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6.2.2 Statistical Process Control and Process Capability
統(tǒng)計過程控制和過程能力
Statistical Process Control (SPC) may be used to determine if a process is stable, predictable, and in statistical control. Process Capability is used to determine if the process is capable of consistently meeting specifications. A process is considered stable or “in statistical control” when only random variation around a stable process mean is observed, i.e., only natural, common causes of variation are present. Figure 6.2.2-1 illustrates a stable process that is in classical statistical control. Figure 6.2.2-2shows a process that is not in statistical control and had a special cause of variation occur at lot 5.
統(tǒng)計過程控制可被用于判定工藝是否穩(wěn)定、可預(yù)測、處于統(tǒng)計控制狀態(tài)。過程能力分析被用于確定過程是否能夠持續(xù)符合規(guī)定。一個過程被認(rèn)為穩(wěn)定或者“處于統(tǒng)計控制狀態(tài)”是指該過程的觀測值全部在“穩(wěn)定過程均值”附近，也就是說此時只存在自然的常見原因的變化。 圖 6.2.2-1 給出了一個處于統(tǒng)計狀態(tài)的穩(wěn)定過程控制圖。 圖 6.2.2-2 展示了一個不處于統(tǒng)計控制狀態(tài)的控制圖，其中第 5 批存在特殊原因。
A more complex form of a process that is also stable and in control is shown in Figure 6.2.2-3. This pattern is typical of many processes where there is variation both within and between lots, but the variation between lots is in control. One purpose of validation and CPV is to determine both within and between-lot variations.
一個更復(fù)雜的過程（穩(wěn)定并處于統(tǒng)計控制狀態(tài)）見圖 6.2.2-3。該圖是很多既有批內(nèi)變化又有批間變化的過程的一個典型例子，但是批間變化處于控制狀態(tài)。確定批內(nèi)和批間的變化是驗(yàn)證和持續(xù)工藝確證的目的之一。
6.2.2.1 Statistical Process Control Charts
控制圖
Statistical process control charts are used to determine if a process is stable and in statistical control, or if there are special causes of variation present in the process. The basic procedure to construct a Statistical Process Control (SPC) chart to assess process stability is:
控制圖常被用于判定過程是否穩(wěn)定或處于統(tǒng)計控制狀態(tài)，或被用于確定過程中是否存在特殊變化。通過繪制控制圖（ SPC）來評價過程能力的基本步驟是：
· Collect data from the process over time. Ideally, at least 20 subgroups should be collected, but preliminary limits may be made with less data and updated as more data become available (40). Other references, such as ASTM E2587 (45), have more detailed recommendations for the amount of data to collect initially. Plot the summary statistics from each subgroup over time, such as mean (Xbar), standard deviation (S), percent nonconforming, or individuals.
從過程中收集資料（以時間序列）。理論上，應(yīng)至少收集20個子組，但初期限制時，先使用較少數(shù)據(jù)，后續(xù)更新更多數(shù)據(jù)也是可行的。對于最初需要收集數(shù)據(jù)的量，其他參考文獻(xiàn)如： ASTM E2587（ 45）有更詳細(xì)的建議。以時間順序繪制每個子組匯總的統(tǒng)計量，如：平均值（ Xbar）、標(biāo)準(zhǔn)差（ S）、不合格率或者單值。
· Draw centerlines at the grand average of the statistic being plotted.
以總平均值為中心畫中心線。
Calculate the standard error of the plotted statistics and draw control limits at three standard errors on either side of the centerlines. These limits are called “3-sigma” control limits.
計算繪圖統(tǒng)計數(shù)據(jù)的標(biāo)準(zhǔn)差，畫控制限（以中心線兩側(cè)3倍標(biāo)準(zhǔn)差為控制限）。該控制限常被稱為“ 3西格瑪”控制限。
Values that fall outside the control limits indicate that special cause variation is likely present, and the causes for these excursions should be investigated. In addition to a single value beyond the 3-sigma limits, there are many other rules that may be used to check for process stability. Of these, the most commonly used are (40,41):
數(shù)據(jù)超出控制限表示極有可能存在特殊變化，超限的原因應(yīng)調(diào)查。除此之外，如果數(shù)據(jù)在3西格瑪控制限內(nèi)，還需滿足許多其他過程能力檢查的準(zhǔn)則。這些準(zhǔn)則中最常用的如下（ 40,41）：
· 8 in a row above or below the mean;
連續(xù)8點(diǎn)在中心線的同一側(cè)；
· 2 out of 3 beyond 2-sigma limits;
3點(diǎn)中有2點(diǎn)在2西格瑪限外；
· 4 out of 5 beyond 1-sigma limits;
5點(diǎn)中有4點(diǎn)在1西格瑪限外；
· 6 in a row increasing or decreasing.
連續(xù)6點(diǎn)遞增或遞減。
Figure 6.2.2.1-1 shows an example of an Xbar/S chart for fill weight, where five vials from a singlehead filler were sampled every 15 minutes over a six hour production order or lot, for 24 samples. Both the mean and standard deviation appear to be stable, with no values exceeding the 3-sigma control limits. The process appears to be stable and in a reasonable state of statistical control.
圖 6.2.2.1-1 是一個 Xbar-S 圖（裝量）的例子，其中在超過 6 小時或更長的生產(chǎn)指令中每隔 15 分鐘對單灌裝頭取樣一次，一次 5 小瓶，共計 24 組樣本。均值和標(biāo)準(zhǔn)差都處于穩(wěn)態(tài)，沒有數(shù)據(jù)超出 3西格瑪控制限。過程呈現(xiàn)穩(wěn)定且處于統(tǒng)計控制狀態(tài)。
Control charts can be used during all three validation stages for within- or between-lot data. During Stages 1 and 2, they can be used to determine if the process is stable and in control in order to commence commercial production. Control charts are particularly useful during Stage 3 (CPV Stage). Special causes of variation affect almost every process at some point. Control charts help identify when such a special cause has occurred and when an investigation may be needed. As special causes are identified and corrective actions taken, process variability is reduced and quality improved. Control charts are easy to construct and can be used by operators for ongoing process control. They also create a common language for discussing process performance, and can prevent unnecessary adjustments and investigations. They encourage staff to be responsible for monitoring and improving their process, rather than just taking action when QC test results fail.
控制圖能被用于分析工藝驗(yàn)證的三個階段中批內(nèi)或批間的數(shù)據(jù)。在第 1、 2 階段可以用它來確定工藝是否穩(wěn)定受控以便決定是否開始商業(yè)生產(chǎn)。在第 3 階段（持續(xù)工藝確證階段）控制圖特別有用。變化的特殊原因在某一個時刻幾乎能影響到所有過程。控制圖能幫助確定特殊原因何時會發(fā)生，何時需要對特殊原因進(jìn)行調(diào)查。因?yàn)樘厥庠虮蛔R別并采取了糾正措施，所以過程的可變性減少了，產(chǎn)品質(zhì)量也就提高了。對于持續(xù)過程控制，操作員能夠很容易的繪制和應(yīng)用控制圖。控制圖為討論過程能力建立了一種通用語言，并能避免不必要的調(diào)整和調(diào)查。控制圖鼓勵員工監(jiān)控和改善他們的過程，而不是僅僅在 QC 檢驗(yàn)失敗后采取行動。
6.2.2.1.1 Factors to Consider in Designing a Control Chart
設(shè)計控制圖時需要考慮的因素
There are many factors to take into consideration when designing control charts, including:
在設(shè)計控制圖時，有許多因素需要考慮，包括：
· Characteristic(s) to chart
控制圖的特征
· Type of control chart to use
需要使用的控制圖類型
· Sample size and frequency of sampling
樣本大小和采樣頻率
· How quickly the chart will detect a problem of a given magnitude
對于一個給定的量，控制圖多快能發(fā)現(xiàn)問題
· Economic factors (costs of sampling and testing, costs associated with investigating out-of-control signals, costs of allowing defective units to reach the customer)
經(jīng)濟(jì)因素（取樣和測試的成本，對超過控制限調(diào)查的成本，允許發(fā)給客戶的不合格品的成本）
· Production rate
生產(chǎn)率
6.2.2.1.2 Types of Control Charts
控制圖的種類
Control charts may be used for both variables and attributes data. Variables data are those that are measured quantitatively, such as potency, weight, and pH. Attributes data are those obtained by counting, such as number of rejected lots per month and percent of tablets rejected. For variables data, it is important to control both the process mean and variation, and both should be charted. A change in either indicates special causes acting on the process that should be investigated. For attributes data, such as percent nonconforming units or number of cosmetic flaws in 100 glass vials, only a single chart for the variable of interest might be kept. A separate chart for variation is not necessary because the variation of attributes data is related to the mean value; for example, the number of cosmetic flaws in 100 glass vials is usually modeled by the Poisson distribution, where the standard deviation is the square root of the mean.
控制圖既可用于計量型數(shù)據(jù)也可用于屬性數(shù)據(jù)。計量型數(shù)據(jù)指那些可以被測量的數(shù)據(jù)，如：效價、重量和 pH。屬性數(shù)據(jù)指通過計數(shù)獲得的數(shù)據(jù)，如：每月的拒收批次數(shù)和藥片的拒收率。對于計量型數(shù)據(jù)，控制過程的均值和變化非常重要，因此 2 者均需要做控制圖。過程中出現(xiàn)的任何變化都表明有特殊原因起了作用，應(yīng)調(diào)查。對于屬性數(shù)據(jù)（如：不合格率單位數(shù)或 100 個小玻璃瓶的表面缺陷數(shù) ）可能僅需要一個關(guān)于變化的控制圖就行。一個單獨(dú)的變化圖不是必需的，因?yàn)閷傩詳?shù)據(jù)與均值有關(guān)；例如： 100 個玻璃瓶的表面缺陷數(shù)通常符合泊松分布，其中泊松分布的標(biāo)準(zhǔn)差是均值的 0.5次方。
When possible, it is preferable to use variables data rather than attributes data. A measured value contains more information than an attributes value, such as conforming/nonconforming. Control charts for variables data have more statistical power and can use smaller sample sizes than attributes data charts. Although the underlying theory for control charts assumes normally distributed and uncorrelated data, control charts are robust and generally work well even when these assumptions are not met (40). One exception is for attributes data with low values, which have a highly skewed non-normal distribution. Bioburden monitoring is an example of a process with low attributes data values, where many or most of the data are zeroes. Exact probability control limits use of the negative binomial, Poisson, or other suitable distribution that might be used to prevent too high of a false alarm rate; see “Understanding Statistical Process Control, 2nd ed. (42). Additional information on control charts is provided in Appendix 8.2, Types of Control
Charts.
如果可能的話，盡量使用計量型數(shù)據(jù)而不使用屬性數(shù)據(jù)。因?yàn)闇y量的數(shù)據(jù)比屬性數(shù)據(jù)包含更多的信息，如：符合/不符合。計量型數(shù)據(jù)的控制圖比屬性數(shù)據(jù)控制圖有更多的統(tǒng)計功效，因此樣本量也相對較小。雖然控制圖的基礎(chǔ)理論假設(shè)數(shù)據(jù)隨機(jī)且符合正態(tài)分布，但當(dāng)數(shù)據(jù)不符合假設(shè)（數(shù)據(jù)隨機(jī)且符合正態(tài)分布）時，控制圖仍然是穩(wěn)健的且普遍能很好地工作（ 40）。但較低值的屬性數(shù)據(jù)是一個例外，因?yàn)樗且粋€高度傾斜的非正態(tài)分布。日常監(jiān)測的微生物數(shù)據(jù)（其中大部分?jǐn)?shù)據(jù)都是 0）就是這樣的一個例子。準(zhǔn)確的能力控制應(yīng)使用負(fù)二項分布、泊松分布或其他合適的分布，這樣可以避免較高的虛發(fā)警報；參見 Understanding Statistical Process Control, 2nd ed. (42)。關(guān)于控制圖更多的信息在附錄 8.2 控制圖的類型中給出。
6.2.2.1.3 Process Capability
過程能力
Statistical process control charts answer the question, “Is the process stable and consistent?” Process capability statistics answer the question, “Is the process capable of meeting specifications?” Process capability is the ability of a process to manufacture product that meets pre-defined requirements. It can be assessed using a variety of tools, including histograms and process capability statistics. The two most common process capability statistics, Cp and Cpk, are shown in Figure 6.2.2.1.3-1. Cp measures the capability of a process to meet specifications if it is centered between the specification limits. Cpk assesses if the process is actually meeting specifications when any lack of centering is considered. Examples of normally distributed processes with various values of Cp and Cpk are shown in Figure6.2.2.1.3-2.
控制圖回答了“過程始終保持穩(wěn)定嗎？”。過程能力分析回答了“過程能夠滿足標(biāo)準(zhǔn)嗎？”。過程能力是指一個過程能生產(chǎn)出符合預(yù)定要求的產(chǎn)品的能力。可以采用包括直方圖和過程能力分析的多種工具對其進(jìn)行評估。最常用的 2 個過程能力統(tǒng)計量 Cp 和 Cpk 見圖 6.2.2.1.3-1. Cp 是衡量一個過程符合標(biāo)準(zhǔn)的能力（如果它處于標(biāo)準(zhǔn)限度之間的話）。 Cpk 評估過程（當(dāng)過程被認(rèn)為缺少中心值時）是否真正符合規(guī)定。不同的 Cp 和 Cpk 對應(yīng)的控制圖（其數(shù)據(jù)均符合正態(tài)分布）見圖 6.2.2.1.3-2。
If the process is in statistical control, the standard deviation (s) used to calculate Cp and Cpk in Figure 6.2.2.1.3-1 is usually based on estimates derived from the control chart for the standard deviation or range. These estimates of s will not include between-subgroup variation that may have occurred in the mean. For an individuals chart where n=1 per subgroup, the standard deviation is usually based on the moving range, which minimizes the effect of between-subgroup variation. If the standard deviation is calculated by the familiar equation 
of all the data combined, this estimate will include between-subgroup variation, such as between-lot variation, and the indices are then called Pp and Ppk. If a process is in statistical control, there will be little difference between Cp and Pp or between Cpk and Ppk. If a process is not in statistical control, it is difficult to determine process capability because of the lack of
process stability; see Figure 6.2.2-2. If a process is not in statistical control, Pp and Ppk are preferred as they include variation due to lack of stability. However, this practice is somewhat controversial; see “Introduction to Statistical Quality Control, 6th ed.” (43)
如果過程處于統(tǒng)計控制狀態(tài)，圖 6.2.2.1.3-1 中被用于計算 Cp 和 Cpk 的標(biāo)準(zhǔn)差(s)通常用是基于控制圖標(biāo)準(zhǔn)差或極差的估計值。對于單值圖而言，每個子組的子組大小 n=1,此時標(biāo)準(zhǔn)差常用移動極差進(jìn)行估計（子組間的差異被忽略了）。如果標(biāo)準(zhǔn)差采用的是最常見的公式
計算，那么該估計值包含了子組間的差異（如：批間差異），此時按圖 6.2.2.1.3-1 公式計算出的指標(biāo)我們稱為 Pp 和 Ppk。如果過程處于統(tǒng)計控制狀態(tài)，此時 Cp 和 Pp 或 Cpk 和 Ppk 之間有細(xì)微的不同。如果過程不處于統(tǒng)計控制狀態(tài)，那么過程能力將很難確定（因?yàn)檫^程缺少穩(wěn)定性）， 如圖 6.2.2-2。
如果過程不處于統(tǒng)計控制狀態(tài)，那么計算 Pp 和 Ppk 是更合適的，因?yàn)樗麄儼瞬町悾ㄓ捎谌鄙俜€(wěn)定性）。但是，這種做法是有爭議的，參見《質(zhì)量統(tǒng)計入門》第 6 版（ 43）。
Figure 6.2.2.1.3-2 shows the relationship between the process capability index Cpk and the probability the process output will be out of specification. The table assumes the process is in statistical control, normally distributed, and centered between the lower specification limits (LSL) and upper two-sided specification limits (USL). If the process is not normally distributed, process capability methods for non-normal distributions should be used.
圖 6.2.2.1.3-2 展示了過程能力指數(shù)與過程輸出值超限可能性之間的關(guān)系。這張表假定過程處于統(tǒng)計控制狀態(tài)，數(shù)據(jù)符合正態(tài)分布且處于規(guī)定下限(LSL)與上限之間(USL)。如果過程數(shù)據(jù)不符合正態(tài)分布（符合其他分布），那么過程能力將采用其他分布計算。
Acceptable values for Cpk depend on the criticality of the characteristic, but 1.0 and 1.33 are commonly selected minimum values. Six-sigma quality is usually defined as Cp≥ 2.0 and Cpk ≥ 1.5 for a normally distributed process in statistical control. See Wheeler (40) or Montgomery (43) for more complete treatments of SPC and process capability.
Cpk 的可接受值取決于特性的重要性，但 1.0 和 1.33 是最常用的最小值。 6 西格瑪質(zhì)量管理通常解釋為過程（數(shù)據(jù)符合正態(tài)分布且處于統(tǒng)計控制狀態(tài)）的 Cp≥2.0 并且 Cpk≥1.5。關(guān)于 SPC 和過程能力更完整的方法見 Wheeler (40) or Montgomery (43)。
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