【正文】 組內(nèi)隨機(jī)選擇 . 行進(jìn)中的過程 每隔 n個柚樣 18 一般準(zhǔn)則 計數(shù)數(shù)據(jù) :50100 計量數(shù)據(jù) :每個分組最少是 30 19 ? 均值 : 一 組 值的算 術(shù) 平均 均值 : 反映所有值的影響 受極值影響嚴(yán)重 ? 中位數(shù) : 反應(yīng) 50% 的序一組數(shù)排序後居中的數(shù) 在計算中不必包含所有值 相對於極值具有 “可靠性 ” ? 眾數(shù)值 : 在一組資料中最常發(fā)生的值 nnn nxx??? 1Median (Mean平均 ) (Median中數(shù) ) 眾數(shù) Center(中心 ) 50% 50% 20 1n)X(Xn1i2i?????s1n)X(Xn1i2i2?????全距 : 在一組資料中，最高值和最低值 間的數(shù)值距離 變異 (s2): 每個資料點與均值的平均平方偏差 標(biāo)準(zhǔn)偏差 (s): 變異數(shù)的平方根 . 量化變動最常用的量 全距＝最大值－最小值 Spread(散佈 ) 6s 21 The s Rule states how m and s can be used to describe the entire distribution: ? Roughly 6075% of the data are within ?1s of m. ? Roughly 9098% of the data are within ?2s of m. ? Roughly 99100% of the data are within ?3s of m. 6075% 9098% 99100% m m s m 2 s m + s m + 2 s m + 3 s m 3 s Spread(散佈 ) 22 The shape of a distribution can be described by skewness 歪斜 (denoted by ?1) and by kurtosis凹擊平坦 (denoted by ?2). ?1 0 ?1 = 0 ?1 0 ?2 0 ?2 = 0 ?2 0 歪斜 凹擊平坦 Shape (形狀 ) 23 N)(Xn1i2i2????msNX= 1i??Nimnx=xn1=ii?N) (X= N1=i2i??ms ? ?1 21?????nxxniis母體均值 樣本均值 母體標(biāo)準(zhǔn)偏差 樣本標(biāo)準(zhǔn)偏差 常用 計算公式 ~ 母體 變異 樣本 變異 1n)X(Xn1i2i2?????s~ 24 The most important and useful distribution shape is called the Normal distribution, which is symmetric(對稱 ), unimodal(單峰 ), and free of outliers (沒有特異點 ): Normal Distribution常態(tài)分佈 “ 常態(tài) ” 分佈是具有某些一致屬性的資料的分佈 這些屬性對理解基礎(chǔ)過程 （ 資料從該過程中收集 ） 的特徵非常有用 . 大多數(shù)自然現(xiàn)象和人爲(wèi)過程都符合常態(tài)分配 ， 可以用常態(tài)分配表示 , 故大部份統(tǒng)計都假設(shè)是常態(tài)分佈 。 即使在資料不完全符合常態(tài)分配時 ， 分析結(jié)果也很接近 。 8 07 06 05 04 03 02 0100.9 9 9. 9 9. 9 5. 8 0. 5 0. 2 0. 0 5.0 1. 0 0 1負(fù)偏斜分佈負(fù)偏斜平均： 70標(biāo)準(zhǔn)偏差： 10資料個數(shù)： 500Anderson Darling 常態(tài)測試A 平方： P 值 :概率負(fù)偏斜分佈負(fù)偏斜平均：標(biāo)準(zhǔn)偏差：資料個數(shù)：常態(tài)測試平方：值概率29 資料收集時的重點 How the data are collected affects the statistical appropriateness and analysis of a data set(資料如何收集可影響統(tǒng)計的適切性 ). Conclusions from properly collected data can be applied more generally to the process and output. Inappropriately collected data CANNOT be used to draw valid conclusions about a process. Some aspects of proper data collection that must be accounted for are: The manufacturing environment(製程環(huán)境 )from which the data are collected. When products are manufactured in batches or lots, the data must be collected from several batches or lots. Randomization(隨機(jī) ). When the data collection is not randomized, statistical analysis may lead to faulty conclusions. 30 Continuous Manufacturing (連續(xù) )occurs when an operation is performed on one unit of product at a time. An assembly line is typical of a continuous manufacturing environment, where each unit of product is worked on individually and a continuous stream of finished products roll off the line. The automotive industry is one example of Continuous Manufacturing. Other examples of continuously manufactured product are: ? television sets, ? fast food hamburgers, ? puters. Lot/Batch Manufacturing (批次 ) occurs occurs when operations are performed on products in batches, groups, or lots. The final product es off the line in lots, instead of a stream of individual parts. Product within the same lot are processed together, and receive the same treatment while inprocess. Lot/Batch Manufacturing is typical of the semiconductor industry and many of its suppliers. Other examples of lot/batch manufactured product include: ? chemicals, ? semiconductor packages, ? cookies. 生產(chǎn)製造環(huán)境 31 In Continuous Manufacturing the most important variation is between parts In Lot/Batch Manufacturing, the variation can occur between the parts in a lot and between the lots: ? Product within the same lot is manufactured together. ? Product from different lots are manufactured separately. Because of this, each lot has a different distribution. This is important because Continuous Manufacturing is a basic assumption for many of the standard statistical methods found in most textbooks or QC handbooks. These methods are not appropriate for Lot/Batch Manufacturing. Different statistical methods need to be used to take into account the several sources of variation in Lot/Batch Manufacturing. 要注意 : 連續(xù)和批量生產(chǎn)所用的統(tǒng)計方法有些不同 32 With Lot/Batch Manufacturing, each lot has a different mean. Due to random processing fluctuations, these lots will vary even though the process may be stable. This results in several “l(fā)evels” of distributions, each level with its own variance and mean: ? A distribution of units of product within the same lot. ? A distribution of the means of different lots. ? The total distribution of all units of product across all lots. Lot X 1 2 3 4 5 * * * * * * * * * * Distribution of Individual Lot Distribution of Lot Means Overall Distribution of Combined Lots Variation Within Each Lot Variation Between Lots Total Variation 33 2 2 2 2 2 2 2 X 1 2 X 2 2 1 2 1 2 1 , , 。 按照節(jié)拍對泵的實際流量進(jìn)行了 100次獨立測量 。泵流量點落入指定區(qū)間的次數(shù)決定區(qū)間條的高度。 紅線 (在螢?zāi)簧峡梢钥吹?) 表示累積百分比，而直方圖表示每類缺陷的頻率 (占總量的百分比 ) 。 右側(cè)的百分比只反映該圖占總體的百分比 。 裂紋 Paret