02 spc訓練教材

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Statistical Process ContrStatistical Process Control ol

統計製程管制統計製程管制

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Chapter OutlineChapter Outline 概述概述Statistical Thinking and Statistical Methods 統計思維與統計方法 Statistical Process Control (SPC) 統計製程管制

Types of data 資料型態 Constructing control charts 如何架構管制圖 Interpreting control charts 管制圖之說明 Process capability 製程能力

Acceptance sampling 允收水準 Inspection process 檢驗程序 Quality measures 品質的量測 Sampling vs. screening 抽樣與篩選

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Process 製程

Variation 變異

Data 資料

Statistical Tools 統計方法

Statistical Thinking Statistical Thinking

統計思維統計思維Statistical Methods Statistical Methods

統計方法統計方法

Statistical Thinking and Statistical Thinking and Statistical MethodsStatistical Methods

統計思維與統計方法統計思維與統計方法

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Statistical ThinkingStatistical Thinking統計思維統計思維

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

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“You can’t improve a process that you don’t understand” 你若對製程不懂 , 就無法改善製程

Without a Process ViewWithout a Process View若無製程的觀點若無製程的觀點

•People have problems understanding the problem and their role in its solution (turf). 吾人在其問題的理解與對策執行的角色扮演上會有問題 It is difficult to define the scope of the problem. 難以定義問題範圍 •It is difficult to get to root causes. 難以找到真正的要因 •People get blamed when the process is the problem (80/20 Rule). 吾人在當製程是真正問題時 , 會遭到責備 •Process management is ineffective 製程管理沒有效果 •Improvement is slowed 改善緩慢

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•

Without Understanding VariatiWithout Understanding Variationon 若不了解其變異若不了解其變異

•Management by the last data point 永遠是用最後的資料作管理 ( 永遠在頭痛醫頭 , 腳痛一腳 , 沒有源頭置根本的觀念 ) •There’s lots of fire fighting 火災不斷

•Using special cause methods to solve common cause problems 用特別的方法處理共同要因的 ( 一般性 ) 問題

•Tampering and micromanaging abound •修改與小事的管理老是存在 •Goals and methods to attain them fail •目標與方法無法達成 •Understanding the process is handicapped •只知道製程是個問題

• Learning is slowed 學習慢 •Process management is ineffective 製程管理沒有效果 •Improvement is slowed 改善慢

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Without DataWithout Data若是手上沒有資料若是手上沒有資料

•Everyone is an expert: 每個人都是專家 •Discussions produce more heat than light 討論不斷

•Historical memory is poor 歷史的記憶模糊 •Difficult to get agreement on: 難以得到協議若

•What the problem is 無法得知問題是什麼 •What success looks like 無法得知其成果將如何 •Progress made 或由哪一製程所產出

•Process management is ineffective 製程管理是無效的 •Improvement is slowed 改善慢

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“Early on, we failed to focus adequately on core work processes and statistics.” 初期若核心工作製程與統計無法適當集中 , 其結果…

David Kearns and David Nelder, Xerox Corporation

Without Statistical ThinkingWithout Statistical Thinking若無製程統計的思維若無製程統計的思維

•Your management and improvement processes are handicappe 吾人的管理與改善將有障礙 •It’s like 其像

–Football without a passing attack 足球未經核准即攻擊 –Growing a lawn without fertilizer 草地未經施肥 –Doing research without measurements 研究未做量測資料 –Playing golf without your irons 不用自己的球竿打高爾書球

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SECURE

STORE

KIT

Load Program Load Pick/Place Load Reflow Profile Load Stencil

Screen Solder Paste

Parts SMT

Placement

I / R ReFlow

Clean

PEM Parts (ASIC, ADC, DAC) Placement

& Hand Solder

Clean

Second Level Assy. Touch-up solder joints

Mechanical Installations

Staking/Bonding

Clean

Electrical Functional

Test

Clean Bake Conformal Coat

Post Test InspectionAcceptanc

e Test

Electrical

Controlled

Storage

Inspection Checkpoint







Through-hole and Plastic Parts Preparation Tin Components

Form & Cut Axial Leads

Through-hole Component Placement

& Hand Solder

Clean & Inspection Checkpoint

PWB Preparation: Clean

Ink Stamp Bake

Production Operation

Inspection Operation

Test Operation

Material Control Operation

KEY

Manufacturing Flow Diagram of PWB AssemManufacturing Flow Diagram of PWB Assembly PWB bly PWB 組裝之製造流程圖組裝之製造流程圖

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SECURE

STORE

KIT

Load Program Load Pick/Place Load Reflow Profile Load Stencil

Screen Solder Paste

Parts SMT

Placement

I / R ReFlow

Clean

PEM Parts (ASIC, ADC, DAC) Placement

& Hand Solder

Clean

Second Level Assy. Touch-up solder joints

Mechanical Installations

Staking/Bonding

Clean

Electrical Functional

Test

Clean Bake Conformal Coat

Post Test InspectionAcceptanc

e Test

Electrical

Controlled

Storage








Through-hole and Plastic Parts Preparation Tin Components

Form & Cut Axial Leads

Through-hole Component Placement

& Hand Solder

Clean & Inspection Checkpoint

PWB Preparation: Clean

Ink Stamp Bake

Production Operation

Inspection Operation

Test Operation

Material Control Operation

KEY

Manufacturing Flow Diagram of PWB AsseManufacturing Flow Diagram of PWB Assembly PWB mbly PWB 組裝之製造流程圖組裝之製造流程圖

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Depends on levels of activity and job responsibility. Depends on levels of activity and job responsibility. 依據活動的層級與工作執掌依據活動的層級與工作執掌

Where we're headed Where we're headed 我們朝何方我們朝何方

Managerial processes Managerial processes to guide us to guide us 用管理的程序來指導我們用管理的程序來指導我們

Where the work gets Where the work gets Done Done 讓所需的工作被執行完成讓所需的工作被執行完成

Strategic Strategic 策略上的策略上的

Managerial Managerial 管理上的管理上的

Operational Operational 作業性的作業性的

Executives Executives 高階決策層高階決策層

Managers Managers 經理階層經理階層

Workers Workers 現場員工現場員工

Use of Statistical ThinkingUse of Statistical Thinking運用統計思維運用統計思維

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• Executives use systems approach. • 決策者運用系統導向策略 • Core processes have been flow charted • 主要程序已被流程圖表化 • Strategic direction defined and deployed. • 策略方向的訂定與展開 • Measurement systems in place. • 適當的量測系統 • Employee, customer, and benchmarking studies are used to

drive improvement. • 是以員工 , 客戶與 benchmarking 的研究被用來主導改

善 • Experimentation is encouraged. 鼓勵實驗 •

Statistical Thinking at the Strategic LevStatistical Thinking at the Strategic Levelel

決策者之統計思維決策者之統計思維

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.

• Managers use meeting management techniques • 經理利用會議管理技巧 • Standardized project management systems are in place. • 適當的標準化專案管理系統 • Both project process and results are reviewed. • 此專案的流程與結果已被審核 • Process variation is considered when setting goals. • 當設定目標時 , 流程的變異已被考慮 • Measurement is viewed as a process. • 量測點被視為一個流程 • The number of suppliers is reduced • 供應者數目減少 • A variety of communication media are used. • 廣泛的傳訊媒體被採用

Statistical Thinking at the Statistical Thinking at the Managerial Level Managerial Level

經理階層統計思維經理階層統計思維

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• Work processes are flowcharted & documented • 工作程序已被流程圖表化與書面化 • Key measurements are identified. 主要量測點已被確認

– Time plots displayed 時間的圖示被展現 • Process management and improvement utilize: • 製程管理與改善採用

– Knowledge of variation, and 變異觀念的知識及 – Data analysis 資料分析

• Improvement activities focus on the process, not blaming employees. 改善工具著重於製程 ,而非責備員工

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Statistical Thinking at the Operational LevelStatistical Thinking at the Operational Level

現場員工的統計思維範例現場員工的統計思維範例

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Statistical Thinking at the Operational LStatistical Thinking at the Operational Levelevel

現場員工的統計思維範例現場員工的統計思維範例A Recent Experience 最近的經驗 Huge quantities of data 大量的資料 Limited understanding of structure 在有限度理解的結構上 Consultants applied artificial neural nets 顧問群運用人工神經網狀系統 Didn’t work但不成功

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Statistical Thinking at the Operational LeStatistical Thinking at the Operational Levelvel

現場員工的統計思維範例現場員工的統計思維範例A Recent Experience 最近的經驗 Artificial Neural Nets apply nicely in many situations (NIST Examples): 人工神經網狀系統出色地運用於許多領域 :

Optical Character Recognition光學文字辨識系統 Finger Printing 指紋辨識 Face Printing for the FBI 相貌辨識

Example等案例上

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…….But, .But, 但但•Unless you sample the process taking the right amount of the right kind of data (rational subgroups) you will never approach process understanding. •在抽驗的流 ( 製 ) 程裡若你無法取得正確的數量與資料 (合理的樣組 ),你將無法深入了解此一流 ( 製 ) 程 •Without process understanding, there is no process control. •流 ( 製 ) 程若不了解 ,就無所謂的流 ( 製 )程管制

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Key Learnings from Key Learnings from Statistical Thinking EffortsStatistical Thinking Efforts

由統計思維的努力中由統計思維的努力中 ,, 吾人學到的吾人學到的要點要點Statisticians don’t understand Statistical Thinking as

well as they think they do. 統計的思維不僅要懂而且也要會做 Those who do understand it have limited access to managerial and strategic levels. 真正了解統計思維的人 , 在管理與決策上之能力較少受限制 There’s much more work to be done. 較多的事能被完成

Spread the word 口令的展開 Focus on process 著重製程

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Characteristics for which you focus on defects 其特性著重於缺點 Classify products as either ‘good’ or ‘bad’, or count # defects

以產品的好 .壞 ,缺點數量來看e.g., radio works or not

如收音機是否可以播放

Categorical or discrete random variables屬不連續的雖機變數

AttributesAttributes 計數值計數值 VariablesVariables 計量值計量值

Quality CharacteristicsQuality Characteristics 品質特性品質特性

Characteristics that you measure, e.g., weight, length

其特性可被量測而得 , 如重量,長度等 May be in whole or in fractional numbers

可以以整數或分數表達

Continuous random variables

連續的隨機變數

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Types Of DataTypes Of Data資料型態資料型態

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

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Types of VariationsTypes of Variations 變異型態變異型態

Common Cause 共同原因Random隨機

Chronic長期的Small影響小

System problems 系統問題

Mgt controllable 管理上的控制Process improvement 製程改善

Process capability 製程能力

Special Cause 特殊原因Situational局部Sporadic偶而發生Large影響大Local problems局部問題

Locally controllable 可局部控制

Process control 製程管制 Process stability 製程的穩定性

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Statistical technique used to ensure process is making product to standard 統計技術用於確保製程所製出的產品合乎標準 All process are subject to variability 所有製程受變異性所支配Natural or Common causes 自然或共同原因 :

Random variations隨機變異如設備損耗Assignable causes 特殊原因

Correctable problems 可改善的問題Machine wear, unskilled workers, poor material

如生手 ,材料不良…Objective: Identify assignable causes

目標 :確認特殊原因Uses process control charts

利用管制圖表

Statistical Process ControlStatistical Process Control統計製程管制統計製程管制

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Causes of VariationCauses of Variation變異的原因變異的原因

Inherent to process固有製程 Random隨機 Cannot be controlled 不可控 Cannot be prevented 無法預防 Examples 如 :

Weather氣候 accuracy of measurements

量測精度 capability of machine

設備能力

Exogenous to process外來因子影響製程

Not random非隨機 Controllable 可控 Preventable 可預防 Examples 如

tool wear 工具磨耗 “Monday” effect週一效應 poor maintenance 維護差

Common Causes 共同原因 Assignable Causes 特殊原因

What prevents perfection? Process variation... 何事阻礙完美 ? 製程變異…

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Product Specification and Process VariationProduct Specification and Process Variation產品規格與製程變異產品規格與製程變異

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 !

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Grams(a) Location

Average(平均值 )

Common CausesCommon Causes共同原因共同原因

26 (a) Location

Grams

Average

Assignable CausesAssignable Causes特殊原因特殊原因

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-3 -2 -1 +1 +2 +3Mean 平均值

68.26% 95.44% 99.74%

= Standard deviation = 標準差

The NormaThe Normal l DistributionDistribution常態分配常態分配

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X

Mean 平均值

Central Limit Theorem

x

x

n

xx

nμX =μX =

Standard deviation

樣本標準差

μX =μX =

Theoretical Basis of Control Theoretical Basis of Control ChartsCharts

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UCL 管制規格上限

Nominal 中心線

LCL 管制規格下限

1 2 3 Samples

Control ChartsControl Charts 管制圖管制圖

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1 2 3 Samples

Control ChartsControl Charts 管制圖管制圖UCL 管制規格上限

Nominal 中心線


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Assignable causes likely 可能的特殊原因

1 2 3 Samples

Control ChartsControl Charts 管制圖管制圖UCL 管制規格上限

Nominal 中心線


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Process Control: Process Control: Three Types of Process OutputsThree Types of Process Outputs

製程管制的三種顯示型態製程管制的三種顯示型態

Frequency

Lower control limit

Size Weight, length, speed, etc.

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

(a) In statistical control and capable of producing within control limits. A process with only natural causes of variation and capable of producing within the specified control limits. 正常型

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The Relationship Between The Relationship Between Population and Sampling DistributionsPopulation and Sampling Distributions群體與樣本間之關係群體與樣本間之關係

Uniform

Normal

BetaDistribution of sample means 樣本平均值分配

x means sample of Mean

n

xx

Standard deviation of

the sample means

(mean)

x2 withinfall x all of 95.5%

x3 withinfall x all of 99.7%

x3 x2 x x x1 x2 x3

Three population distributions群體分配

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Visualizing Chance CausesVisualizing Chance Causes機遇原因之觀察機遇原因之觀察

Target

At a fixed point in time 固定時間

Time Targe

t

Over time 連續時間

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

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Process Control ChartsProcess Control Charts製程管制圖製程管制圖

Plot of Sample Data Over Time

0

20

40

60

80

1 5 9 13 17 21

Time

Sam

ple

Valu

e

SampleValueUCL

Average

LCL

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Control Charts

Variables Charts

Attributes Charts

Continuous

連續的

Numerical Data

Categorical or Discrete

離散的

Numerical Data

Control Chart TypesControl Chart Types管制圖型態管制圖型態

計量計數

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Control Chart SelectionControl Chart Selection管制圖的選定管制圖的選定Quality CharacteristicQuality Characteristic

variablevariable attributeattribute

n>1?n>1?

n>=10 or n>=10 or computer?computer?

x and MRx and MRnono

yesyes

x and sx and s

x and Rx and Rnono

yesyes

defectivedefective defectdefect

constant constant sample sample size?size?

p-chart with p-chart with variable sample variable sample sizesize

nono

p or p or npnp

yesyes constant constant sampling sampling unit?unit?

c uc u

yesyes nono

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Produce Good Provide Service

Stop Process

Yes

No

Assign. Causes? Take Sample

Inspect Sample

Find Out Why Create

Control Chart

Start

Statistical Process Control SteStatistical Process Control Stepsps

統計製程管制控制步驟統計製程管制控制步驟

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Statistical Thinking is a philosophy of lStatistical Thinking is a philosophy of learning and Action based on the followearning and Action based on the following fundamental principles:ing fundamental principles:統計思維哲學之學習與行動基於以下原則統計思維哲學之學習與行動基於以下原則

•All work occurs in a system of interconnected processes, •Variation exists in all processes, and •Understanding and reducing variation are keys to success. •所有工作的產生源於系統互相連結之製程 ,而變異存在於所有製程 , 了解並降低製程的變異是成功的關鍵

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Using Control ChartsUsing Control Charts如何使用管制圖如何使用管制圖

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 outs

ide 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

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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

監控製程平均數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

XX Chart Chart 平均值管制圖平均值管制圖

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Basic Probabilities Concerning the DistriBasic Probabilities Concerning the Distribution of Sample Meansbution of Sample Means

有關樣本平均數之機率分佈有關樣本平均數之機率分佈

{ }{ } 0006.0=4<4+>

0027.0=3<3+>

xx

xx

σμxorσμx

σμxorσμx

-Prob

-Prob

nσσ x /=Std. dev. of the sample means 樣本平均數標準差 :

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Estimation of Mean and Std. Dev. Estimation of Mean and Std. Dev. of the Underlying Processof the Underlying Process

在製程控制之下之平均值與標準差估計在製程控制之下之平均值與標準差估計 use historical data taken from the process when it was “known” to be i

n 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 siz

e) taken at regular intervals 樣本資料是在一定間隔的時間裡取得 process mean estimated as the average of the sample means (the gr

and mean or nominal value)假設製程平均值與與與與與與與與 process standard deviation estimated by: 製程標準差與與與

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

R R

i

n

1i ==∑

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X-bar vs. R chartsX-bar vs. R charts平均值平均值 VSVS 全距管制圖全距管制圖

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 )

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How to Construct a Control ChaHow to Construct a Control Chartrt

如何建立管制圖如何建立管制圖 1. Take samples and measure them. 取樣量測 2. For each subgroup, calculate the sample average and ra

nge. 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 revis

e 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

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Type 1 and Type 2 ErrorType 1 and Type 2 Error第一種與第二種錯誤第一種與第二種錯誤

Type 1 ( alpha]

Error

No Error

No Error

Type 2 (Beta)

Error

Alarm No Alarm

In-Control 管制內

Out-of-Control 失控

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Common Tests to Determine if the Common Tests to Determine if the Process is Out of ControlProcess is Out of Control

管制圖異常之判定管制圖異常之判定 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

48

Type 1 Errors for these Tests Type 1 Errors for these Tests 第一種錯誤第一種錯誤

Test Probability Type 1 Error

2/3

7/7

10/11

16/20

1/1 2(0.00135) 0.0027

0.0052

(0.5)7 0.0078

11)5.0(11

11)5.0(10)5.0(

10

11

0.00586

iii

20)5.0()5.0(

20

16

20

0.0059

3)0228.0()9772.0(2)0228.0(2

3

49

Type 2 ErrorType 2 Error第二種錯誤第二種錯誤 Suppose 1 >

Type 2 Error =

1x3xProb

/3

/3

1

1

n

xx

where (z) denotes the the cumulative probability of a standard normal variate at z • Power = 1- Type 2 Error. Power increases as … n increases, as () increases, and as decreases. • Extension to is straightforward

50

X Chart Control LimitsX Chart Control Limits

Sample Range at Time i

# Samples

Sample Mean at Time i

From Table

RAxx

LCL

RAxx

UCL

2=

2+=

n

R R

i

n

1i ==∑

n

x x

i

n

i 1==∑

51

Factors for Computing Factors for Computing Control Chart LimitsControl Chart Limits

管制圖之係數表管制圖之係數表Sample Size, n

Mean Factor, A2

Upper Range, D4

Lower Range, D3

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 0.184

Table

52

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

RR Chart Chart 全距管制圖全距管制圖

53

Sample Range at Time i 某時間間隔之全距

Samples size

樣本大小

From Table查表

R Chart Control LimitsR Chart Control LimitsRR 管制圖管制界限公式管制圖管制界限公式

n

R R

RD LCL

RD UCL

i

n

1i

3R

4R

==

=

=

∑

Setting up a X-BAR R ChartSetting up a X-BAR R Chart建立建立 X-bar R X-bar R 管制圖管制圖

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

RAxx

LCL

RAxx

UCL

2

2

+=

+=

n

x x

i

n

i 1==∑

RD LCL

RD UCL

3R

4R

=

=

n

R R

i

n

1i==∑

Using an s-Chart Using an s-Chart Instead of an R-ChartInstead of an R-Chart

利用標準差圖取代利用標準差圖取代 RR 管制圖管制圖S-Charts are used when: Tight control of process variation is essential.Sample size equals 10 or more.

a computer can be used to simplify & speed up calculations.

Formulas:

i

i

n

1i

n

)x(xΣs

-==

sBLCL

sBUCL

s

s

3

4

=

=

Control Limits for s-Chart Control Limits for X-bar Chart

sAxLCL

sAxUCL

x

x

3

3

=

+=

56

Example: The first 20 days samples are as follows:SampleNumber X-Bar R

1 45.87 43 44.55 39.23 38.34 47.68 43.11 9.3332 57.1 37.23 51.39 54.83 50.02 50.16 50.12 19.863 29.93 61.78 39.65 32.54 68.48 66.42 49.8 38.554 57.01 59 54 54.48 52 44.57 53.51 14.435 68.38 35.84 55.12 35.64 50.75 55.92 50.28 32.746 69.76 64.21 62.43 67.34 54.43 57.34 62.59 15.337 57.01 27.27 44.8 46.41 67.61 32.5 45.93 40.348 46.65 50.41 54.02 44.3 63.19 45.59 50.69 18.899 33.97 45.59 35.07 55.95 51.41 58.94 46.82 24.9610 54.56 64.9 54.53 57.34 53.34 59.43 57.35 11.5611 45.27 47.11 61.7 46.84 50.79 53.42 50.85 16.4412 41.76 34.34 51.04 45.5 44.98 65.77 47.23 31.4313 31.9 44.12 41.27 59.17 49.03 65.48 48.5 33.5814 45.32 33.91 39.43 37.34 41.43 38.34 39.3 11.4215 60.91 46.36 54.27 26.29 43.53 47.51 46.48 34.6216 64.49 67.11 58.33 62.23 59.23 58.34 61.62 8.77917 48.53 48.56 41.29 44.92 47.8 28.07 43.2 20.4918 54.44 58.49 58.54 63.34 65.43 69.23 61.58 14.819 50.65 44.97 55.32 60.92 35.37 43.18 48.4 25.5420 51.89 50.26 40.28 54.33 61.67 47.83 51.04 21.39

X double-bar R-bar50.42 22.2

57

UCL

LCL

X-bar ChartX-bar Chart

Is the process in control? Are the specifications being met? How can we tell if the variability is in control?

30

35

40

45

50

55

60

65

0 5 10 15 20 25

58

R-ChartR-Chart The R chart measures the change in the spread over time. Plot R, the range for each sample. Lower Control Limit = Upper Control Limit =

RD3RD4

UCL

LCL0

5

10

15

20

25

30

35

40

45

50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

59

Ex: Control “Commuting times” Ex: Control “Commuting times” Step 1Step 1 Commuting Times (min.) - A.M.Commuting Times (min.) - A.M.

WEEKWEEK1 2 3 4 5 6 7 8 9 10

55 90 100 70 55 75 120 65 70 100

75 95 75 110 65 85 110 65 85 80

65 60 75 65 95 65 65 90 60 65

80 60 65 60 70 65 85 90 65 60

80 55 65 60 70 65 70 60 75 80

71 72 76 73 71 71 90 74 71 77

25 40 35 50 40 20 55 30 25 40

Min

ute

sM

inu

tes

Xbar =Xbar =R =R =

Step Step 22

Step Step 33

X = 74.6 X = 74.6

R = 36 R = 36

n = 5n = 5

UCLUCLLL = X + A = X + A22*R *R

= 74.6 + (.58)*(36) = 74.6 + (.58)*(36)

= 95.48 = 95.48

LCLLCLLL= X - A= X - A22*R *R

= 74.6 - 20.88 = 74.6 - 20.88

= 53.72= 53.72

UCLUCLRR = D = D44*R *R

= (2.11)*(36.0) = (2.11)*(36.0)

= 75.96 = 75.96

LCLLCLRR = D = D33*R *R

= 0= 0

60

Control “Commuting times” Control “Commuting times” (cont.)(cont.)step 4step 4 Commuting times - A.M.Commuting times - A.M.

UCL = 95.48UCL = 95.48

Xbarbar = 74.6Xbarbar = 74.6

LCL = 53.72LCL = 53.72

Xbar ChartXbar Chart

11 101022 33 44 55 66 77 88 995050

100100

7575

R ChartR Chart UCL = 75.96UCL = 75.96

Rbar = 36.0Rbar = 36.0

LCL = 0LCL = 0

11 101022 33 44 55 66 77 88 99

7575

55

3535

61

FigureFigure

62

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

p Chartp Chart不良率管制圖不良率管制圖

Setting up a p ChartSetting up a p Chart建立建立 pp 管制圖管制圖•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:

inpp

p)1(*

*3

64

p Chart Control Limitsp Chart Control Limits不良率管制圖管制界限不良率管制圖管制界限

# Defective Items in Sample iSize of sample i

•If individual samples are within 25% of the average sample size then control limits can be calculated using the average sample size:

•z = 2 for 95.5% limits; •z = 3 for 99.7% limits

i

k

1i

i

k

1ii

k

i

p

p

n

xp and

k

nn

n

ppzpLCL

n

ppzpUCL

=

=1=

∑

∑=

∑=

)1(=

)1(+=

•If sample sizes vary by more than 25% of the average sample size then control limits should be computed for each sample.

ipp n

pppLCLUCL

)1(**3±=,

65

Example: p-ChartExample: p-ChartM&M Mars wants to institute a statistical process control on a new candy bar. In order to do so, every shift they sample 50 bars and determine the number of defective ones. They obtain the following data:

Shift # Rejected Shift # Rejected1 7 11 12 11 12 183 5 13 94 18 14 85 6 15 146 8 16 117 22 17 88 9 18 69 2 19 310 1 20 3

66

20 groups of 50 = 1000 samples Total defective = 170 p-bar = 0.17 UCL = 0.17 + 3 x 0.053 = 0.329 LCL = 0.17 - 3 x 0.053 = 0.010 Plotting the % defective shows:

.17.83 50 0.053

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

1 3 5 7 9 11

13

15

17

19

67

Identifying Special CausesIdentifying Special Causes確認特殊要因確認特殊要因

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:

68

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:

0

0.05

0.1

0.15

0.2

0.25

0.3

1 2 3 5 6 8 9 10 11 13 14 15 16 17 18 19 20

Identifying Special Identifying Special CausesCauses

69

Final p ChartFinal p Chart

UCL = 0.122 + 3 x 0.046 = 0.260 LCL = 0.122 - 3 x 0.046 = -0.016 = 0.0

(negative control limits should be set to 0) Now they should use this chart for all subsequent

sampling until the process changes

0

0.05

0.1

0.15

0.2

0.25

0.3

1 2 3 5 6 8 9 10 11 13 14 16 17 18 19 20

70

Determining if Your Process isDetermining if Your Process is “Out of Control” “Out of Control”

決定你的製程是否在穩定狀態決定你的製程是否在穩定狀態 Establish regions A, B, and C as one, two, and three 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

AB

C

71

Using an np ChartUsing an np Chart建立不良數管制圖建立不良數管制圖

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:

)1(*3

)1(*3

ppnpnLCL

ppnpnUCL

p

p

Setting up a c chartSetting up a c chart建立缺點數管制圖建立缺點數管制圖

•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:

c3cLCL,UCL pp ±=

73

Using an u ChartUsing an u Chart建立單位缺點犐赯建立單位缺點犐赯 ?/span>?/span>

• A u chart is used when the unit size inspected for defects • is not constant. In these cases the unit is often referred to • as an area of opportunity (ni). • The average occurrence per area of opportunity • (i.e. the center line) is calculated as: • The same 25% variation rule discussed for p-charts • applies here as well. Control limits are calculated as:

i

iu

nuuLCLu

nuuUCL

/3±=

/3±=

•

•

74

FigureFigure

75 425 Grams

Mean 平均值

Process Distribution 製程分配

Distribution of sample means 樣本平均值分配

Sample Means and theSample Means and theProcess DistributionProcess Distribution

樣本平均值與製程分配樣本平均值與製程分配

76

Process CapabilityProcess Capability 製程能力製程能力

µ , Nominal value

800 1000 1200 Hours

Upper specification

Lower specification

Process distribution

(a) Process is capable

77

Process CapabilityProcess Capability 製程能製程能力力

Lower specification

Mean

Upper specification

Two sigma

µ, Nominal value

78


Lower specification

Mean

Upper specification

Four sigma

Two sigma

µ , Nominal value

79


Lower specification

Mean

Upper specification

Six sigma

Four sigma

Two sigma

µ , Nominal value

80

Process CapabilityProcess Capability 製程能力製程能力

Capable

Very capable

Not capable

LSL USLSpecProcess variation

81

Process Capability CProcess Capability Cpkpk

製程能力指數製程能力指數Assumes that the process is:

•under control •normally distributed

•假設製程為穩定且為常態分配

LSL)-(USLoleranceTT ,T

µ(XCa

σ6LSL)-(USL

σ6δ2

σ 6

Tolerance

capabilityProcess Tolerance

Cp

==2/

)=

====

-

Cpk =min(Cpu , Cpl)

Cpu=(USL-µ)/3

Cpl =(µ-LSL)/3

Precision精密度

Capability 準確度

82

Meanings of CMeanings of Cpkpk Measures Measures

CCpkpk 量測之意義量測之意義Cpk = negative number

Cpk = zero

Cpk = between 0 and 1

Cpk = 1

Cpk > 1

83

Statistical Process Control – Statistical Process Control – Identify and Reduce Process VariabilityIdentify and Reduce Process Variability統計製程管制統計製程管制 -- 確認並降低製程變異確認並降低製程變異

Lower specification

limit

Upper specification

limit

(a) Acceptance sampling

(b) Statistical process control

(c) cpk >1

84

Quality Control ApproachesQuality Control Approaches品質管制方法品質管制方法

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

85

Sampling vs. ScreeningSampling vs. Screening抽樣與篩選抽樣與篩選

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

86

Acceptance SamplingAcceptance Sampling允收抽樣允收抽樣

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

87

Sampling PlanSampling Plan抽樣計劃抽樣計劃

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

88

Producer’s & Consumer’s RiskProducer’s & Consumer’s Risk生產者與消費者冒險率生產者與消費者冒險率

TYPE I ERROR = P(reject good lot) 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)

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

89

Quality DefinitionsQuality Definitions品質的定義品質的定義

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

90

Operating CharacteristicOperating Characteristic (OC) Curve (OC) Curve

作業特性曲線作業特性曲線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

91

Operating Characteristic Curve Operating Characteristic Curve OCOC曲線曲線

AQL LTPD

= 0.10

= 0.05

Pro

babi

lity

of a

cce

pta

nce,

Pa

{

0.60

0.40

0.20

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

0.80

{

Proportion defective 不良比例

1.00

OC curve for n and c 樣本大小與 c 允收數

允

收

機

率

92

Average Outgoing Quality (AOQ)Average Outgoing Quality (AOQ)平均出廠品質平均出廠品質

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

93

AOQ CurveAOQ Curve平均出廠品質曲線平均出廠品質曲線

0.015

0.010

0.005

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

AOQL

Average Outgoing Quality

(Incoming) Percent Defective

AQL LTPD

94

Double Sampling PlansDouble Sampling Plans雙次抽樣計劃雙次抽樣計劃

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

95

Multiple (Sequential) Sampling PlansMultiple (Sequential) Sampling Plans 多重多重 ((連連續續 )) 抽樣計劃抽樣計劃

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

96

Choosing A Sampling MethodChoosing A Sampling Method如何選擇抽樣之方法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

02 spc訓練教材

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Transcript of 02 spc訓練教材