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基于轮廓监控方法的质盞髋饧嗫匮芯?
Research on Warranty Claims Monitoring Based on Profile
Monitoring Methodology
一级学科：工商管理
研究方向：质量管理
作者姓名：宋丽莎
指导教师：何曙光教授
答辩日期2021年12月09日
答辩委员会姓名职称工作单位
主席李健教授天津理工大学
李勇建教授天津大学
张慧颖教授天津大学
委员
吴晓丹教授河北工业大学
张敏教授天津大学
天津大学管理与经济学部
二〇二一年十二月摘摘摘要要要
随着市场竞争的加剧，以汽车为代表的耐用品的质量和可靠性在市场竞争
中发挥着越来越重要的作用陀闷肪哂胁芳壑蹈摺⑹褂弥芷诔さ忍氐悖圃?
商需要为此类产品提供售后服务，即质保（Warranty）时J侵圃焐涛颜?
提供的与产品质量有关的售后盫ぺ质盕谀冢啡绻谡５氖褂锰跫?
下发生失效或故障，则制造商需要对产品进行免费维修或更换，由此导致的消
费者索赔称为质盞髋猓╓arranty claims）巳繁J鄢霾返闹柿亢涂煽啃裕?
制造商会在设计和制造过程中对产品进行严格的可靠性测试，受测试周期和成
本的限制，测试是不完备的，部分质量和可靠性问题会在用户使用过程中暴露，
从而给制造商造成经济和商誉的损失时K髋馐葜邪挪吩谠缙谑褂?
阶段质量和可靠性的有用信息，为产品质量和可靠性问题的早期预警提供了重
要的数据源。
统计过程控制（Statistical process control，SPC）是砈玫募嗫毓袒虿?
稳定性，检测可能出现的异常波动的有效工具。本研究将SPC方法应用于对质保
索赔数据的监控，及时发现产品设计制造缺陷和现场可靠性问题，实现对耐用品
质量和可靠性问题的早期预警氪砈PC的应用场景有所不同，质盞髋馐?
具有如下几个显著特点：1）索赔数受产品使用时间等因素的影响；2）索赔的发
生具有时序性；3）索赔数属于属性数据（Attribute data）。基于以上数据特征，
本文将质盞髋饧嗫匚侍庾煊ξ粜允莸穆掷嗫兀≒rofile monitoring）
问题，构建了基于轮廓监控方法的质盞髋饧嗫胤桨福⑼ü抡媸笛楹推笠凳?
际数据对所提出的监控方案进行了验证。
根据质盞髋馐莸奶卣鳎疚姆直鹛骄苛舜嬖诼掷谙喙兀╓ithin-profile
correlation）的质盞髋馐荨⒋嬖诼掷湎喙兀˙etween-profile correlation）的
质盞髋馐菀约岸时K髋馐莸募嗫匚侍狻＞咛灏ㄒ韵氯龇矫妫?
1）针对存在轮廓内相关的质盞髋馐莘直鹛岢隽擞糜诮锥蜪变点检测的改
进得分（Modified score）统计量和阶段II实时监控的经验似然比（Empirical like-
lihood ratio，ELR）控制图。采用广义估计方程（Generalized estimating equation，
GEE）方法对轮廓内相关建模，提高了变点检测的准确性和控制图的监控性能。
仿真实验和质盞髋馐道τ帽砻鳎贝嬖诼掷谙喙厥保疚乃岢霰涞慵觳?
方法和ELR控制图优于现有方法，不仅适用于存在轮廓内相关的轮廓，还适用于
I 天津大学博士学位论文
独立轮廓。此外，所提出的ELR控制图可以同时监控均值和相关性的变化。
2）针对存在轮廓间相关的质盞髋馐荩捎霉阋宥味嘞钍侥p投月掷?
关系建模，并采用学习效应膒涂袒掷湎喙匦裕岢隽擞糜诙源嬖诼掷湎?
关的质盞髋馐萁屑嗫氐木哂卸刂葡薜腅WMA控制图。仿真结果表明，
所提出的EWMA控制图具有较好的受控和失控性能詈螅ü抵时K髋?
实例应用进一步说明了所提出EWMA控制图的有效性。
3）针对二维质盞髋馐荩笨悸鞘褂檬奔浜托惺焕锍潭运髋馐挠跋欤?
此外，单一产品在质盕谀诜⑸髋獾拇问换崽啵诖耍疚难芯苛嗽诼?
廓内样本量比较小的情形，对于二维质盞髋馐莸陌氩问嗫匚侍狻１疚牟捎?
广义半参数膒投远时K髋馐萁＃⑻岢隽肆街钟糜诙云浣屑嗫氐?
具有动态控制限的监控方案：加权似然比（Weighted likelihood ratio，WLR）和
加权F（Weighted F，WF）控制图詈螅ü抡媸笛楹褪道τ闷拦篮脱橹?
了所提出监控方案的性能。
本研究对轮廓监控方法的发展及应用具有重要意义，为质盞髋馐菁嗫?
提供了新的技术支撑，并为后续故障诊断、过程能力提升、索赔欺诈检测等方面
的研究奠定基础保疚乃岢龅穆掷嗫胤椒ú唤隹梢杂τ糜谥时K髋饧?
控，还可以应用于其它类似的具有轮廓特征的过程或产品的监控。
关键词：质盞髋馐荩掷嗫兀粜允荩掷谙喙兀掷湎喙兀?
参数监控，统计过程控制
II ABSTRACT
With the intensified market competition,the quality and reliability of durable good-
s are playing a more and more important role in marketing.Durable goods often have
the characteristics of long service time and high prices.The manufacturers of durable
goods are required to provide warranties for products sold.Awarranty is a guarantee
provided by the manufacturer to the customers on the reliability of the products.Under
warranty,the manufacturer has obligation to repair or replace the failed products under
normal using conditions in the warranty period.To ensure the quality and reliability of
the products sold,manufacturers conduct strict reliability tests on the products during
the design and manufacturing process.The reliability tests are often incomplete since
this kind of test is time-consuming and very costly.The undetected design and man-
ufacturing defects may break out in the field and bring huge economic and goodwill
losses to the manufacturer.Warranty claims data contains useful information on prod-
uct quality and reliability in the early use stage and therefore is an important data source
for the early warning of quality and reliability problems.
Statistical process control (SPC)is a widely used tool for detecting anomalies in
processes.In this research,the SPCmethod is applied to monitor warranty claims for
detecting design and manufacturing defects and providing early warning about quali-
ty and reliability risks.The warranty claims data to be monitored have the following
characteristics:1)the number of claims is aected by factors such as the service time
of the product;2)the occurrence of claims is time-sequential;3)the number of claim-
s is attribute data.Based on the above data characteristics,this research transforms
the monitoring of warranty claims into the monitoring of profiles with attribute data
and designs several monitoring schemes based on the profile monitoring methodology.
Then,the proposed monitoring schemes are evaluated and verified through simulation
experiments and real enterprise data.
In view of the characteristics of warranty claims data,this research considers the
monitoring in three scenarios,i.e.,warranty claims data with within-profile correlation,
warranty claims data with between-profile correlation,and two-dimensional warranty
claims data.Specifically,this research includes the following three aspects.
Firstly,for warranty claims data with within-profile correlation,the modified score
III 天津大学博士学位论文
statistic for retrospective change-point detection and the empirical likelihood ratio (EL-
R)control chart for real-time monitoring are proposed respectively.The generalized es-
timating equation (GEE)method is used to model the within-profile correlation,which
improves the accuracy of the change-point detection and the monitoring performance of
the control chart.Simulation experiments and a real example of warranty claims show
that the proposed change-point detection method and the ELRcontrol chart outperform
the existing methods in the presence of within-profile correlation.They can be applied
not only to autocorrelated profiles but also to independent profiles.In addition,the ELR
chart can detect changes in the mean and the correlation simultaneously.
Secondly,for warranty claims data with between-profile correlation,the gener-
alized quadratic polynomial model is used to model the profile relationship,and the
learning-eect model is adopted to describe the between-profile correlation.Then,an
EWMAchart with dynamic control limits is proposed for monitoring warranty claims
data with between-profile correlation.Simulation results show that the proposed EW-
MAcontrol chart has a satisfactory performance in both in-control and out-of-control
states.Areal example of automobile warranty claims is analyzed to demonstrate the
eectiveness of the proposed EWMAcontrol chart.
Thirdly,for the two-dimensional warranty claims data,considering the eect of
service time and mileage on the number of claims and the small number of claims for
a single product during the warranty period,this research focuses on the semiparamet-
ric monitoring of the two-dimensional warranty claims data under small within-pro
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