Practical Applications of the RIAC System Reliability Toolkit

Practical Applications of the RIAC System Reliability Toolkit

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The purpose of this publication is to provide illustrative examples of the more common mathematical calculations and statistical techniques utilized by reliability engineers in the practical performance of their daily activities. It is intended to be used as a companion to the RIAC “System Reliability Toolkit”, as the foundations of all of the techniques illustrated in this publication are discussed therein.

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Product Description

As any practitioner in the field of reliability can attest, there exists a multitude of mathematical calculations and statistical techniques that can be used to assist the engineer in determining how system requirements should be allocated and how the system design should be modeled, assessed and re-designed in order to maximize the likelihood of satisfying the customer’s expectations or formal requirements. The purpose of this publication is to provide illustrative examples of the more common mathematical calculations and statistical techniques utilized by reliability engineers in the practical performance of their daily activities. It is intended to be used as a companion to the RIAC “System Reliability Toolkit”, as the foundations of all of the techniques illustrated in this publication are discussed therein.

The mathematical and statistical examples illustrated in this publication revolve around a single hypothetical case study, namely, a Flight Control System for a jet aircraft. In addition to providing a common thread throughout this publication, it is hoped that by basing all calculations on a single case study, the reader will come to understand that individual calculations do not exist in a vacuum. Rather, it will reinforce the notion that each phase of a project is linked to (and affects) other phases, and that conclusions drawn from a calculation are often used to influence design decisions, which may then require that previous analyses and calculations be revisited and updated.

Copyright © 2014 by Quanterion Solutions Incorporated. This handbook was developed by Quanterion Solutions Incorporated, in support of the prime contractor (Wyle Laboratories) in the operation of the Department of Defense Reliability Information Analysis Center (RIAC) under Contract HC1047-05-D-4005. The Government has a fully paid up perpetual license for free use of and access to this publication and its contents among all the DOD IACs in both hardcopy and electronic versions, without limitation on the number of users or servers. Subject to the rights of the Government, this document (hardcopy and electronic versions) and the content contained within it are protected by U.S. Copyright Law and may not be copied, automated, re-sold, or redistributed to multiple users without the express written permission. The copyrighted work may not be made available on a server for use by more than one person simultaneously without the express written permission. If automation of the technical content for other than personal use, or for multiple simultaneous user access to a copyrighted work is desired, please contact 877.808.0097 (toll free) or 315.732.0097 for licensing information.

Additional information

ISBN-10:

1-933904-46-1

ISBN-13:

978-1-933904-46-7

Table of Contents

1. Introduction       1
  1.1 CASE STUDY EXAMPLE     1
  1.2 STRUCTURE OF THE BOOK     2
  1.3 RELIABILITY ALLOCATION     3
  1.4 RELIABILITY MODELING     3
  1.5 RELIABILITY PREDICTION     3
  1.6 DATA ANALYSIS OVERVIEW     3
  1.7 DATA ANALYSIS TECHNIQUES     4
  1.8 RELIABILITY GROWTH     4
  1.9 RELIABILITY DEMONSTRATION TESTING     4
  1.10 DESIGN OF EXPERIMENTS     5
  1.11 STATISTICAL PROCESS CONTROL     5
2. Allocation of Hardware Reliability Requirements       7
  2.1 CASE STUDY     7
  2.2 EQUAL APPORTIONMENT TECHNIQUE     8
  2.3 ARINC APPORTIONMENT TECHNIQUE     8
  2.4 FEASIBILITY OF OBJECTIVES TECHNIQUE     10
  2.5 SUMMARY     12
3. Hardware Reliability Modeling       13
  3.1 CASE STUDY     13
  3.2 RELIABILITY BLOCK DIAGRAM     14
  3.3 RELIABILITY MATH MODEL     15
  3.4 SUMMARY     16
4. Hardware Reliability Prediction       17
  4.1 CASE STUDY     17
  4.2 RELIABILITY PREDICTION PROCESS     18
  4.3 RELIABILITY PREDICTION – ACTIVE STICK     18
  4.4 RELIABILITY PREDICTION – ACTUATOR     18
  4.5 RELIABILITY PREDICTION – CONTROL SURFACE INTERFACE     19
  4.6 RELIABILITY PREDICTION – SIGNAL PROCESSING COMPUTER     19
  4.7 RELIABILITY PREDICTION – FLIGHT CONTROL SYSTEM     21
  4.8 SUMMARY     21
5. Overview of Data Collection and Analysis       23
  5.1 CASE STUDY     23
  5.2 ORDER DATA     24
  5.3 QUICK TEST TO DETERMINE IF EXPONENTIAL DISTRIBUTION MIGHT APPLY     24
  5.4 RANKING DATA     25
  5.5 NORMAL DISTRIBUTION     26
  5.6 WEIBULL DISTRIBUTION     27
  5.7 FAILURE DENSITY, HAZARD RATE AND RELIABILITY – TIME INTERVAL DATA     28
  5.8 FAILURE DENSITY, HAZARD RATE AND RELIABILITY – FAILURE INTERVAL DATA     30
  5.9 LAPLACE STATISTIC     32
6. Data Analysis Techniques       33
  6.1 CASE STUDY     33
  6.2 ORDER DATA     34
  6.3 WEIBULL ANALYSIS     35
  6.4 REGRESSION ANALYSIS     37
  6.5 ANALYSIS OF VARIANCE     39
  6.6 HYPOTHESIS TESTING     42
  6.7 CONFIDENCE INTERVALS     46
  6.8 SUMMARY     47
7. Reliability Growth Testing       49
  7.1 CASE STUDY     49
  7.2 DUANE MODEL – RGT PLANNING     51
  7.3 CROW/AMSAA MODEL – RELIABILITY GROWTH TRACKING MODEL CONTINUOUS (RGTMC)     53
  7.4 SUMMARY     58
8. Reliability Demonstration/Qualification Testing       59
  8.1 CASE STUDY     59
  8.2 OVERVIEW OF THE RDT DEFINITION PROCESS     61
  8.3 ZERO-FAILURE TEST     61
  8.4 FIXED-LENGTH RDT/RQT     62
  8.5 PROBABILITY-RATIO SEQUENTIAL TEST (PRST)     63
  8.6 RDT PERFORMANCE     66
  8.7 SUMMARY     66
9. Design of Experiments       67
  9.1 CASE STUDY     67
  9.2 FULL-FACTORIAL DOE     69
  9.3 CONCLUSION OF FULL-FACTORIAL EXPERIMENT EXAMPLE     73
  9.4 FRACTIONAL-FACTORIAL DOE     74
  9.5 CONCLUSION OF FRACTIONAL-FACTORIAL EXPERIMENT EXAMPLE     76
10. Statistical Process Control       77
  10.1 CASE STUDY     77
  10.2 X̅ AND R CONTROL CHARTS     79
11. Summary and Conclusions       87
  11.1 CASE STUDY SUMMARY     87
  11.2 CONCLUSION     92