A Primer. & EVFILURTION of SYSTEfYl RELlfiBILITY fwlllfibility and fnrintrinrbility. Department OF DEFENSE DIRECTOR TEST RND EVRLUFITION. DoD 3235.

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1 DoD H Department OF DEFENSE... - TEST & EVFILURTION of SYSTEfYl RELlfiBILITY fwlllfibility and fnrintrinrbility A Primer DIRECTOR TEST RND EVRLUFITION Office of the Under Secretary of Defense for Resemch md Engineering (TMRCH 1982

2 TEST AND EVALUATION OF SYSTEM RELIABILITY AVAILABILITY MAINTAINABILITY - A PRIMER - Dr. John C. Conlon Army Materiel Systems Analysis Activity Mr. Walter A. Lilius Army Management Engineering Training Activity Lt. Col. Frank H. Tubbesing, Jr., USAF Office of the Director Defense Test and Evaluation Third Edition March 1982 Published by Office of the Director Defense Test and Evaluation Under Secretary of Defense for Research and Engineering Washington, D.C.

3 THE UNDER SECRETARY OF DEFENSE WASHINGTON. D C RESEARCH AND ENGINEERING FOREWORD This handbook is issued under the authority of DoD Instruction , Test and Evaluation of System Reliability, Availability, and Maintainability, February 1, Its purpose is to provide instruction in the analytical assessment of System Reliability, Availability, and Maintainability (RAM) performance. The provisions of this handbook apply to the Office of the Secretary of Defense, the Military Departments, the Organization of the Joint Chiefs of Staff, and the Defense Agencies (hereafter referred to as DoD Components ). This handbook is effective immediately and may be used on an optional basis by DoD Components engaged in system RAM. Send recommended changes to the handbook to: Office of the Director Defense Test and Evaluation OUSDRE/DDTE Washington, D.C DoD Components may obtain copies of this handbook through their own publication channels- Other federal agencies and the public may obtain copies from the Naval Publication and Forma Center, 5801 Tabor Avenue, Philadelphta,Pa &49_ ISHAM LINDER Director Defense Test and Evaluation

4 OFFICE OF THE UNDER SECRETARY OF DEFENSE WASHINGTON. D.C RESEARCH AND ENGINEERING MEMORANDUM FOR TEXT USERS SUBJECT : The Application of Statistical Concepts to Test and Evaluation Test and Evaluation of military systems and equipment is conducted by DoD to support the assessment of system performance characteristics. These assessments are an integral part of the decision process inherent in the acquisition cycle. In many hardware and software controversial issue. Questions development programs, testing has become a which often arise are: How much testing is enough? Is the hardware/software ready for testing? Are hardware requ~re - ments, assessment parameters and critical issues adequately defined? Does the test effort represent the minimum time and resource program consistent with meaningful results? Have the development and operational testing cycles been integrated so as to form an efficient evaluation program? And so on. This text presents concepts and techniques for designing test plans which can verify that previously established system suitability requirements have been achieved. We realize, of course, that test resource availability ay be adversely affected by cost, schedule and operational urgency constraints. In such cases, alternate test plans which represent the most meaningful, timely and cost effective approach, consistent with these constraints, must be developed. In any event, it is essential that all participants understand the critical issues being addressed and the acquisition risks inherent in conducting a limited test program. The design and execution of sound test programs is NO accident. It requires numerous hours of research and planning and a thorough understanding of testing techniques, the test system and its operating scenario. Further, the test results must support the development of realistic performance estimates for the entire production run, after having tested relatively few systems. Herein lies the usefulness of the statistical concepts contained in this text. The topics addressed in this text will familiarize the reader with the statistical concepts relevant to test design and performance assessment. In short, these topics, when combined with common sense and technical expertise formulate the basis of all sound test programs. ii u. Isham Lind;r f Director Defense Test and Evaluation

5 TABLE OF CONTENTS MEMORANDUM FOR TEXT USERS.. CHAPTER 1. INTRODUCTION CHAPTER 2. RELIABILITY... Definition of Terms and Concepts. Reliability Mean Time Between Failures. Failure Rate System Reliability Design Objectives Missicn Reliability..... Logistics (Maintenance/Supply) Related Reliability Reliability Incident Classification Mission Failures System Failures Unscheduled Spares Demands. System/Mission Failures Requiring Spares.... Contractually Chargeable Failures System Reliability Models.... Series Model Redundant Models Redundancy Characteristics Implications of Redundant Design Mixed Models Functional Models Reliability Allocation Summary of Allocation.... Case Study No. 2-l..,..... Case Study No Case Study No Case Study No Case Study No Case Study No Case Study No CHAPTER 3. MAINTAINABILITY. Introduction. Definition of Terms and Concepts. Maintainability Maintenance Preventive Maintenance... Corrective Maintenance... Considerations In Planning Maintainability Assessment. Quantitative Maintainability Indices Mean-Time-To-Repair (MTTR) or Met.....,.. Maximura-Time-To-Repair (MaxTTR) or MmaxC.... Maintenance Ratio (lfr)... Mean-Time-Between-Maintenance-Actions (MRBMA).. Average Number of Technicians Required..... Off-System Maintainability Indices o iii

6 CHAPTER 3. MAINTAINABILITY (continued) Annual Support Cost (ASC).. Diagnostic Systems Introduction Need for Automatic Diagnostic Systems - BIT... Specifying BIT Performance. Percent Detection... Percent Isolation... Automatic Fault Isolation Capability (AFIC). Percent of False Alarms Characteristics External to BIT Case Description.... Basic System/BIT Development and Evaluation Considerations Determination of Basic System Failure Modes and Frequency of Occurrence.. Test and Evaluation of BIT Systems..... Case Study No. 3-l o CHAPTER 4. AVAILABILITY.. Introduction. Definition of Availability.... Elements of Availability..... Definition of Terms Mathematical Expressions of Availability Inherent Availability (Ai). Operational Availability (Ao) Achieved Availability (As). A General Approach for Evaluating Availability.... General Procedure System Availability Assessment Considerations. Recovery Time..... Hardware Requirement Establishment and Trade-Offs.. Availability for Multi-Mission Systems Simulation Models Case Study No. 4-l Case Study No Case Study No Case Study No Case Study No o CHAPTER 5. MATHEMATICAL MODELS OF REL Introduction..... Discrete Models... Continuous Models.. ABILITY Binomial Model Poisson Model Exponential Model Case Study No. 5-l Case Study No Case Study No iv

7 CHAPTER 5. MATHEMATICAL MODELS OF RELIABILITY (continued) Page Case Study No Case Study No Case Study No CHAPTER 6. STATISTICAL CONCEPTS Introduction Point Estimates Confidence Statements Hypothesis Testing Producer s and Consumer s Risks. 6-5 Interface Between Hypothesis Testing and Confidence Statements Test Exposure Case Study No. 6-l Case Study No CHAPTER 7. RELIABLITY DATA ANALYSIS Introduction Types of Reliability Tests Fixed Configuration and Growth Tests Discrete and Continuous Tests. 7-2 Discrete Time Testing Binomial Model: Point Estimate of Failure Probability Binomial Model: Confidence Limits for Failure Probability Binomial Model: Confidence Levels for Preestablished Reliability Limits Approximate Binomial Confidence Limits (Normal Approximation) Approximate Binomial Confidence Limits (Poisson/ Exponential Approximation) 7-5 Point Estimates and Confidence Limits for the Difference/Ratio of Proportions Continuous Time Testing Continuous Time Testing: Failure Pattern Identification Exponential Model: Point Estimate of MTBF Exponential Model: Point Estimates of Reliability andfailurerate Exponential Model: Confidence Intervals and Limits for MTBF o Exponential Model: Confidence Intervals and Limits for Reliability and Failure Rate Case Study No. 7-l Case Study No Case Study No Case Study No Case Study No v

8 CHAPTER 7. RELIABILITY DATA ANALYSIS (continued) PaJ?g Case Study No Case Study No Case Study No Case Study No CHAPTER 8. RELIABILITY TEST PLANNING Introduction. Primary Test Design Parameters.. Test Test Upper and Lower Test Values. Consumer s Risk ( ) and Producer s Risk ( )... Pre- and Post-Test Risk Considerations..... Design for Discrete Time Testing: Binomial Model Exact Solution Procedure.. Approximate Solution Procedures Test Planning Using Normal Approximation.. Test Planning Using Poisson Approximation. Design for Continuous Time Testing: Exponential Model.... Requirement Interpretation. Constant System Failure Rate Assumption..... Discrimination Ratio.... Sources of Exponential Test Plans MIL-STD 105D and MIL-HBK MIL-STD 781 C Appendix B, Table 6: Exponential Test Plans for Standard Discrimination Ratios How To Use Appendix B Table Appendix B, Table 7: Supplemental Exponential Test Plans How To Use Appendix B, Table Graphical Representation of Test Plaming Parameters Poisson Distribution Equations Graphical Poisson Solution Procedure.... Operating Characteristic (OC) Curves Introduction OC Curve Construction.... CaseStudyNo. 8-l Case Study No Case Study No Case Study No Case Study No Case Study No Case Study No vi

9 CHAPTER 9. RELIABILITY GROWTH Introduction. Reliability Growth Concepts... Idealized Growth Planned Growth Growth Tracking Idealized Growth Curve Development Planned Growth Curve Development. Reliability Growth Tracking... Case Study No Case Study No Page CHAPTER 10. DATA BASE CONSIDERATIONS Introduction Test Exposure Considerations One System vs. Several Systems Accelerated Testing and External Environment Prototypes vs. Production Models Composing the Reliability Data Base Age-Dependent Analysis Growth Analysis Combining DTand OT Data Early Deployment Data Early Field Data Retrieval System Lead-The-Force Program Case Study No. 10-l Case Study No O-10 APPENDIX A A-1 Normal Approximation to Binomial... A- 2 A-2 Poisson Approximation to Binomial.... A- 3 A-3 Normal Approximation to Poisson.... A- 4 APPENDIX B Table 1 Table 2 Table 3 Table 4 Table 5 Table 6 Table 7 Table 8 Table 9 Chart I Binomial Tables Normal Tables Cumulative Poisson Probabilities Confidence Limits for A Proportion Chi Square Table Exponential Test Plans for Standard Discrimination Ratios. Supplemental Exponential Test Plans Exponential Confidence Limit Multipliers for MTBF Confidence Limit for MTBF - Time Terminated Reliability Growth Tests... CummuIative Poisson Probabilities B- 2.. B-41.. B-45.. B-51.. B-61.. B-63.. B-64.. B-65.. B vii