part 01 기초 개념 및 이론

Chapter 01 신뢰성 개론 ····················································································3

1.1 신뢰성과 신뢰성 기술 ····························································5

1.1.1 품질관리와 신뢰성······················································7

1.1.2 신뢰성과 안전성························································10

1.1.3 제조물 책임·······························································12

1.1.4 신뢰성 기술의 중요성 ···············································13

1.2 신뢰성 기술의 발전과정······················································15

1.3 신뢰성 척도··········································································21

1.3.1 신뢰성과 신뢰도························································21

1.3.2 보전도와 가용도························································22

1.3.3 기계와 전자 부품의 신뢰성······································23

1.4 Minitab의 신뢰성 분석 기능 ·············································24

1.4.1 Minitab 개요 ····························································24

1.4.2 Minitab의 신뢰성/생존 분석 기능··························24

1.4.3 Minitab의 신뢰성/생존 분석 메뉴··························27

1.4.4 Minitab의 Release 별 신뢰성/생존 분석 기능의 차이점 ········································································31

1.5 신뢰성 분야에서 통계방법의 활용 영역 ·····························32

1.5.1 설계/개발/출시 검증 단계 ········································33

1.5.2 제조 단계 ··································································34

1.5.3 사용현장 행적 단계 ··················································35

Chapter 02 신뢰성 기초 이론 ·········································································37

2.1 수명자료의 특성···································································39

2.1.1 수명자료와 성능자료·················································39

2.1.2 수명자료의 유형························································39

2.1.3 수명자료의 특징························································42

2.2 고장률과 신뢰도 함수 ··························································42

2.2.1 고장의 종류·······························································42

2.2.2 수명과 수명분포························································43

2.2.3 신뢰도와 고장률························································46

2.2.4 욕조곡선(Bathtub curve) ········································48

2.3 수명분포···············································································50

2.3.1 정규분포(Normal distribution) ·····························50

2.3.2 대수정규분포(Lognormal distribution) ·················52

2.3.3 지수분포(Exponential distribution) ·····················53

2.3.4 와이블 분포(Weibull distribution) ························55

2.3.5 최소 및 최대 극단치분포(Smallest and largest extreme value distribution) ································58

2.3.6 로지스틱 분포(Logistic distribution) ····················61

2.3.7 대수로지스틱 분포(Loglogistic distribution) ·······62

2.3.8 감마 분포(Gamma distribution) ···························63

2.3.9 역치(threshold)모수를 가지는 분포························64

2.3.10 수명분포들의 관계와 고장률 유형 ·························66

2.3.11 Minitab을 이용한 신뢰도 및 분위수 계산···········67

● 연습문제 ························································································73

part 02 수명자료 분석: 기본

Chapter 03 확률지와 와이블 분석 ··································································77

3.1 누적 고장확률과 신뢰도의 추정·········································79

3.1.1 경험분포법·································································79

3.1.2 Kaplan-Meier 추정법 ·············································87

3.2 확률지에 의한 신뢰성 분석법·············································92

3.2.1 확률지에 의한 추정 ··················································92

3.2.2 P-P 도시와 Q-Q 도시 ············································95

3.3 와이블 분석: 와이블 확률지···············································95

3.3.1 와이블 확률지의 구성 ···············································96

3.3.2 와이블 확률지의 사용법···········································96

3.3.3 3-모수 와이블 분포일 경우···································107

3.3.4 와이블 확률지의 해석 및 대처 ······························111

3.4 정규와 대수정규 확률지의 활용·······································116

3.4.1 정규확률지의 구성과 활용······································116

3.4.2 대수정규 확률지의 구성과 활용·····························118

3.5 와이블 분석: 누적고장률 용지··········································121

3.5.1 누적고장률 용지의 구성·········································122

3.5.2 와이블 누적고장률 용지의 구성·····························122

3.5.3 와이블 누적고장률 용지 사용법·····························122

● 연습문제 ······················································································131

Chapter 04 모수적 수명자료 분석방법 ··························································135

4.1 분포 적합도 검정과 모수 추정법·····································137

4.1.1 주요 분포 적합도 검정···········································137

4.1.2 모수 추정법 ·····························································138

4.2 지수 수명분포일 경우 ·······················································146

4.2.1 점추정 ······································································146

4.2.2 신뢰구간의 설정······················································148

4.2.3 가설검정··································································152

4.2.4 Minitab을 활용한 분석·········································155

4.3 와이블 수명분포일 경우····················································160

4.3.1 최우추정법을 이용한 모수 추정·····························160

4.3.2 단순 회귀분석을 이용한 모수 추정 ·······················162

4.3.3 고장개수가 하나도 없는 경우································167

4.3.4 sudden death 시험을 채택할 경우 ···················172

4.4 대수정규 수명분포일 경우················································174

4.4.1 관측중단될 경우의 모수추정··································174

4.4.2 Minitab을 활용한 분석 ·······································175

● 연습문제 ······················································································178

Chapter 05 Minitab을 활용한 체계적 신뢰성 분석 ······································181

5.1 체계적 분석절차································································183

5.1.1 Minitab의 선택가능 수명분포·······························183

5.1.2 Minitab을 활용한 수명자료 분석 절차················185

5.2 모수적 방법-완전자료·······················································189

5.3 모수적 방법-우측 관측중단자료·······································205

5.4 모수적 방법-임의 관측중단자료·······································218

5.5 모수적 방법-다중 고장모드··············································225

5.5.1 다중 고장모드·························································225

5.5.2 분석방법··································································225

● 연습문제 ······················································································237

Chapter 06 보증자료 분석 ············································································243

6.1 개요 ····················································································245

6.1.1 보증자료의 특성······················································247

6.2 보증정책·············································································248

6.3 보증자료의 분석방법·························································250

6.3.1 보증자료 분석의 어려움·········································250

6.3.2 보증청구 자료에 의한 신뢰성 분석·······················251

6.4 Minitab을 활용한 보증자료 분석 ··································257

6.5 이차원 보증자료의 분석····················································273

6.5.1 이차원 보증자료의 특징 및 분석절차····················273

6.5.2 이차원 보증자료 분석방법······································275

6.5.3 이차원 보증: 복합척도 분석법 ·····························276

6.5.4 이차원 보증: Lu의 일차원 분석법·························283

● 연습문제 ······················································································292

part 03 신뢰성 시험

Chapter 07 신뢰성 시험계획 ·········································································299

7.1 신뢰성 시험········································································301

7.1.1 신뢰성 시험의 종류 ················································301

7.1.2 신뢰성 시험의 목적에 따른 분류 ···························302

7.1.3 신뢰성 시험계획의 수립·········································305

7.2 신뢰도 결정시험 계획: 모형 및 기초이론························305

7.2.1 기본 개념 ································································305

7.2.2 대표본 근사를 이용한 시험계획·····························310

7.3 Minitab을 활용한 신뢰도 결정시험 계획························314

7.3.1 Minitab 신뢰성 시험계획 기능·····························314

7.3.2 추정 시험계획·························································315

7.3.3 간헐적 검사방법······················································322

7.4 신뢰성 실증시험 및 계획··················································326

7.4.1 신뢰성 실증시험······················································326

7.4.2 무고장 시험계획······················································327

7.4.3 고장 허용 신뢰성 실증시험 계획···························333

7.4.4 지수분포하의 실증시험 계획··································337

● 연습문제 ······················································································343

Chapter 08 가속수명시험 자료의 분석 ··························································345

8.1 가속시험 방법····································································347

8.1.1 가속시험 절차·························································348

8.1.2 가속수명시험···························································349

8.1.3 가속열화시험···························································354

8.2 가속모형·············································································355

8.2.1 아레니우스 모형(Arrhenius model) ·····················356

8.2.2 역누승 모형(Inverse power law model) ···········358

8.2.3 일반화 아이링 모형(Generalized Eyring model)360

8.2.4 온․습도 가속모형·····················································361

8.2.5 온도-비열 스트레스 모형 ·······································361

8.2.6 사용률 가속모형······················································362

8.2.7 비례 고장률(Proportional Hazards ; PH) 모형 ··363

8.3 가속성과 가속계수·····························································364

8.3.1 가속성의 성립·························································364

8.3.2 가속계수··································································365

8.4 가속수명시험 자료의 분석················································367

8.4.1 확률지에 의한 가속수명자료의 분석·····················367

8.4.2 Minitab을 활용한 가속수명자료의 체계적 분석··373

8.5 복합 가속스트레스시험 자료의 분석 ······························390

8.5.1 위치-척도 회귀모형················································390

8.5.2 가속 수명 검사(Accelerated Life Tesing 메뉴를 이용한 분석 ················································392

8.5.3 수명 데이터 회귀 분석(Regression with LifeData) 메뉴를 이용한 분석·····································399

8.5.4 분석 사례 ································································400

● 연습문제 ······················································································427

Chapter 09 가속수명시험 계획 ·····································································437

9.1 개 요 ··················································································439

9.1.1 계획 정보 ································································439

9.1.2 모형 가정 ································································440

9.1.3 전통적 시험계획······················································441

9.2 가속수명시험의 설계·························································443

9.2.1 몬테카를로 시뮬레이션을 이용한 설계··················443

9.2.2 대표본 근사방법을 이용한 설계·····························444

9.3 가속수명시험 계획의 기초개념·········································446

9.3.1 가속수명시험 계획의 규정······································446

9.3.2 계획 기준 ································································447

9.3.3 전 고장 시험계획 ····················································448

9.4 관측중단 최적시험계획······················································450

9.4.1 기본개념··································································450

9.4.2 최적시험계획 ·························································452

9.5 관측중단 3수준 시험계획··················································456

9.5.1 4：2：1 할당비 시험계획의 개요··························457

9.5.2 최적 4：2：1 할당비 시험계획의 활용·················458

9.6 Minitab을 이용한 가속수명시험 계획의 도출················459

9.6.1 연속검사: 표본크기가 주어질 경우························460

9.6.2 간헐적 검사: 표본크기가 주어질 경우··················469

9.6.3 연속 검사: 신뢰구간 간격이 주어질 경우·············474

● 연습문제 ······················································································476

Chapter 10 열화시험과 가속열화시험 자료의 분석 ·····································479

10.1 개 요 ··················································································481

10.2 열화모형·············································································483

10.2.1 열화경로 모형과 분석법·······································484

10.2.2 선형 열화경로 모형··············································486

10.3 일정계수 열화모형의 분석················································487

10.4 확률계수 열화율 모형의 분석: 의사 고장시간 방법········495

10.5 확률계수 열화율 모형의 분석: 해석적 방법····················514