments, please feedback…

任何意见或建议，请不吝反馈……



eliability vailability aintainability afety

ife

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Reliability Analysis of Life Testing --（加速）寿命试验可靠性分析hnthinkertest.com/uploads/files/201811/1541031923931597.pdf · 2018-11-01 · reliability analyses have