1、 8.1 Appendix 1: Statistical Methods for Determining the Number of Lots 附件1：决定批数量的统计学方法 Listed below are statistical approaches used to determine the number of lots that may be required at the PPQ stage. Other approaches may also be suitable. As there is no standard industry approach to statisticall
2、y determine the number of lots, multiple options are offered. This section will provide applied statistical methods for determining the number of lots. It will also stimulate further discussion on this issue. Regardless of the number of lots selected and the acceptance criteria used, the data collec
3、ted during PPQ as well as CPV should be statistically analyzed to help understand process stability, capability, and within (intra-) and between-lot (inter-lot) variation. 下面列举的是在 PPQ 阶段用于决定批次数量的统计学方法。除此之外的方法当然也可能适用。因为行业中并没有从统计学上决定批次的数量的标准方法，所以其他多种方法同样可以提供。本章节将提供决定批次数量实用的统计学方法，并鼓励在这个方面更加深入的讨论。无论选择的批
4、次数量以及采用的可接受标准是多少，PPQ 中收集的数据都应进行统计分析以帮助理解工艺的稳定性、工艺能力以及批内和批间的变异。 8.1.1 Average Run Length (ARL) to detect a p100% lot failure rate 用以检测批失败率（p100%）的平均运行长度（ARL） The average number of lots until the first lot failure is ARL =1/p. where p is the lot failure rate that is important to detect. 直到出现第一批失败的平均批数
5、量（ARL）=1/p,其中p为批失败率，检测出p是很重要的。 Example: A lot failure rate of 20% is deemed unacceptable for a given process. A lot failure rate of 20% would be detected on average in 1/0.2=5 lots. 例子：往往一个工艺出现 20%的批失败率是被认为不可接受的。而 20%的批失败率可以从平均1/0.2=5 批中被检测出。 Common choices for p would be 25%, 20%, 10%, and 5%, depe
6、nding on the other factors given earlier (e.g., prior knowledge, risk, production rate) Five (5%) would generally be the tightest value to consider since a process running right at the Acceptance Quality Limit is still expected to have a 5% lot rejection rate. If applicable, this approach can also b
7、e used to determine the number of lots to use with tightened sampling during CPV (continued process verification). It may be particularly useful when there are many quality attributes to assess. Rather than determine the number of lots required separately for each attribute, the PPQ stage is complet
8、e when all attributes pass for the required number of lots. 通常p的取值可以有25%，20%，10%和5%，其取决于早期的因素（比如先前的经验、风险、生产率）。一般 5%的 p 值被认为是最严格的取值，因为即使此工艺在可接受质量限度中运行正常，但其仍有5%批的废品率。如果合适的话，这个方法也可以用于在CPV（持续的工艺核实）中以决定加强取样的批次的数量，特别当工艺有许多质量属性可以评估时非常有用。当要求的数量的批次所有属性均通过时，PPQ 阶段才是完整的，而不是针对每一个属性来决定批次的数量。 8.0 Appendices 附件 8.
9、1.2 Range of between-lot (inter-lot) variation expected to be covered in nL lots 在nL批中覆盖到预期批间变异的范围 Table 8.1.2-1 outlines the expected between-lot variation coverage in nL lots. 表8.1.2-1简述在nL批中预期批间变异覆盖范围 Table 8.1.2-1 Expected Between-Lot Variation Coverage in nL lots Expected Coverage 预期的覆盖范围 Numbe
10、r of lots nL 批次数量nL 33% 2 50% 3 60% 4 67% 5 75% 7 80% 9 85% 12 90% 19 95% 39 Example: It is desired to represent two-thirds =67% of the betweenlot variation during PPQ. The number of lots required is nL =5 lots. 举例：如果在PPQ阶段要求2/3（67%）的批间变异，那么要求的批次数量为nL=5批 Expected coverage is calculated as (nL-1)/( n
11、L+1). This follows from the expected percentile of an order statistic being its rank divided by n+1 (53). This approach does not require between-lot normality. The method may be modified to provide confidence levels of coverage instead of expected coverage. The approach may be used to determine “ste
12、p-down sampling” during CPV. For example, highly tightened sampling may be used in PPQ for the first three lots until 50% coverage is reached. At that time, the PPQ is considered complete. Moderately tightened sampling for critical characteristics could continue into Stage 3 CPV for four more lots u
13、ntil 75% coverage is reached, at which point routine sampling begins. 期望的覆盖率计算公式为(nL-1)/( nL+1)。这公式由次序统计量百分点等级除以n+1推断得到。这种方法不需要批间正态。该方法可能会进行修订，即以规定覆盖率的置信水平来取代期望的覆盖率。该方法也可以用在CPV阶段决定“逐渐减少取样”。例如：PPQ阶段的前3批需要更严格的取样直至50%的覆盖率达到，此时，PPQ就可以认为完成了。在阶段3 CPV 4批或更多批中只需要对关键特性进行中等程度的取样直到 75%的覆盖率达到，随后只需要进行日常取样。 8.1.3
14、 Within and Between Lot Normal Tolerance Intervals 批内及批间正常公差区间 Statistical tolerance intervals are commonly used in validation. For example, a capping process may have a validation criterion of “demonstrate with 90% confidence that at least 99% of the removal torques for the lot are within specifica
15、tion limits.” Tables of normal tolerance interval factors for variables data are widely available and also implemented in statistical software. Specialized software is available to optimally calculate the desired confidence statement. Normal tolerance intervals for the total process variation over t
16、ime are more complicated; they include both within- and between-lot variation. Standard normal tolerance interval factors assume that there is only one population in the data. However, most PPQs contain multiple populations since each lot is a separate population. 验证中普遍用到统计学公差区间。例如，轧盖工艺的一个验证标准是“证明至少
17、 99%的批松开力矩均在标准限度且有90%置信度”。计量型数据的普通公差区间因子在许多统计软件都可以查到并应用。可以使用专业的软件以优化计算出期望的置信区间。整个工艺变异的普通公差区间会越来越复杂，他们包括了批内以及批间的变异。标准普通公差区间因子假设数据中只有一个总体。然而，由于每一批都是一个单独的总体，因此大多数 PPQ 包括了多个总体。 If there are no significant differences between the lots, the simplest way to deal with multiple lots is to combine the data. A
18、NOA may be used to compare lot means; within-lot variation may be compared with the Levene / Brown-Forsyth, Bartlett, Cochran, or Fmax tests (54-57). An omnibus test may also be used. If there are no significant differences between lots or if the between-lot variance component is not statistically,
19、the standard normal tolerance interval for the combined data may be used. The sample size per lot and number of lots should be statistically determined to have adequate power to detect any between-lot variation. 如果批间无显著的差异，处理多个批次最简单的方法是合并数据。ANOA（方差分析）用于比较批均数。批内的差异用Levene / Brown-Forsyth, Bartlett, C
20、ochran, 或 Fmax 检验进行比较，也可以用多项混合测试。如果批间没有显著差异或批间方差分量没有统计学意义，那么就可以使用合并后数据的标准普通正常公差区间。每批的样本量以及批数量由统计学决定并足以检测到任何批间的变异。 Example: The specification for cap removal torque for a small volume parenteral (SVP) product is 8.0-12.0 inch-pounds. Limited data from Stage 1 showed a standard deviation of about 0.5.
21、 The production AQL (Acceptance Quality Limit) for removal torque is 1.0%. The acceptance criterion for the PPQ is to show with 90% confidence that at least 99% (1 minus the AQL) of the cap torques are within specifications. 举例：小容量注射剂产品的瓶盖松开力矩的标准是8.0-12.0英寸磅。阶段1有限的数据表明标准偏差在0.5左右。产品松开力矩的AQL（可接受质量限度）为
22、1.0%。那么PPQ的可接受标准则为至少99%（1减去AQL）的瓶盖松开力矩在指标内的置信度为90%。 Three lots are included in the PPQ to evaluate the within- and between-lot variations. A sample size of 30 units per PPQ lot was tested to detect between-lot variation as large as the within-lot variation with 90% confidence (58). Samples were test
23、ed from throughout each of the three lots, and the acceptance criteria for each lot was met. An I/MR SPC chart indicated that the process was in control during each lot. Normality tests for each lot did not indicate significant non-normality. Since ANOVA and Levenes test showed no significant differ
24、ence between the three lots, the data were combined. The 90 test results had a mean of 9.59 and standard deviation of 0.51. PPQ中用3个批次来评价批内以及批间的变异。每个PPQ批次用30个样本量来检测批间以及批内的变异，置信度为90%（58）。取样测试始终贯穿3个PPQ批次的每一批，并且每一批都符合可接受标准。已使用I/MR（单值-移动极差）统计过程控制（SPC）图表明每一批工艺均受控。每一批正态性检验表明没有明显的非正态性。由于 ANOVA 和 Levene检验表明3
25、批无显著,数据就可以合并在一起。90个测试结果的平均值为9.59，标准偏差为0.51. A 90% confidence normal tolerance interval for 99% of the population is 9.592.872 x 0.51=(8.13,11.05). This interval is within the specification limits of 8.0-12.0. Thus, the PPQ has shown with 90% confidence that at least 99% of torque results are expecte
26、d to meet specifications. 99%总体在90%置信度普通公差区间为9.592.872 0.51=(8.13,11.05).此区间在标准限度8.0-12.0以内。因此，PPQ显示至少99%的力矩有90%置信度是符合预期指标的。 If there are statistically significant differences between lots, the tolerance interval should be constructed with more advanced methods that take the between-lot variance com
27、ponent into account (56,57). 如果批间有着显著的统计学上的差异，应建立更先进的方法来建立公差区间，此方法应将批间的方差分量考虑在内。 8.1.4 Statistical Process Control Charts (45) 统计过程控制图（45） Most SPC references suggest obtaining data from 20-30 time periods before calculating control limits to assess whether the process is in control. Samples could b
28、e taken at 30 time periods across three or more lots. For three lots, 10 sets of rational subgroup” samples could be selected from each lot. The SPC chart limits are then calculated and the process assessed for statistical control. The number of lots to use can be based on the power of the SPC chart
29、 to detect undesirable between-lot variation. 大多数的 SPC 参考文献都建议收集 20-30 组数据来计算控制限以评估工艺是否受控。可以从3批或更多批中取30组的样本。对于3批来说，可以将每批分为10组合理子群并取样。然后计算SPC图的限度并对工艺进行统计学控制评估。使用批次的数量就取决于SPC图检测到非期望的批间变异的能力。 A potential problem with the use of SPC charts, such as Xbar/S chart plotted across lots, is that they define a
30、 process as being in statistical control if there is no underlying lot-to-lot variation (Figure 6.2.2.1-1). This is often not the case, and some lot-to-lot variation is typical and expected, especially for lot means. In these cases, an I/MR chart for the mean and/or standard deviation or three-way b
31、etween/within chart can be used to detect out-of-statisticalcontrol between-lot variation. SPC图使用中会有一些问题，比如跨批用Xbar/S图，而该图是定义工艺已处于统计学控制条件是，没有潜在的批与批变异，（图6.2.2.1-1）。但这往往并非如此，一些批与批的变异是典型的并且是可以预料到的，特别对于批均数。对于这些情况，可以使用I/MR图对均值和/或标准偏差或三相间/内控制图进行统计以检测出批间不符合统计控制的变异。 If there is only one test result per lot,
32、such as lot assay or pH of a tank of solution, the 20-30 time periods become 20-30 lots. This is seldom feasible for PPQ. An alternative is to select a smaller number of lots, perhaps 5-10, and construct a preliminary I/MR control chart. If it shows an in-control process, the PPQ would be complete a
33、nd the control chart extended into Stage 3 to verify longer term statistical control during CPV. 如果每批只有1个测试结果，例如批含量或罐内溶液的pH，那么20-30组就可以变为20-30批。这在PPQ中很少可行。另一种方法是选择小的批次数量，比如5-10批，然后建立初步的I/MR控制图。如果显示工艺受控，那么PPQ就是完整的并且将控制图延伸至阶段3以确认CPV中的长期统计控制。 8.1.5 Ppk, Cpk Process Capability Metrics (59) Ppk, Cpk工艺能力指
34、标（59） Ppk (see Figure 6.2.2.1.3-1) is the most common statistic used to assess long-term process capability. Acceptable values of Ppk depend on the criticality of the characteristic, but 1.0 and 1.33 are commonly used. Smaller or larger values may be used depending on the risk factors involved. The
35、Ppk acceptance criterion may be based on a point estimate or a one-sided lower confidence interval. If there is significant bewteen-lot variation, caution should be exercised in using confidence intervals for Ppk calculated by statistical software. Most statistical software programs do not take betw
36、een-lot variation into account, and may provide optimistic confidence intervals that are too narrow. 在统计学上最常用Ppk（见图 6.2.2.1.3-1）来评估长期工艺稳定性。Ppk的可接受的值基于工艺特性的关键性，但一般使用1.0和1.33。其他更小或更大的取值可以根据涉及到的风险因子来决定。Ppk 的可接受标准可以基于点估计（定值估计）或单面下置信区间。如果批间有显著的变异，在用统计学软件计算Ppk使用置信区间时多加注意。大多数统计学软件程序并没有考虑批间的变异，并可能给出较宽松的置信区间
37、，而这显然太过于狭隘了。 Example: Fill volume specification limits for a small-volume parenteral product are 98-102. PPQ acceptance criteria are that each lots Ppk1.0; also, that the overall process Ppk is 1.0 with 95% confidence. To detect a between-lot standard deviation that is half of the within-lot standar
38、d deviation with 90% confidence, 33 units will need to be tested form across each of five PPQ lots. 举例：小容量注射剂产品的灌装体积标准限度为 98-102。PPQ 可接受标准为每次的Ppk1.0，同时，总工艺的Ppk1.0，置信度为95%。为了检测出批间标准偏差，其为批内标准偏差的一半，置信度为90%，需要从5个PPQ批次中每批取33个样本。 The data from the five lots were analyzed by control charts, histograms, nor
39、mality tests, Levenes test, and ANOVA. These analyses indicated that the data from the five lots could be combined. Each of the five lots Ppks were 1.0. The calculated Ppk from the combined data was 1.14, with a lower 95% confidence interval of 1.03. Since each lot met its Ppk requirement and the lo
40、wer confidence interval for the overall process, Ppk was above the acceptance limit of 1.0. Thus the PPQ acceptance criteria were met. 5批中收集的数据使用控制图、直方图、正态性检验、Levene检验以及ANOVA进行分析。这些分析表明5批的数据可以合并。5批中每一批的Ppk均大于1.0。合并后的数据计算出的Ppk为1.14，95%下置信区间为1.03。因为每一批均符合其Ppk要求且整个工艺的Ppk下置信区间在可接受限度1.0以上，所以该PPQ满足其可接受标准。
41、 An alternative to calculating a parametric confidence interval for Ppk is to require four or five lots in a row to each meet the Ppk acceptance criteria. For example, four PPQ lots, each with Ppk1.0, provides over 90% confidence that the process median Ppk is 1.0. Five lots provide over 95% confide
42、nce. 另外一种计算参数Ppk置信区间的方法是要求连续4批或5批并且每一批均符合其Ppk可接受标准。例如，4个PPQ批次，其中每一批Ppk均1.0，工艺中值Ppk1.0的置信度在90%以上。5批的置信度则在95%以上。 8.1.6 Assure The Lot Conformance Rate is Above An Acceptable Rate With Specified Confidence 确保批合格率在可接受标准之上并具有规定的置信度 This approach demonstrates that the percent of lot conformance is accepta
43、ble. It identifies unacceptable variation due to either common or special causes. Table 8.1.6-1 shows the required number of conforming lots. This method is sometimes called “confidence for reliability.” 该方法证明批合格率是可接受的。其识别出由于通常或特定原因导致不可接受的变异。表8.1.6-1展示了需要合格的批次数量。该方法有时也称为“可靠性置信度”。 Table 8.1.6-1 Numbe
44、r of lots to demonstrate confidence for lot conformance rate 表8.1.6-1 证明批合格率置信度的批次数量 Confidence 置信度 Conformance Rate 合格率 Accept # 接受# n 数量 50% 90% 0 7 95% 0 14 99% 0 69 90% 90% 0 22 95% 0 45 99% 0 230 95% 90% 0 29 95% 0 59 99% 0 299 Example: To demonstrate the process is acceptable, the PPQ acceptan
45、ce criterion will be show with 90% confidence that the process lot conformance rate (the lot pass rate) is at least 90%. A total of 22 passing lots in a row will demonstrate this. 举例：为了证明工艺是可接受的，PPQ 的可接受标准必须要求工艺批合格率（批通过率）至少达到90%，置信度为90%。那么连续22批合格批次即能证明这点。 Requiring such a large number of lots during
46、 PPQ to reach 90% or 95% confidence is difficult. An alternative is to use 50% confidence in PPQ and monitor the process further during CPV to reach the final desired confidence. Crossing the 50% confidence threshold is the point at which it is more likely that the selected lot conformance rate is m
47、et. For the example above, once 7 passing lots are reached, it is more likely that the conformance rate is greater than 90% rather than less than 90%, and the PPQ could be considered complete. An additional 15 lots during early CPV would reach the required 22 lots. This approach may be particularly
48、useful when there are many quality attributes to assess. Rather than determine the number of lots required separately for each attribute, the PPQ stage is complete when all attributes pass for the required number of lots. 在PPQ中达到90%的置信度需要大量的批次，但实际上是很困难的。另外一种方法是PPQ中使用50%的置信度，在CPV中进行更进一步的监测并最终达到期望的置信度
49、。超过50%的置信度阈值是所选批合格率符合的更有可能的点。就上面来举例：一旦达到7批通过批次，批合格率更有可能大于90%而不是低于90%，那么PPQ就认为是完整了。在CPV早期阶段增加15批即达到了要求的22批。该方法可能特别适用于需要评估的质量属性有很多的情况。只有当要求数量的批次的所有质量属性均合格，PPQ 阶段才算是完整的，而不是对每一个属性进行单独的判定。 8.1.7 Wald Sequential Probability Ratio 瓦尔德序贯概率比 Walds sequential probability ratio (SPR) test can be used to determine when a suitable number of PPQ lots have been made for decision-marking. No fixed number is specified in advance; the PPQ continues until either the failure or pass decision line is crossed. The SPR test is most often used for percent of passing units or lots, but it can als
