AMCP 706-200: Математическое приложение и глоссарий - Руководство по надежности (EN)

Downloaded from https://www.everyspec.com I AMC PAMPHLET c~ ENGINEERING DESIGN I -_-"-"-""'- DEVELOPMENTGUIDE 4 FOR ELIABILITY MATHEMATICAL JPPENDIX' AND GLOSSARY_ .;pmvcd ior public releau -, ;"* , ........ :)ution Unlimzit~i I : D!STIUBUTIOi4 STA'TEMENT A HEADQUARTERS, US ARMY MATERIEL COMMAND A' rI

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Downloaded from https://www.everyspec.com At4CP 706-200J DEPARTMENT OF THE ARMY HEADQUARTERS UNITED STATES ARMY MATERIEL COMMAND 5001 Eisenhower Ave., Alexandria. VA 22333 AMC PAMPHLET NO. 706-20 8 January 1976 ENGINEERING DE §(GN HANDBOOK DEVELOPMENT GUIDE FOP RELIABILITY, PART SIX MATHEMATICAL APP NDIX AND GLOSSARY TABLE OI0CONTENTS Pararaph //Page LIST OF ILLUSTRATIONS....... ........... vii LIST OF TABLES .................. ix PREFACE................................ xi CHAPTER 1. GLOSSARY CHAPTER 2!PROJBABILITY DISI iUBUTIONS, SOME CAUTIONS AND NAMES 2-1 Cautions .. . . . . . . . . . . . ... . . . 2-1 2-2 Naming Probability Distributlons. .............. 2-2 CHAPTER 1.

BINOMIAL DISTRIBUTION 3-0 List of Symbols........................~... 3-1 3-1 Introduction ............................. 3-1 3-2 Formulas ................................ 3-2 3-3 Tables and Curves.......................... 3-2 3-5 Randomized Exact s-Conf idence Intervals .......... 3-4 3-6 Choosing a s-Confidence Level .. ............... 3-12 3-7 Examples ................................ 3-12 3-7.1 Example No. 1 .. .................... 3-42 3-7.2 Example No. 2 ........................... 3-24 ----- a. - References ................................ 3-25 ** CHAPTER 4. POISSON DISTRIBUTION ?A, 6f t I 4-0 List of Symbols ............................ 4-1 .. ........... ...

4-1 Introduction ............................. 4-1 .......-... . ... 4-2 Formulas ................................ 4-2 4-3 Tables and Curves.......................... 4-2 1OA~~rc. 4--4 Parameter Estimation ........................ 4-2 ~ ;-~ 4-5 Ranoomized Exact s-Confidence Intervals ......... 4-6 4-7 Example, Life Test Results....................... A References............................... 4-12 {*

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Downloaded from https://www.everyspec.com AMCP 706.2% Paragraph J Page TABLE OF;CONTENTS (Cont'd) CHAPTER 5. GAUSSIAN (s-NORMAL) DISTRIBUTION' 5-0 List of Symbols ........................... 5-I 5-1 Introduction ............................ 5-2 5-2 Formulas ......... ......................... 5-2 5-3 Tables and Curves ........................... 5-2 5-4 Parameter Estimation, Uncensored Samples ........ 5-13 5-5 Examples .................................... 5- 13 5-6 Parameter Estimation, Censored Samples ......... 5-14 References ................................. 5-15 CHAPTER 6. PROBABILITY DISTRIBUTIONS DERIVED FROM THE GAUSSIAN DISTRIBUTION 6-0 List of Symbols ...........................

6-1 6-1 Tntroduction ............................... 6-2 6-2 Chi-square (x 2 ) Distribution .................. 6-2 6-2.1 Formulas ............................... 6-2 6-2.2 Tables ................................... 6-3 6-3 Chi-squarefnu (xe /v) Distribution ............... 6-3 6-3.1 Formulas ................................. 6-3 6-3.2 Tables ................................ 6-7 6-4 Student's t-Distribution ....................... 6-7 6-4.1 Formulas ............................... 6-7 6-4.2 Tables ................................. 6-7 6-5 Fisher-Snedecor F Distribotion ................ 6-12 6-5.1 Formulas ......... /....................... 6-12 6-5.2 Tables ........ ..........................

6-13 Refetences ................................. 6-22 CHAPTER 7 'EXPONENTIAL DISTRIBUTION 7-0 List of Symbols ............................. 7-1 7-1 Introduction ............................... 7-1 7-2 Foimulas ................................... 7-I 7-3 Tables ............................ ........ 7-2 7-4 Paameter Estimation ....................... 7-2 References .............................. 7-8 CHAPTER 8. WEIBULL DISTRIBUTION 8-0 List of Symbols ........................... 8-1 8-1 Introduction ............................... 8-1 ( i . ....... . . . ...... . .. ' , . ? " : ,

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Downloaded from https://www.everyspec.com MP 706-200 TABLE OF CONTENTS (Cont'd) Paragraph Page 8-2 Form ulas ................................... 8-2 8-3 Tables ..................................... 8-2 8-4 Parameter Estimation ......................... 8-2 8-4.1 Graphical Method ............................ 8-7 8-4.2 Maximum Likelihood Method -.......... 8-7 8-4.3 Linear Estimation Methods................... 8-10 8-4.4 Test for Failure Rate: Increasing, Decreasing, or Constant ................................. 8-10 8-5 Comparison With Lognormal Distribution ........ 8-10 References ................................. 8-11 CHAPTER 0.

LOGNORMAL DISTRIBUTION \ 9-,0 list of Symbols ......................... ' 9-1 9-1 Introduction ............................. .9-1 9-2 Formulas ................................... 9-2 9-3 Tables ....................................... 9-4 9-4 Parameter Estimation ......................... 9-4 9-4.1 Uncensored Data ......................... 9-6 9-4.2 Censored Data ............................. 9-10 References ................................. 9-10 CHAPTER 10. BETA DISTRIBUTION, 1O-0 List of Symbols .................. .......... 10--i 10-1 introduction ............................... 10 -2 10-2 Formulas ... ............................... . 10-2 10-3 Tables .

.................................... 10-3 10-4 Parameter EAtimation ......................... 10-3 References ................................. 10-7 CHAPTER 11. GAMMA DISTRIBUTION ' 11-0 List of Symbols ............................. 11-1 11-1 Introduction .......... .................... 11-1 11-2 Form ulas ................................... 11-1 11-3 Tables ..................................... 11-2 11-4 Parar-,zter Estimation ......................... 11-2 11-5 Gamn.a Function ........................... 11-4 References...............................11-4 CHAPTER 12. s-CONFIDENCE 12-0 List of Symbols ........... ... ........ .. 12-1 12-1 Introduction ..... .........................

12-1 0_.,, , _ .. - . -- .-- . ., : , .... o1, W . - - . , . ',-, .... .. - - - - - - . . .. ,, ...... , r: '

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