[校对]第九篇——A Simple Way to Test Data Without Doing a Gage R&R

本帖最后由 小编H 于 2011-6-14 14:48 编辑

请对以下文章有校对兴趣的组员留下你的预计完成时间，并发短信息联系小编H，以便小编登记校对者信息以及文章最终完成时的奖惩工作。PS：请把您的邮箱地址通过短信息发给小编，原文由大量图片，以便发送文档校对~~ **A Simple Way to Test Data Without Doing a Gage R&R****不做量具R&R****来测试数据的一个简单方法** Six Sigma teams, for a variety of reasons, sometimes skip doing a gage R&R study assuming their data is free from measurement variations. There is, however, a simple test that practitioners can use to check data without doing a gage R&R. 六西格玛小组，出于各种各样的原因，有时假设数据不受测量变差的影响，而省去量具R&R的研究分析。这里，你可以用一个很简单的不做量具R&R的方法来检查数据。By Chew Jian Chieh In Six Sigma work, practitioners normally are expected to conduct a gage R&R study to verify that that the measurement systems being used are providing measurements free from variations due to repeatability and reproducibility problems. This is usually done in the Measure phase of DMAIC prior to data analysis so that a project team does not end up with conclusions that are based on measurement system variation instead of process variation. 在六西格玛研究中，一般情况下成员希望进行量具R&R的研究来验证所使用的测量系统不受重复性和再现性问题的影响。通常在数据分析之前的DMAIC测量阶段进行，以致于项目小组不能做出基于测量系统变差替代过程变差的结论。 Especially in data-mature sites like most manufacturing plants, a gage R&R is sometimes skipped because past data is always readily available and assumed to be reliable. Or, pressed for time, Six Sigma teams sometimes assume that the data that they have is free from gage R&R problems and proceed to draw conclusions from the data. Using inaccurate measurements of process variation can result in a team failing to identify real root causes or, even worse, the wrong solutions to the problem. 特别像大多数制造工厂那样有成熟数据的地方，由于历史数据总是很容易得到，并假设这些数据是可靠的，这样量具R&R有时就省略掉了。或者，由于时间紧张，六西格玛小组不时假设他们的数据是不受量具R&R问题的影响，可以根据这些数据得出结论。使用过程变差的错误测量会导致小组无法识别根本原因，甚至更糟糕的是，会得到错误的结论。 While it is wrong, the practice of moving forward without a gage R&R is undoubtedly wide spread. 虽然这样不对，但不做量具R&R的做法毫无疑问得到广泛的传播。 **A Simple Test for Measurement System Reliability****针对测量系统可靠性的一个简单测试**There is another way to check measurement reliability that is not well-known and thus little used. Six Sigma project teams can perform a simple hypothesis test using the data they have to check for measurement system problems without a formal gage R&R study. The approach is especially focused on reproducibility problems and can be used whenever there is a potential issue using different appraisers and/or different types of measurement equipment.还有一种方法可以检查测量系统可靠性，这个方法并不出名，因此很少被用到。六西格玛项目小组可对现有数据进行一个简单的假设检验，不用进行正式的量具R&R分析来检查测量系统的问题。这个方法特别关注重复性问题，也可随时应用于因不同的评价人和/或不同类型的测量设备引起的潜在问题中。 The validity of the test is best illustrated by an example: Suppose a school administers the same math test to 1,000 students. Ten math teachers are assigned to mark these 1,000 test papers. The test papers are assigned randomly so that each teacher has 100 test papers to mark. Because these teachers are math teachers, it is assumed there is no need to give them the correct answers. The teachers throw away the actual tests and report only the scores for each of their 100 papers. It suddenly dawns on the school's administration that some of the teachers may be either consistently giving higher or lower marks. How can the school find out if this is true?有个例子可以很好地对测试的有效性进行阐明：假设一个学校对1000名学生进行相同的数学考试。安排10名数学教师来对这1000份试卷进行评分。这些试卷随机分配，每位教师有100份。假设没必要给他们正确的答案，因为他们都是数学教师。撇开这些实际的考卷和报告，只列出他们100份试卷的分数。一下就可看出有的教师评分要么偏高要么偏低。学校如何能发现这些分数正确与否呢？ The logic of the test is: The 1,000 test scores have an underlying distribution. This can be any distribution but most probably, it is a normal distribution. In the case of a very brilliant group of students, the distribution is skewed to the left, or in the case of a group of very dull students, the distribution is skewed to the right. 这个测试的逻辑是：1000个考试分数有一个总体分布。最有可能的是一个正态分布。当这组学生很聪明的情况下，分布会向左偏；或当这组学生相当愚笨时，分布会向右偏。 Whatever the population distribution, the teacher's sample distribution should have the same shape and almost same mean/median unless the teacher is either too lenient or too strict or just plain incompetent. 无论母体分布如何，除非教师评分太宽或太严或者是不能胜任，不然教师的样本分布应有相同的形态，有几乎相同的均值/中值。 **Using the Appropriate Hypothesis Test****使用适当的假设试验**Hence, using the appropriate hypothesis test (ANOVA, Kruskal-Wallis, Mood's Median Test), one can find out if there is in fact any difference between teachers, i.e., are teachers causing the variation in the test scores. If the teachers are all good, the test should not be significant.因此，使用适当的假设试验（方差分析，KW测试/非参数性测试，中位数检验），就会发现教师间是否确实存在着差异，如：是教师的原因导致分数的差异吗。如果教师都很优秀的话，这种测试就不重要了。




**Figure 1:** Box Plot of Test Scoring Versus Teachers图1：盒须图——考卷分数对应教师








**Figure 2:** Probability Plot of Test Scoring图2：概率图——考卷分数




In the example, since the data is not normal as shown by the Anderson Darling Test (in the probability plot), it would be more appropriate to test using a non-parametric test:例中，A-D检定（见概率图）显示数据不是正态分布，所以更适合应用非参数性测试方法。

**Figure 3:** Kruskal-Wallis Test: Scoring Versus Teachers图3：KW测试——分数对应教师


In this case, since the test is not significant (p-value is greater than 0.05), the school can conclude that the measurement system (the teachers) are okay.这个案例中，测试没必要（P值大于0.05），学校就可以断定这个测量系统（教师）是好的。 Applying the Example to Use in Industry在企业中应用该方法In most industry data, there is data similar to the math test example. For instance, in a project, the Six Sigma team might be wondering if inspectors were all equally diligent in spotting a particular type of defect in a product. Given the large volume of production, it would reasonable to expect the distribution of the percent defect across a long time (half a year) to show no significant difference between inspectors. However, to the team's dismay, it did. This means that some inspectors are either spotting too many or too few defects, and the project team cannot be sure that the time variation in defects is due to inspectors or the process. Hence, the team must discard that data (of which it had a lot) and recollect data using trained inspectors verified by a formal gage R&R study. 大多数企业数据与数学考试的案例相似。例如，六西格玛小组在一个项目中，想知道检验员指出某一产品上一个特别缺陷的能力是否一致。若产量足够大，时间较长（半年），各检验员之间指出的缺陷分布应没有多大差异。然而，让小组沮丧的是存在着差异。这就意味着有的检验员指出的缺陷太多，有的检验员指出的缺陷太少。正因为检验员能力差异或过程变差让小组不相信时间变化引起的缺陷变化。因此，小组必须抛开这些数据，让通过正式量具R&R研究分析受训过的检验员来重新收集数据。 About the Author: Chew Jian Chieh is a senior consultant with Valeocon Management Consulting in Asia and supports clients mainly in Singapore and China. He has experience in organizational learning, organization development and change management as well as Six Sigma consulting. He specializes in process redesign, improvement and simulation, and is pioneering the application of Lean principles in transactional organizations. He received his Six Sigma Black Belt certification with the Singapore government. Chew JC is a Singapore national. He can be reached at mailto:jian-chieh.chew@valeocon.com.关于作者：Chew Jian Chieh是慧凯咨询公司亚洲区的高级咨询师，主要在新加坡、中国服务顾客。他的经历包括组织架构、机构发展、变更管理、六西格玛咨询方面。擅长过程重新设计、改进和模型。最早将精益方法应用到组织事物处理中。通过新加坡政府的六西格玛黑带认证。Chew JC是新加坡人，通过信箱mailto:jian-chieh.chew@valeocon.com可联系到他。