第四十二篇 Divide and Conquer In Reliability Analyses

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Divide and Conquer In Reliability Analyses可靠性分析中的“分而治之”Gain understanding by looking at different population segments通过观察不同的客户细分而得出的结论
by NecipDoganaksoy, Gerald J. Hahn andWilliam Q. Meeker
作者：Necip Doganaksoy, Gerald J. Hahn， William Q. Meeker

All product is not created equal. Some units are more likely to fail in servicethan others. Thus, in reliability evaluations, you need to identifysubpopulations with different failure susceptibility. This is accomplishedthrough segmentation—a divide-and-conquer strategy that breaks down the productpopulation into meaningful subpopulations so you can conduct separate analyseson each and then act on the resulting information.
所有产品被制造出来的时候并不完全一致，从服务上来讲，一部分可能是客户不能够接受的，这样一来，在可靠性评估阶段，你就需要通过不同失效模式敏感性来区分子群体。通过这样的划分就完成了“分而治之”的战略规划，这样就把产品的客户群体划分为更有意义的子群体，我们也就能够根据不同的群体分别对产品进行分析，之后也能根据响应信息做出更有效的行动。
Segmentation (also known as data stratification) is one of the so-called sevenbasic quality tools.1 In thiscolumn, we describe and illustrate the use of segmentation for, principally,reliability applications.2细分（也就是数据分层法，即层别法）被称作是质量七工具中的一种，在本专栏，我们会对层别法的原则、可靠性的运用进行描叙并举例进行说明。
What creates subpopulations?什么创立了子群体？
In a specificproduct application, subpopulations result from differences in the manufactureand use of a product. Differences in reliability may, for example, be due tovariability in raw materials and components or differences in manufacturingprocessing conditions.
在特定的产品应用领域，制造工艺和产品用途的不同导致了子群体的产生。比如说，由于原材料和原件的多样性及生产加工状态的不同导致了可靠性的差异。
In a recent application, Yili Hong,William Q. Meeker and James D. McCalleysegmented data on a fleet of high-voltage power transformers according tomanufacturer and manufacturing period—first to model lifetime and then topredict the remaining life for the units in the fleet.3 In another application dealing with the predictionof warranty costs for an electronic product, the population was broken downinto component genealogy groups consisting of combinations of part numbers.在最近的应用中，YiliHong,William Q. Meeker and James D. McCalley把车上应用的高压变压器的相关数据按照制造商和生产时间的不同进行了划分，首先建立了产品寿命的模型，接着又预测了车上应用变压器部件的剩余寿命。另一个应用的案例是对某电子产品的保修成本成功进行预测，提供给不同客户群的产品按照元件的供应商进行了区分，元件的供应包括组立元件的各个组成部分。

Segmentation is especially appropriate when failures due to a particular defectoccur in only some production lots. In studying the cracking of the plasticcasing of a laptop computer, for example, segmentation revealed such failurestook place exclusively on units built during a one-month period at one of severalassembly plants. This led to further study, which revealed the wrong type ofscrew was used in assembly at this plant during this time period, and grease onthe screws led to chemical degradation of the plastic casing.当不良发生的原因只是某些产品的某些批次发生特定的不良时，细分就显得特别准确到位了。举例来说，在对便携式电脑的塑料外壳的开裂不良分析过程中，层别法细分过程中发现，这样的不良只是集中发生在某一个月的某几个组装工厂，于是再进行深入的调查，结果发现这些工厂在这一期间内，工人装配时用错了螺丝，而螺丝上的润滑油造成了塑料盒的化学降解。

Isolating the problem facilitated root cause identification and steps to ensurethe problem would not recur in future product. More immediately, it led toidentifying and, when needed, repairing previously built computers that werevulnerable to this failure.将这些问题分离出来有助于找出根本原因和确保在今后的产品中不会再发生同样的问题需要采取的步骤。更直接的来看，如果需要的话，这能够识别并预先在设计电脑的时候就发现可能发生问题的部位从而避免不良的发生。

Also, different units of a product population often experience different useenvironments. A problem may be accentuated or perhaps limited to occur at onlyextreme ambient conditions, such as severe heat or cold. Moreover, theperformance of a dishwasher may depend on the characteristics of the localwater supply. In such cases, you might focus immediate corrective action onproduct in the most vulnerable geographical regions; segmentation of the databy region will help identify the subpopulations that warrant special attention.同时，提供给不同客户的不同产品会在不同的环境中使用，一种问题可能只在某种极端条件下发生，比如说极冷或过热。比方说，洗碗机的工作状况可能会跟当地的供水状况相关，这种情况发生时，你就得迅速的关注一下该地区的所有客户以便做出正确的响应；数据的区域层别划分会帮助你识别那些需要特别关注的亚客户群。
Example: aircraft engine例：飞机引擎
The followingexample deals with a system that bleeds off air pressure from an aircraftengine to operate a compressor:
下面的例子是对飞机引擎释放气压驱动空气压缩机系统的分析结果：
Initial analysis. Lifetime data were available on bleed systems from 2,256engines in military aircraft operating from various bases. Figure 1 shows aWeibull distribution probability plot for the 19 failures that occurred. Notethat unfailed units, although not shown in the plot, are taken intoconsideration in arriving at the plotting positions.初步分析。使用寿命数据可以从服役于各个基地的2256架军用飞机的引擎排气驱动压缩机系统的统计数据得到。图1中所示是Weibull概率分布图，其中有19个不良发生。注意没有不良发生的部件，虽然图中没有进行标识，但是在绘图中会考虑到。
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The slope of the plot seems to change around 600 hours, indicating that asimple Weibull distribution does not provide an adequate representation for thelifetimes. This pattern, which is common in our experience, suggests a mixtureof early (infant mortality)failures (on the left side of the plot) and wear-outfailures (on the right side Segmented data analysis.Examination of the data revealed that 10 of the 19 failures occurred at base D,one of the bases where aircraft were stationed. Separate Weibull probabilityplots for the lifetimes of the systems at base D and those at all other basesare shown in Figure 2.看起来点群的斜率在600小时左右发生了变化，这表明简单的Weibull分布不能充分的正确提供使用寿命图。在我们的经验中这是很常见的，这种情况表明初期故障（初期故障率，位于点图的左侧）和磨损故障（位于右侧的）混合的层别数据分析。查看这些数据发现，第10~19发生不良的数据点都发生在从D基地的飞机采集的数据中。图2所示就是将D基地飞机引擎的使用寿命数据和其他基地进行分离后重新作的Weibull概率分布图。


The data in eachof these two plots scatter around straight lines, suggesting that simpleWeibull distributions provide adequate representations if you consider base Dand the other bases separately. Moreover, the probability of failure by 3,000hours is estimated from the plot to be 0.467 for the systems at base D, ascompared to 0.013 for the systems at the other bases.6这两组数据中的点都几乎呈直线分布，这表明如果将D基地的数据和其他基地分开来进行分别考虑，用简单的Weibull分布就能得到有准确的曲线，能够充分的代表产品的使用寿命。另外，概率图中3000小时的不良率0.467是根据D基地及比较其他基地的0.013数据推测出的。

A recent analysis suggested that log normal distributions might provide abetter fit to the data than Weibull distributions. Fortunately, both analysesled to similar findings. 最近的分析表明，正态分布的对数分布要比Weibull分布的数据吻合性更高，幸运的是，这两种分析都能得到相似的结论。
Resulting action. Further investigationrevealed the serious failure problem at base D was caused by corrosion acceleratedby salty air (base D was near the ocean), and a change in maintenanceprocedures was implemented there. This resulted in essentially eliminating thefailure mode.结果响应。深入的研究发现D基地一系列的不良源自于空气中的盐分对飞机的加速腐蚀（D基地位于海边），于是变更了相应的维护、维修方法。对这一分析结论所采取的措施基本消除了这项失效模式。
Note thatsegmentation analyses typically do not provide cause-and-effect conclusions bythemselves. The difference in failure probabilities between base D and the otherbases could have been due to one factor or a combination of many factors. Thedetermination that the underlying cause was corrosion due to salty air involvedan engineering assessment of failed parts. The segmentation analysis, however,helped focus and expedite the physical evaluations.注意，这样的层别分析结果并不能通过层别划分的数据本身得到“因果关系”的结论。造成D基地和其他基地之间不同失效概率的原因可能是一个因子或多个因子的组合，空气中的盐分导致飞机加速腐蚀的结论包括失效的零件在内。然而层别分析法能够帮助你迅速聚焦问题点进行评价。
Identification of subpopulations识别子群体
If at allpossible, the selection of subpopulations should be based on physicalconsiderations. This requires an in-depth understanding of the design,manufacture and use conditions of the product. 在所有可能的情况下，子群体的选择都要基于物理因素，这需要对产品的设计，制造以及使用条件都有深入的了解。

In practice, however, the reasons for differences between subpopulations maynot be known and, therefore, effective subpopulations often cannot be readilydetermined. If you knew what created the differences—at least, to the degreethat these pertain to the manufacture of the product and are controllable—youwould, in fact, want to act to remove them. Thus, identifying subpopulationsmay be a trial-and-error process.
然而在实践过程中，我们并不清楚造成不同子群体之间差异的原因，因此，很难定义真正有效的子群体。如果你知道怎么建立、区分子群体，至少在某种程度上这涉及到产品的制造和控制，实际上，这些可用于区分子群体的因素正是你想去除的影响因子，这样一来识别子群体的就会成为一个不断摸索的过程。
Initially, subpopulations are often arrived at somewhat arbitrarily, basedupon, for example, the period of production(week, month, quarter oryear Such choices should, however, be trumped by manufacturingknowledge. The times at which changes are introduced on line, for example,generally provide an improved criterion for segmentation. Segmentation mightalso be based on factors such as parts supplier, the geographical region wherethe product is being used, customer type or a combination of these.
首先，对于子群体的识别通常有点武断，比如说，基于产品的生产周期（周、月、季或年），这样的选择方法直接来自于生产。比如生产线的更换次数通常就给出了层别发的改善标准，层别法就要按照以下因素进行划分，比如部品的供给，产品要使用的地理环境，顾客类型或者这些因素的组合。
The fact that a Weibull probability plot of the data does not result in astraight line, as in the bleed system example, also suggests the existence ofsubpopulations (and multiple failure modes, as discussed later) and mightprovide clues for defining subpopulations.事实上，像排气系统的例子中，用Weibull概率分布的数据并不能得到一条直线，这也表明子群体的存在（多重失效模式，后面将会讨论）同时也表明了定义子群体的线索。
Segmenting data elsewhere进行数据细分的位置
We have discussedsegmentation in the context of reliability data tracking for non repairableproducts. Segmentation of data, however, is useful in many other situations.
在上文中，我们讨论了对于不可修复的产品通过可靠性进行层别划分的方法，实际上，在很多情况下层别法都是很有用的。
For example, a chemical cure process showed inconsistent results. To gain improvedunderstanding, the data were segmented and plotted in various ways, includingby shift. The resulting plot showed two of the shifts were providingsatisfactory product, but the night shift was not.
比如说，化学固化过程会出现不同的结果，为了更好的理解，我们把数据按照不同的方式进行划分，包括班次的差异。结果曲线显示2个白班的产品都得到了比较满意的结果，夜班的结果却不好。
To find the cause for this difference, a late-night visit to the factory floorrevealed the third-shift operators frequently turned off the plant’s airconditioning. This increased humidity, which in turn had a negative impact onproduct performance. After correcting the problem, it was decided to controlchart the performance segmented by shift.
为了查明期间的差异，对夜班的临时抽查发现了问题，第三个班次也就是夜班的操作人员频繁的关掉公差的空调，这就增加了空气湿度，这对产品的特性会造成不良的影响，纠正这个问题之后，决定采用控制图来对不同的班次进行区分管理。
Another example arises in the comparison of drugs, an area that has becomeknown as comparative effectiveness research and was part of the 2009 U.S.economic stimulus bill. In assessing the effectiveness of competing drugs ormedical devices, you want to know if a particular drug is effective in one ormore parts of the population, such as the elderly, even if it may not be so inother parts. This calls for segmentation in the data analysis.7另一个例子是对药物的比较研究，这一研究结果被作为相对有效性研究的一部分获得了美国2009年经济激励奖。在新研制的药品或医疗设备的效果评估过程中， 你会想知道某种药是否对某一人群或某些人群有效，比如说老人，甚至说对哪些人群是无效的。这就要用到层别分析法了。
Multiple failure mode analyses多重失效模式的分析
Segmentation bearssome similarity to the analysis of multiple failure modes discussed in one ofour earlier columns.8 Inboth cases, the life data cannot be described adequately by a single, simpledistribution.
在之前的例子中，对多重失效模式进行层别分析时会出现近似的结果，在每个例子中，使用寿命的数据并不能仅用单一的简单的分布就能充分说明。
In studying multiple failure modes, information on the mode of failure of eachfailed unit is required. All of the data is then used in each analysis, butobservations from failure modes other than the one under consideration aretaken as censored.在对多重失效模式的研究中，我们需要知道每个失效单元的失效模式信息，所有的数据会被用于后续的每一个分析，但是失效模式以外的一个观察数据只能作为参考。

In contrast, for the bleed system example, failure mode information was not availableat the time of the analysis (and possibly one or more of the base D failureswas not actually from corrosion Thus, the data were segmented intosubpopulations, and separate analyses were conducted for each subpopulation.相反的，还是以排气系统为例，在那次分析的时候我们并不知道失效模式的信息（D基地飞机腐蚀的真正原因是一个或多个可能因素并不知道）这样，数据被分为子群体，然后对每一个子群体的产品进行分别分析。

In both situations, the results of the individual analyses can subsequently becombined to obtain an omnibus analysis for the entire population. Forsegmentation, this requires knowledge of the proportion of units in thepopulation belonging to each subpopulation.在这两种情况下，单独的分析结果在后续的分析中会综合成为一个整体的分析结果，对于层别分析法，需要知道每个子群体中所包含的数量及比例。
Short term vs. long term短期Vs.长期
In the short term, segmentation may result in the speedyand accurate isolation of field problems to well-identified segments of thetotal product population, so you can identify the most susceptible units andtake corrective action. Segmentation may, for example, help determine whether arecall is needed, and if so, what part of the product population needs to berecalled.在短期内，层别法能够迅速、准确的将问题进行区分，把产品按照不同的子群体分为能够识别的层级，这样你既能够根据不同子群体对于不良的敏感度采取正确的行动。比如说，层别分析法能够帮助你决定是否需要召回，如果需要的话，你能够确定哪些子客户群使用的产品需要被召回。

By isolating a problem to a relatively small part of the population, you may beable to address an otherwise extremely costly problem without inconveniencingcustomers not impacted by the problem. The long-term answer, however, is toeliminate the problem in future units, perhaps by designing a sufficientlyrobust product whose performance is insensitive to the use environment.当把问题划分为相对较小的子群体，你能够准确的为客户解决某一类特定的问题，而不受其它问题干扰，也不产生太多的不相干的费用问题。然而对于长期而言，能够消除问题发生的可能性，比如设计一个不受使用环境影响的功能充分强大的产品。
Necip Doganaksoy is a principal technologist-statisticianat the GE Global Research Center in Schenectady, NY. He has a doctorate inadministrative and engineering systems from UnionCollege in Schenectady. Doganaksoy is a fellow of ASQand the American Statistical Association.Necip Doganaksoy是GE位于纽约斯克内克塔迪的全球研发中心的首席技术统计分析师，他获得斯克内克塔迪联合学院的管理系统工程专业博士学位，他是美国质量协会（ASQ）和美国统计协会的会员。
Gerald J. Hahn is a retired manager of statistics at the GE Global Research Center in Schenectady, NY.He has a doctorate in statistics and operations research from RensselaerPolytechnic Institute in Troy, NY. Hahn is a fellow of ASQ andthe American Statistical Association.Gerald J. Hahn曾任GE位于纽约斯克内克塔迪的全球研发中心统计分析中心的经理，现已退休，他获得位于纽约特洛伊的伦斯勒理工学院统计学和运筹学博士学位，他是美国质量协会（ASQ）和美国统计协会的会员。
William Q. Meeker is professor of statistics and distinguished professor of liberal artsand sciences at Iowa State Universityin Ames, IA.He has a doctorate in administrative and engineering systems from Union Collegein Schenectady, NY. Meeker is a fellow of ASQ and theAmerican Statistical Association.William Q. Meeker是美国爱荷华州立大学自由艺术与科学院的统计学特聘教授，他获得斯克内克塔迪联合学院的管理系统工程专业博士学位，他是美国质量协会（ASQ）和美国统计协会的会员。