请注意本系列第一篇原文链接 及 感谢语。本系列能够最终成册，感谢 915_雨 在最后阶段的审核校对。仅以本文分享对 该文件的编写机构和专家 致以最诚挚的敬意。
篇外：公式的研究内容整段略过，因为粘贴两行系统卡死好几次都没成功。容连载后纠正个别问题按资源整体发布。
Parameter estimation
There are multiple approachesto estimating the parameters of the RCR model. See references 4, 6 and 7 on page 34. Trending analysis may beperformed across multiple analysis platformsfor example, SAS, R, JMP, Minitab.
有多种方法可以估计RCR模型的参数,见第34页参考文献4、6和7。趋势分析可以跨多个分析平台执行，例如SAS、R、JMP、Minitab。
An approach that requires only algebraiccalculations and not numerical optimization oriterative re-weighting schemes is a modified version of the estimationscheme described by Carter and Yang(4 on page 34).
一种只需要代数计算而不需要数值优化或迭代重新加权方案的方法是Carter和Yang（第34页第4页）描述的估算方案的改进版本。
Theestimation of the parameters of the RCR model is performed in three steps:
RCR模型参数的估计分三步进行：
Step 1) A simple linear regression is fitted toeach individual lot of stability data as used in the simple approach 简单线性回归适用于简单方法中使用的每个单独批次的稳定性数据
Step 2) The covariance matrix, S, and errorvariance, s2 are estimated using the regressionresults obtained in Step 1) 协方差矩阵S,和误差方差s2，使用步骤1中获得的回归结果估计2）
Step 3) The mean vector, , is estimated as a weightedaverage of the individual slopes andintercepts obtained in Step 1, with weights depending on the estimates obtainedin Step 2 平均向量 ，作为步骤1中获得的各个斜率和截距的加权平均值进行估计，权重取决于步骤2中获得的估计值
Oncethe parameters of the RCR model have been estimated, an approximate prediction interval can be constructed at any time point.
一旦估计了RCR模型的参数，就可以在任何时间点构造一个近似的预测区间。
Step1) Fitting a simple linear regression
步骤1）拟合简单线性回归
Step2) Estimating the error variance and covariance matrix
步骤2）估计误差方差和协方差矩阵
An alternate approach is that if either the slopeor intercept variance is negative, the estimate along with the estimated covariance are replaced with 0. Thisis a standard approach for negativevariance estimates [4.10] and is equivalent to converting a random effect intoa fixed effect in the model.
另一种方法是，如果斜率或截距方差为负，则估计值连同估计协方差一起替换为0。这是负方差估计的标准方法[4.10]，相当于将模型中的随机效应转换为固定效应。
Step3) Estimating the mean vector
步骤3）估计平均向量
Process flow for evaluating trending of stability data
将稳定性测试结果与趋势限度进行比较
2.Ifa stability test result is out of trend limits, evaluate the cause for the outof trend result as defined within thequality system. For example see a process flow in Figure 8.
如果稳定性测试结果超出趋势限度，根据质量体系中的定义，评估超出趋势结果的原因。例如，请参见图8中的流程。
3.Thelevel of the investigation for out of trend results depends on the frequency(single out of trend point, multipleout of trend results), risk of future out of specification result, precision of stability test, product history andknown characteristics (consider a risk basedassessment), and potential impact to patient safety and productefficacy. Test results for other parametersshould be considered. Be alert to process improvements and manufacturing changes.
趋势外结果的调查水平取决于频率（单个趋势外点、多个趋势外结果）、未来标准外结果的风险、稳定性测试的精度、产品历史和已知特性（考虑基于风险的评估），以及对患者安全和产品疗效的潜在影响。应考虑其他参数的试验结果。对工艺改进和生产变更保持警惕。
4.Anout of trend result should not automatically require a new stability time point.
趋势外结果不应自动要求新的稳定时间点。
5.Withina single stability lot, if the value is significantly different from the time zero (degradation), compare the value tothe previous time point(s). If the value issignificantly different from the expected value (OOE) and the methodperformance, the value is suspectand should be evaluated as an out of trend value.
在单个稳定性批次内，如果该值与时间零点（降解）显著不同，则将该值与之前的时间点进行比较。如果该值与预期值（OOE）和方法性能显著不同，则该值是可疑的，应作为趋势外值进行评估。
6.Incases where there are no established stability trend limits, evaluate thesuspect value by comparing to knownhistoric stability data. The result may be out of trend based on the historic pattern.
在没有确定稳定性趋势限值的情况下，通过与已知的历史稳定性数据进行比较来评估可疑值。根据历史模式，结果可能不符合趋势。
7.Periodicreassessment of trend limits is required. This reassessment will help detectdrifts or other changes over time.Additional data will likely change the trendlimits.
需要定期重新评估趋势限值。这种重新评估将有助于检测随时间推移的漂移或其他变化。其他数据可能会改变趋势限制。
8. Assess prediction intervals according to adefined interval (annually, or at a minimumof every 3 years, for example) to confirm stability trend limits.Include appropriate graphs,investigations, and/or supporting documentation in the annual evaluation.
根据定义的时间间隔（例如，每年或至少每3年）评估预测时间间隔，以确认稳定性趋势限值。在年度评估中包括适当的图表、调查和/或支持文件。
9.Assessmentof trend limits may also be used to evaluate site or post-change differences
趋势限值评估也可用于评估现场或变更后差异
Figure 8 Example of a ProcessFlow for OOT stability test results
图8:稳定性测试结果的OOT流程示例
Trend Analysis for Investigations
多数情况下，实验室面临在发现问题后需要进行历史数据分析（事后）。一个对数据提出的问题通常是有变化吗，如果有，是什么时候发生的。
[1][2]
虽然休哈特图对测量序列中的突然和/或大的变化很敏感，但它在检测小的但持续的偏离基准点方面是无效的。该基准点可以是目标值或标准值，或者更常见的是，在事后调查中是数据集的平均值。在这种情况下，选择的方法是采用事后分析。该技术由帝国化学工业有限公司【9】于1950年代开发，该技术也在旧英国标准BS5703第2部分中描述，该标准最近取代了ISO标准【10】。
This is a simple but powerful techniquewhich is not as widely known as it should be. As the name CuSumimplies it is merely the cumulative sum of differencesfrom a bench mark.
这是一种简单但功能强大的技术，但并不像它应该的那样广为人知。正如CuSum这个名字所暗示的，它仅仅是基准点差异的累积总和。
The objective of this technique is to;
这项技术的目的是：
·detect changes from successive differences
·estimate when the change occurred
·estimate the average value before and after the change.
It is importantto note that this techniqueattempts to identifyif a special cause variationhas occurred andwhen it happened not why it happened.
需要注意的是，该技术试图确定是否发生了特殊原因变异，以及变异发生的时间，而不是变异发生的原因。
Theory of post mortem CuSum analysis 事后CuSum分析的理论
CuSum的最后一个值始终为0。
如果一个过程处于统计控制之下，即不包含特殊原因变异，则平均值的累积值将仅具有共同原因变异，即噪声。此时，该CuSum关于时间（或批次）的曲线将是平行于X轴的直线。
However if thereis a downward slope this would indicatethat the processaverage was belowthe benchmark and conversely an upwardor positive slope would indicate that process average was above the benchmark. The steeper the slope thegreater is the difference. Hence the objective is to detect changes in slopethereby partitioning the data into segments. The keyaspect is to determine if a slope change is due to a real effect or merely chancethrough noise. The distance betweenthe successive real turning points is called the span.
因此，如果存在向下的斜率，则表明过程平均值低于基准值，反之，向上或正斜率则过程平均值高于基准值。
坡度越陡，差异越大。因此，目标是检测斜率的变化，从而将数据划分为多个段。关键是确定斜率变化是由于实际影响，还是仅仅是偶然噪声引起的。连续实际转折点之间的距离称为跨度。
In an ideal noise free world, the interpretation of the CuSum plot would be trivialas illustrated in Figure 9.
理想的无噪声情况下，CuSum图的理解简单如图9
Figure 9 Idealised CuSum plot
图9:理想化的CuSum图
The start and endpoints on a CuSum from the mean are always zero.between the 1point and the 10pointthe slopeis negativeindicating that the process averageis less than the mean and also between 30point and the 50point.
Between the 10point andthe 30pointthe reverse is true.
从平均值起，CuSum上的起点和终点始终为零。
在第1点和第10点之间，斜率为负值，表明过程平均值小于平均值，第30点和第50点之间也是同样情况。
而在第10点和第30点之间，情况正好相反。
重要的是，这种事后技术不是一种精确的统计评估，而是一种指示在何处发现变化的方法。
累了，手指头疼，这篇中止，然后我把整个上传资源中心，稍后更新链接。哎，小库啊，加油！
