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QM-081-品質控制統計製程管制
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QM-081-品質控制統計製程管制

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QM-081-品質控制統計製程管制 QM-081-品質控制統計製程管制 Presentation Transcript

  • 國立中山大學人力資源管理研究所 POM2007 Unit 6 品質控制 (統計製程管制) 余德成 國立高雄海洋科技大學運籌管理系 2007.5.13
  • 大綱 ‧前言 ‧基本的控制模式 ‧TQC ‧SPC ‧抽樣方法 ‧品質管制方法 ‧More
  • 前言 • TQM 失敗的原因 • 管理有兩種 • 連續改善 • 基本的控制模式
  • TQM 失敗的原因
  • 連續改善 • Concepts • 如何連續改善? • 5-Why • 改善工具
  • Concept-1
  • Concept-2
  • 如何連續改善?
  • 5-Why
  • 改善工具
  • 魚骨圖
  • 基本的控制模式 基本概念
  • TQC
  • 戴明獎審查檢點表
  • SPC ‧ 統計製程管制(Statistical Process Control; SPC) ‧ 統計思維(Statistical Thinking ) ‧ 品質特性(Quality Characteristics) ‧ 資料型態(Types Of Data) ‧ 變異型態(Types of Variations) ‧ 統計方法(Statistical Methods) ‧ 抽樣方法(Sampling Methods)
  • 統計思維 ¨ Key Concepts主要觀念 ¨ Process and systems thinking 製程與系統的思維 ¨ Variation 變異 ¨ Analysis increases knowledge 分析可以增加知識 ¨ Taking action 可以採取行動 ¨ Improvement 可以用來改善 ¨ Role of Data 資料的角色 ¨ Quantify variation 量化的變異(變動) ¨ Measure effects 量測的效應
  • 品質特性 Variables計量值 Attributes計數值 ♦ Characteristics that you measure, e.g., weight, length ♦ Characteristics for which you focus on defects ♦ 其特性可被量測而得,如 ♦ 其特性著重於缺點 重量,長度等 ♦ Classify products as either ‘good’ or ♦ May be in whole or in ‘bad’, or count # defects fractional numbers ♦ 以產品的好.壞,缺點數量來看 ♦ 可以以整數或分數表達 ♦ e.g., radio works or not ♦ Continuous random ♦ 如收音機是否可以播放 variables ♦ Categorical or discrete random variables屬不連續的雖機變數 ♦ 連續的隨機變數
  • 資料型態 ♦ Attribute data計數資料 ♦ Product characteristic evaluated with a discrete choice ♦ 產品資料特性以離散的評估方式選定 ♦ Good/bad, yes/no 良品/不良品, 好/壞 ♦ Variable data計量資料 ♦ Product characteristic that can be measured ♦ 產品特性能被量測而得 ♦ Length, size, weight, height, time, velocity ♦ 長度,大小,重量,高度,時間,,速度
  • 變異型態 ♦ Common Cause共同原因 ♦ Special Cause特殊原因 ♦ Random隨機 ♦ Situational局部 ♦ Chronic長期的 ♦ Sporadic偶而發生 ♦ Small影響小 ♦ Large影響大 ♦ System problems系統問題 ♦ Local problems局部問題 ♦ Mgt controllable管理上的控制 ♦ Locally controllable可局部控制 ♦ Process improvement製程改善 ♦ Process control製程管制 ♦ Process capability製程能力 ♦ Process stability製程的穩定性
  • 變異的原因 What prevents perfection? Process variation... 何事阻礙完美?製程變異… Common Causes共同原因 Assignable Causes特殊原因 ♦ Inherent to process固有製程 ♦ Exogenous to process外來因子影 ♦ Random隨機 響製程 ♦ Cannot be controlled不可控 ♦ Not random非隨機 ♦ Cannot be prevented無法預防 ♦ Controllable可控 ♦ Examples如: ♦ Preventable可預防 ♦ Weather氣候 ♦ Examples如 ♦ accuracy of ♦ tool wear工具磨耗 measurements量測精度 ♦ “Monday” effect週一效 ♦ capability of machine 應 設備能力 ♦ poor maintenance維護差
  • 產品規格與品變異 ♦ Product specification產品規格 ♦ desired range of product attribute產品屬性之期望範圍 ♦ part of product design產品設計的一部份 ♦ length, weight, thickness, color, …長度,重量,厚度,顏色…等 ♦ nominal specification(公稱規格) ♦ upper and lower specification limits(規格上下限) ♦ Process variability製程變異 ♦ inherent variation in processes製程中固有的變異 ♦ limits what can actually be achieved其實際能被達成之界限值 ♦ defines and limits process capability定義並限制製程能力 ♦ Process may not be capable of meeting specification! ♦ 製程是有可能無法達到規格的要求!
  • 共同原因 Average(平均值) Grams (a) Location
  • 特殊原因 Average Grams (a) Location
  • 統計方法 • 統計圖表 • 統計分配 • 管制圖 • 檢定 • 迴歸 • 讓資料說話….Know-why
  • 常態分配 The Normal Distribution σ= Standard deviation σ=標準差 Mean -3σ -2σ -1σ平均值 +1σ +2σ +3σ 68.26% 95.44% 99.74%
  • Theoretical Basis of Control Charts Central Limit Theorem Standard deviation Mean平均值 樣本標準差 X
  • 管制圖 Control Charts UCL 管制規格上限 Nominal 中心線 LCL 管制規格下限 1 2 3 Samples
  • 管制圖 UCL 管制規格上限 1 2 3 Samples
  • 管制圖 UCL 管制規格上限 Nominal 中心線 LCL 管制規格下限 Assignable causes likely 可能的特殊原因 1 2 3 Samples
  • 製程管制的三種顯示型態 (a) In statistical control and capable of producing within control limits. A process with only natural causes of variation and capable of Frequency producing within the specified control limits. 正常型 Lower control limit Upper control limit (b) In statistical control, but not capable of producing within control limits. A process in control (only natural causes of variation are present) but not capable of producing within the specified control limits; 共 同原因變異and (c) Out of control. A process out of control having assignable causes of variation.特殊原因變異 Size Weight, length, speed, etc.
  • 群體與樣本間之關係 Three population distributions群體分配 Distribution of sample means樣本平均值分配 Beta Mean of samplemeans = x Normal Standard deviation of σx the sample means = σx = n Uniform − 3σ x − 2σ x − 1σ x x + 1σ x + 2σ x + 3σ x (mean) 95.5% of all x fall within ± 2 σ x 99.7% of all x fall within ± 3σ x
  • 機遇原因之觀察 At a fixed point in time Over time 固定時間 連續時間 Targe t Think of a manufacturing process producing distinct parts with measurable characteristics. These measurements vary because of materials, machines, operators, etc. These sources make up chance causes of variation. 製造各零件 之量測特性會因4M等機遇原因而發生變異
  • 製程管制圖 Process Control Charts Plot of Sample Data Over Time 80 Sample Value Sample 60 Value UCL 40 Average 20 LCL 0 1 5 9 13 17 21 Time
  • 管制圖型態 Control Charts 計量 計數 Variables Attributes Charts Charts Continuous Categorical or 連續的 Discrete Numerical Data 離散的 Numerical Data
  • 管制圖的選定 Quality Characteristic variable attribute defective defect no n>1? x and MR constant yes constant yes p or sampling sample np unit? n>=10 or no size? x and R computer? yes no no yes p-chart with c u x and s variable sample size
  • Statistical Process Control Steps Produce Good No Start Provide Service Take Sample Assign. Causes? Yes Inspect Sample Stop Process Create Find Out Why Control Chart
  • 如何使用管制圖 1) Select the process to be charted選擇需要被圖表化之製程 2) Get 20 - 25 groups of samples 選擇樣組及樣本大小(usually 5-20 per group for X and R-chart or n≥50 for p-chart) 3) Construct the Control Chart建立管制圖 4) Analyze the data relative to the control limits. Points outside of the limits should be explained分析關聯於管制界線之資料,點超出界 限需能被解釋 5) Once they are explained, eliminate them from the data and recalculate the control chart一旦澄清,消除異常點及原因,並重算管制圖資料 6) Use the chart for new data, but DO NOT recalculate the control limits 利用此新資料,但無須重算管制界限
  • X Chart 平均值管制圖 ♦Type of variables control chart計量管制圖 ♦ Interval or ratio scaled numerical data ♦ 間距或比率量測數字資料 ♦Shows sample means over time ♦ 算出樣本平均值 ♦Monitors process average ♦ 間控製程平均數 ♦Example: Measure 5 samples of solder paste & compute means of samples; Plot ♦ 如計算錫膏厚度之平均值,再點圖
  • 平均值與標準差估計 ♦ use historical data taken from the process when it was “known” to be in control當 製程穩定時,利用過去所產生之歷史資料 ♦ usually data is in the form of samples (preferably with fixed sample size) taken at regular intervals樣本資料是在一定間隔的時間裡取得 ♦ process mean μ estimated as the average of the sample means (the grand mean or nominal value)假設製程平均值μ與樣本平均值相同 ♦ process standard deviation σ estimated by:製程標準差σ估算由 ♦ standard deviation of all individual samples 所有個別值樣本之標準差 ♦ OR mean of sample range R/d2, where或樣本平均值/ d2 ♦ sample range R = (Rmax-Rmin), d2 = value from look-up table, 全距為 R, d2可由查表得知, n ∑Ri i =1 R = n
  • X-bar vs. R charts ♦ R charts monitor variability: Is the variability of the process stable over time? Do the items come from one distribution? ♦ R管制圖監控變異性,是否整個製程處於安定狀態?有項 目超出此一分配嗎? ♦ X-bar charts monitor centering (once the R chart is in control): Is the mean stable over time? ♦ X-Bar管制圖監控中心(一旦R管制圖處於管制狀態):平均 值於爭個製程是否穩定? ♦ >> Bring the R-chart under control, then look ♦ at the x-bar chart(先看R圖,再看Xbar圖)
  • 如何建立管制圖 1. Take samples and measure them.取樣量測 2. For each subgroup, calculate the sample average and range. 每個群組,計算平均值與全距 3. Set trial center line and control limits.製作解析用管制圖之 中心線與管制界限 4. Plot the R chart. Remove out-of-control points and revise control limits.畫R圖,移除異常點,再修正管制界限 5. Plot x-bar chart. Remove out-of-control points and revise control limits.畫R圖,移除異常點,再修正管制界限 6. Implement - sample and plot points at standard intervals. Monitor the chart.管制用管制圖,於標準間隔時間取樣,監 控此管制圖
  • Type 1 and Type 2 Error Alarm No Alarm In-Control Type 1 ( alpha] No Error 管制內 Error Out-of-Control No Error Type 2 (Beta) 失控 Error
  • 管制圖異常之判定 ♦ One point outside of either control limit ♦ 一點超出管制界線 ♦ 2 out of 3 points beyond UCL - 2 sigma ♦ 3點有2點在2個標準差或以外 ♦ 7 successive points on same side of the central line ♦ 連續7點在中心線之同一側 ♦ of 11 successive points, at least 10 on the same side of the central line ♦ 連續11點有10點在中心線之同一側 ♦ of 20 successive points, at least 16 on the same side of the central line ♦ 連續20點有16點在中心線之同一側
  • Type 1 Errors for these Tests Test Probability Type 1 Error 1/1 2(0.00135) 0.0027 ⎛3⎞ 2/3 ⎜ ⎟ ( 0 . 0228 ) 2 ( 0 . 9772 ) + ( 0 . 0228 ) 3 ⎜2⎟ 0.0052 ⎝ ⎠ 7/7 (0.5)7 0.0078 ⎛11⎞ 10(0.5) + ⎛11⎞(0.5)11 10/11 ⎜ ⎟(0.5) ⎜10⎟ ⎜ ⎟ ⎜11⎟ 0.00586 ⎝ ⎠ ⎝ ⎠ 20 ⎛ 20 ⎞ i 20 − i 16/20 ∑ ⎜ ⎜ i ⎟ ( 0 .5 ) ( 0 .5 ) ⎟ 0.0059 ⎝ ⎠ 16
  • Type 2 Error • Suppose μ1 > μ ♦ Type 2 Error = Prob {x ≤ μ + 3σ x μ = μ 1} ♦ [( = Φ μ + 3σ x − μ 1 / σ ) x ] = Φ [3 − ( μ 1 − μ ) n / σ ] where Φ(z) denotes the the cumulative probability of a standard normal variate at z • Power = 1- Type 2 Error. Power increases as … n increases, as (μ1−μ) increases, and as σ decreases. • Extension to μ1 < μ is straightforward
  • X Chart Control Limits UCL = x + A R From x 2 Table LCL = x A R Sample x 2 Range at Sample Time i n Mean at ∑x i Time i n i =1 ∑ R i x = R = i =1 n n # Samples
  • 管制圖之係數表 S am p le M ean U p p er L o w er S ize, n F acto r, A 2 R an g e, D 4 R an g e, D 3 2 1.880 3.268 0 3 1.023 2.574 0 4 0.729 2.282 0 5 0.577 2.115 0 6 0.483 2.004 0 7 0.419 1.924 0.076 8 0.373 1.864 0.136 9 0.337 1.816 0.184 10 0.308 1.777 0.223 0 .1 84
  • R Chart全距管制圖 ♦ Type of variables control chart計量管制圖 ♦ Interval or ratio scaled numerical data ♦ 間距或比率量測數字資料 ♦ Shows sample ranges over time ♦ Difference between smallest & largest values in inspection sample 樣本中最大值與最小值之差 ♦ Monitors variability in process間控製程變異性 ♦ Example: Calculate Range of samples of solder paste; Plot 計算全距並點圖
  • R Chart Control Limits UCL R = D4R From Table查表 LCL R = D3R n Sample Range at ∑R i Time i 某時間間 i =1 R = 隔之全距 n Samples size 樣本大小
  • 建立X-bar R 管制圖 ♦ Take about 20-25 sample groups (n) of the process result. Each sample should contain 4 or 5 observations. ♦ For each sample calculate the average and the range. ♦ Average all the sample averages = X-BAR. ♦ Average all the sample ranges = R-BAR. ♦ Calculate the upper & lower control limit for X-BAR ♦ Calculate the upper & lower control limit for R-BAR n n UCL = x + A 2R UCL = D4R x ∑x i R ∑Ri i =1 i=1 LCL =x+A R x = LCL = D3R R = x 2 n R n
  • X-bar Chart 65 60 55 UCL 50 45 40 35 LCL 30 0 5 10 15 20 25 ♦ Is the process in control? ♦ Are the specifications being met? ♦ How can we tell if the variability is in control?
  • R-Chart ♦ The R chart measures the change in the spread over time. ♦ Plot R, the range for each sample. ♦ Lower Control Limit = D3 R ♦ Upper Control Limit = D R 4 50 45 UCL 40 35 30 25 20 15 10 5 LCL 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
  • p Chart 不良率管制圖 ♦Type of attributes control chart計數管制圖 ♦ Nominally scaled categorical data以絕對資料分類 ♦ e.g., good-bad 如好,壞 ♦Shows % of nonconforming items顯示不合格 項目% ♦Example: Count # defective chairs & divide by total chairs inspected; Plot計算椅子的不良 數除以椅子總檢驗數,點圖 ♦ Chair is either defective or not defective椅子只有好 與壞兩種
  • 建立p管制圖 • Take about 20-25 samples of the process result. Each sample should be large enough to contain AT LEAST 1 bad observation. Often for P-Charts samples sizes are in excess of 100. • For each sample calculate the percentage of bad units. • Average all the sample percentages together, this is P-BAR. • Calculate the upper & lower control limit for the P- BAR chart using the following formulas: p * (1 − p ) p±3* ni
  • p Chart Control Limits •If individual samples are within p (1 p ) 25% of the average sample size UCL =p+z p n then control limits can be calculated using the average p (1 p ) sample size: LCL =p z p n •z = 2 for 95.5% limits; •z = 3 for 99.7% limits k ∑n i k ∑xi # Defective Items in n = i =1 and p = i =1 k Sample i k ∑ni Size of sample i i =1 •If sample sizes vary by p * (1 p ) more than 25% of the UCL p , LCL p = p±3* average sample size then ni control limits should be computed for each sample.
  • Identifying Special Causes ♦It appears that shifts 4, 7 and 12 were out of control. ♦Upon further inspection it appears that too much water was added to the process in shifts 4 and 7 and that in shift 12 a new operator started. ♦Since each of the out of control points have assignable causes, we eliminate them from the data. ♦The new control chart is then:
  • Identifying Special Causes 0.3 0.25 0.2 0.15 0.1 0.05 0 1 2 3 5 6 8 9 10 11 13 14 15 16 17 18 19 20 ♦ Now it appears that shift 15 is out-of-control. ♦ Further checking shows that the temperature was set too high during this shift. ♦ Therefore, we want to eliminate this point so that in subsequent tests we can identify when this occurs. ♦ If we eliminate this point the new control chart is:
  • Determining if Your Process is “Out of Control” ♦Establish regions A, B, and C as one, two, and three σ ♦One or more points fall outside the control limits. ♦2 out of 3 consecutive points fall in the same region A ♦4 out of 5 consecutive points fall in the same region A or B ♦6 consecutive points increasing or decreasing ♦9 consecutive points on the same side of the average. ♦14 consecutive points alternating up and down ♦15 consecutive points within region C. A B C C B A
  • 建立不良數管制圖 ♦ Np charts for number of nonconforming units.以不合 格品之數統計 ♦ Converted from basic p-chart 由p管制圖演變而來 ♦ Multiply p by sample size (n). 不良率乘以樣本大小 ♦ Formulas: UCL p = n p + 3 * n p (1 − p ) LCL p = n p − 3 * n p (1 − p )
  • 建立缺點數管制圖 • Take about 20-25 samples from the process. Each sample contains 1 unit. • For each unit count the number of occurrences for the observation of interest. • Calculate the average number of occurrences per unit. This is C-BAR. • Calculate the upper & lower control limit for the C- BAR chart using the following formulas: UCL p , LCL p =c±3 c
  • 樣本平均值與製程分配 Mean 平均值 Distribution of sample means 樣本平均值分配 Process Distribution 製程分配 425 Grams
  • 製程能力 Process Capability µ , Nominal value Process distribution Lower Upper specification specification 800 1000 1200 Hours (a) Process is capable
  • 製程能力 µ, Nominal value Two sigma Lower Upper specification specification Mean
  • 製程能力 µ , Nominal value Four sigma Two sigma Lower Upper specification specification Mean
  • 製程能力 µ , Nominal value Four sigma Two sigma Lower Upper specification specification Mean
  • 製程能力 LSL Spec USL Process variation ♦Capable ♦Very capable ♦Not capable
  • 製程能力指數 Process Capability Cpk Cpk =min(Cpu , Cpl) Assumes that the process is: Cpu=(USL-µ)/3 •under control •normally distributed Cpl =(µ-LSL)/3 •假設製程為穩定且為常態分配 Tolerance Tolerance 2δ (USL - LSL) Cp = = = = Process capability 6σ 6σ 6σ Precision精密度 (X - µ ) Ca = , T = T olerance = (USL - LSL) T /2 Capability準確度
  • Cpk 量測之意義 Cpk = negative number Cpk = zero Cpk = between 0 and 1 Cpk = 1 Cpk > 1
  • 確認並降低製程變異 Lower Upper specification specification limit limit (a) Acceptance sampling (b) Statistical process control (c) cpk >1
  • 生產者與消費者冒險率 ♦ TYPE I ERROR = P(reject good lot)  α or producer’s risk, too nervous ♦ 5% is common ♦ 第一種錯誤=將好批判成壞批的機率,緊 張忙亂的錯誤 ♦ TYPE II ERROR = P(accept bad lot)  β or consumer’s risk, absent- minded ♦ 10% is typical value ♦ 第二種錯誤=將壞批判成好批的機率,心 不在焉的錯誤
  • 品質的定義 ♦Acceptance quality level (AQL) ♦ 允收水準 ♦Acceptable fraction defective in a lot ♦ 允許一批中不良的比例 ♦Lot tolerance percent defective (LTPD) ♦ 拒收水準,批容許不良率 ♦ Maximum fraction defective accepted in a lot ♦ 允許一批中最大不良的比例
  • 作業特性曲線 Operating Characteristic Curve ♦Shows probability of lot acceptance ♦ 顯示批允收的機率 ♦ Based on是基於: ♦ sampling plan抽樣計劃 ♦ quality level of lot批品質的等級 ♦Indicates discriminating power of plan ♦ 顯示不同計劃的差異性
  • OC曲線 Operating Characteristic Curve 1.00 α= { 0.05 Probability of acceptance, Pa 0.80 允 OC curve for n and c 0.60 樣本大小與 c 允收數 收 機 0.40 率 0.20 β = 0.10 { 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 Proportion defective AQL LTPD 不良比例
  • 平均出廠品質 Average Outgoing Quality (AOQ) ♦Expected number of defective items passed to customer ♦ 期望通過客戶之不良項目數 ♦Average outgoing quality limit (AOQL) is ♦ maximum point on AOQ curve ♦ 平均出廠品質界限是AOQ曲線的最大值
  • 平均出廠品質曲線 AOQ Curve 0.015 AOQL Average Outgoing 0.010 Quality 0.005 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 AQL LTPD (Incoming) Percent Defective
  • 從統計思維到統計方法 Process Variation Data Statistical Tools 製程 變異 資料 統計方法 Statistical Thinking Statistical Methods 統計思維 統計方法
  • 統計訓練 • 訓練課程 • 認證體系 • 薪資調整
  • 抽樣方法 • 雙次抽樣計劃 • 多重(連續)抽樣計劃 • 如何選擇抽樣之方法
  • Double Sampling Plans 雙次抽樣計劃 ♦ Take small initial sample ♦ 抽取少量之原始樣本 ♦ If # defective < lower limit, accept ♦ If # defective > upper limit, reject ♦ If # defective between limits, take second sample ♦ 若不良數 < 下界限,允收 ♦ 若不良數 > 上界限,拒收 ♦ 若不良數界於界限內,第二次抽樣 ♦ Accept or reject based on 2 samples ♦ 允收與拒收是站在此二抽樣樣本上 ♦ Less costly than single-sampling plans ♦ 比單次抽樣成本低
  • Multiple (Sequential) Sampling Plans 多重(連續)抽樣計劃 ♦ Uses smaller sample sizes使用較小的樣本大小 ♦ Take initial sample取出原始樣本 ♦ If # defective < lower limit, accept ♦ 若不良數 < 下界限, 允收 ♦ If # defective > upper limit, reject ♦ 若不良數 > 上界限, 拒收 ♦ If # defective between limits, resample ♦ 若不良數界於界限內,重新抽樣 ♦ Continue sampling until accept or reject lot based on all sample data ♦ 連續抽樣必需站在所有的樣本資料以決定允 收或拒收
  • Choosing A Sampling Method 如何選擇抽樣之方法 ♦An economic decision經濟的考量 ♦Single sampling plans單次抽樣計劃 ♦ high sampling costs高抽樣成本 ♦Double/Multiple sampling plans ♦ 雙次/連續抽樣計劃 ♦ low sampling costs低抽樣成本
  • 品質管制方法 ♦Statistical process control (SPC)統計製程管制 ♦Monitors production process to prevent poor quality ♦ 監控產品製程以預防不良品質 ♦Acceptance sampling允收抽樣 ♦ Inspects random sample of product or materials to determine if a lot is acceptable隨機抽樣檢驗產品或物 料以決定此批是否允收
  • 抽樣與篩選 Sampling vs. Screening ♦ Sampling抽樣 ♦ When you inspect a subset of the population ♦ 群體批中檢查小批 ♦ Screening ♦ When you inspect the whole population ♦ 群體批中檢查全數 ♦ The costs consideration ♦ 成本的考量,經濟的原則
  • 允收抽樣 Acceptance Sampling ♦Accept/reject entire lot based on sample results ♦ 整個允收/拒收是樣品結果為基礎 ♦Not consistent with TQM of Zero Defects ♦ 與TQM的零缺點不同 ♦Measures quality in percent defective ♦ 以缺點百分率測量品質
  • 抽樣計劃 Sampling Plan ♦Guidelines for accepting lot允收批之指導作業 ♦Single sampling plan單一抽樣計劃 ♦ N = lot size批量 ♦ n = sample size (random)樣本大小 ♦ c = acceptance number允收數 ♦ d = number of defective items in sample樣本不良項目之數 目 ♦If d <= c, accept lot; else reject ♦ 若 d <= c, 允收此批,其他則批退 ♦
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  • The End 運籌帷幄 決勝全球 觀念與方法!