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Certified Reliability Engineer

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The following information is provided by the American Society for Quality (ASQ):


Certification Requirements

Education and/or Experience

You must have eight years of on-the-job experience in one or more of the areas of the Certified Reliability Engineer Body of Knowledge. A minimum of three years of this experience must be in a decision-making position. “Decision-making” is defined as the authority to define, execute, or control projects/processes and to be responsible for the outcome. This may or may not include management or supervisory positions.

If you are now or were previously certified by ASQ as a Quality Engineer, Quality Auditor, Software Quality Engineer, or Quality Manager, experience used to qualify for certification in these fields often applies to certification as a Reliability Engineer.

If you have completed a degree* from a college, university, or technical school with accreditation accepted by ASQ, part of the eight-year experience requirement will be waived, as follows (only one of these waivers may be claimed):

  • Diploma from a technical or trade school—one year will be waived
  • Associate degree—two years waived
  • Bachelor’s degree—four years waived
  • Master’s or doctorate—five years waived

*Degrees/diplomas from foreign educational institutions must be equivalent to degrees from U.S. educational institutions.

Examination

Each certification candidate is required to pass a written examination that consists of multiple choice questions that measure comprehension of the Body of Knowledge. The Reliability Engineer examination is a one-part, 150-question, four-hour exam and is offered in the English language only.

Examinations are conducted twice a year, in  March and October, by local ASQ sections and international organizations. All examinations are open-book. Each participant must bring his or her own reference materials. Use of reference materials and calculators is explained in the seating letter provided to applicants.

Please Note: The Body of Knowledge for certification is affected by new technologies, policies, and the changing dynamics of manufacturing and service industries. Changed versions of the examination based on the current Body of Knowledge are used at each offering.

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Body of Knowledge

The topics in this Body of Knowledge include additional detail in the form of subtext explanations and the cognitive level at which the questions will be written. This information will provide useful guidance for both the Examination Development Committee and the candidates preparing to take the exam. The subtext is not intended to limit the subject matter or be all-inclusive of what might be covered in an exam. It is intended to clarify the type of content to be included in the exam. The descriptor in parentheses at the end of each entry refers to the highest cognitive level at which the topic will be tested. A more comprehensive description of cognitive levels is provided at the end of this document.
  1. RELIABILITY MANAGEMENT (18 Questions)
    1. Strategic management
      1. Benefits of reliability engineering
        Describe how reliability engineering techniques and methods improve programs, processes, products, systems, and services. (Understand)
      2. Interrelationship of safety, quality, and reliability
        Define and describe the relationships among safety, reliability, and quality. (Understand)
      3. Role of the reliability function in the organization
        Describe how reliability techniques can be applied in other functional areas of the organization, such as marketing, engineering, customer /product support, safety and product liability, etc. (Apply)
      4. Reliability in product and process development
        Integrate reliability engineering techniques with other development activities, concurrent engineering, corporate improvement initiatives such as lean and six sigma methodologies, and emerging technologies. (Apply)
      5. Failure consequence and liability management
        Describe the importance of these concepts in determining reliability acceptance criteria. (Understand)
      6. Warranty management
        Define and describe warranty terms and conditions, including warranty period, conditions of use, failure criteria, etc., and identify the uses and limitations of warranty data. (Understand)
      7. Customer needs assessment
        Use various feedback methods (e.g., quality function deployment (QFD), prototyping, beta testing) to determine customer needs in relation to reliability requirements for products and services. (Apply)
      8. Supplier reliability
        Define and describe supplier reliability assessments that can be monitored in support of the overall reliability program. (Understand)
    2. Reliability program management
      1. Terminology
        Explain basic reliability terms (e.g., MTTF, MTBF, MTTR, availability, failure rate, reliability, maintainability). (Understand)
      2. Elements of a reliability program
        Explain how planning, testing, tracking, and using customer needs and requirements are used to develop a reliability program, and identify various drivers of reliability requirements, including market expectations and standards, as well as safety, liability, and regulatory concerns. (Understand)
      3. Types of risk
        Describe the relationship between reliability and various types of risk, including technical, scheduling, safety, financial, etc. (Understand)
      4. Product lifecycle engineering
        Describe the impact various lifecycle stages (concept/design, introduction, growth, maturity, decline) have on reliability, and the cost issues (product maintenance, life expectation, software defect phase containment, etc.) associated with those stages. (Understand)
      5. Design evaluation
        Use validation, verification, and other review techniques to assess the reliability of a product’s design at various lifecycle stages. (Analyze)
      6. Systems engineering and integration
        Describe how these processes are used to create requirements and prioritize design and development activities. (Understand)
    3. Ethics, safety, and liability
      1. Ethical issues
        Identify appropriate ethical behaviors for a reliability engineer in various situations. (Evaluate)
      2. Roles and responsibilities
        Describe the roles and responsibilities of a reliability engineer in relation to product safety and liability. (Understand)
      3. System safety
        Identify safety-related issues by analyzing customer feedback, design data, field data, and other information. Use risk management tools (e.g., hazard analysis, FMEA, FTA, risk matrix) to identify and prioritize safety concerns, and identify steps that will minimize the misuse of products and processes. (Analyze)

     
  2. PROBABILITY AND STATISTICS FOR RELIABILITY (27 Questions)
    1. Basic concepts
      1. Statistical terms
        Define and use terms such as population, parameter, statistic, sample, the central limit theorem, etc., and compute their values. (Apply)
      2. Basic probability concepts
        Use basic probability concepts (e.g., independence, mutually exclusive, conditional probability) and compute expected values. (Apply)
      3. Discrete and continuous probability distributions
        Compare and contrast various distributions (binomial, Poisson, exponential, Weibull, normal, log-normal, etc.) and their functions (e.g., cumulative distribution functions (CDFs), probability density functions (PDFs), hazard functions), and relate them to the bathtub curve. (Analyze)
      4. Poisson process models
        Define and describe homogeneous and non-homogeneous Poisson process models (HPP and NHPP). (Understand)
      5. Non-parametric statistical methods
        Apply non-parametric statistical methods, including median, Kaplan-Meier, Mann-Whitney, etc., in various situations. (Apply)
      6. Sample size determination
        Use various theories, tables, and formulas to determine appropriate sample sizes for statistical and reliability testing. (Apply)
      7. Statistical process control (SPC) and process capability
        Define and describe SPC and process capability studies (Cp, Cpk, etc.), their control charts, and how they are all related to reliability. (Understand)
    2. Statistical inference
      1. Point estimates of parameters
        Obtain point estimates of model parameters using probability plots, maximum likelihood methods, etc. Analyze the efficiency and bias of the estimators. (Evaluate)
      2. Statistical interval estimates
        Compute confidence intervals, tolerance intervals, etc., and draw conclusions from the results. (Evaluate)
      3. Hypothesis testing (parametric and non-parametric)
        Apply hypothesis testing for parameters such as means, variance, proportions, and distribution parameters. Interpret significance levels and Type I and Type II errors for accepting/rejecting the null hypothesis. (Evaluate)

     
  3. RELIABILITY IN DESIGN AND DEVELOPMENT (26 Questions)
    1. Reliability design techniques
      1. Environmental and use factors
        Identify environmental and use factors (e.g., temperature, humidity, vibration) and stresses (e.g., severity of service, electrostatic discharge (ESD), throughput) to which a product may be subjected. (Apply)
      2. Stress-strength analysis
        Apply stress-strength analysis method of computing probability of failure, and interpret the results. (Evaluate)
      3. FMEA and FMECA
        Define and distinguish between failure mode and effects analysis and failure mode, effects, and criticality analysis and apply these techniques in products, processes, and designs. (Analyze)
      4. Common mode failure analysis
        Describe this type of failure (also known as common cause mode failure) and how it affects design for reliability. (Understand)
      5. Fault tree analysis (FTA) and success tree analysis (STA)
        Apply these techniques to develop models that can be used to evaluate undesirable (FTA) and desirable (STA) events. (Analyze)
      6. Tolerance and worst-case analyses
        Describe how tolerance and worst-case analyses (e.g., root of sum of squares, extreme value) can be used to characterize variation that affects reliability. (Understand)
      7. Design of experiments
        Plan and conduct standard design of experiments (DOE) (e.g., full-factorial, fractional factorial, Latin square design). Implement robust-design approaches (e.g., Taguchi design, parametric design, DOE incorporating noise factors) to improve or optimize design. (Analyze)
      8. Fault tolerance
        Define and describe fault tolerance and the reliability methods used to maintain system functionality. (Understand)
      9. Reliability optimization
        Use various approaches, including redundancy, derating, trade studies, etc., to optimize reliability within the constraints of cost, schedule, weight, design requirements, etc. (Apply)
      10. Human factors
        Describe the relationship between human factors and reliability engineering. (Understand)
      11. Design for X (DFX)
        Apply DFX techniques such as design for assembly, testability, maintainability environment (recycling and disposal), etc., to enhance a product’s producibility and serviceability. (Apply)
      12. Reliability apportionment (allocation) techniques
        Use these techniques to specify subsystem and component reliability requirements. (Analyze)
    2. Parts and systems management
      1. Selection, standardization, and reuse
        Apply techniques for materials selection, parts standardization and reduction, parallel modeling, software reuse, including commercial off-the-shelf (COTS) software, etc. (Apply)
      2. Derating methods and principles
        Use methods such as S-N diagram, stress-life relationship, etc., to determine the relationship between applied stress and rated value, and to improve design. (Analyze)
      3. Parts obsolescence management
        Explain the implications of parts obsolescence and requirements for parts or system requalification. Develop risk mitigation plans such as lifetime buy, backwards compatibility, etc. (Apply)
      4. Establishing specifications
        Develop metrics for reliability, maintainability, and serviceability (e.g., MTBF, MTBR, MTBUMA, service interval) for product specifications. (Create)

     
  4. RELIABILITY MODELING AND PREDICTIONS (22 Questions)
    1. Reliability modeling
      1. Sources and uses of reliability data
        Describe sources of reliability data (prototype, development, test, field, warranty, published, etc.), their advantages and limitations, and how the data can be used to measure and enhance product reliability. (Apply)
      2. Reliability block diagrams and models
        Generate and analyze various types of block diagrams and models, including series, parallel, partial redundancy, time-dependent, etc. (Create)
      3. Physics of failure models
        Identify various failure mechanisms (e.g., fracture, corrosion, memory corruption) and select appropriate theoretical models (e.g., Arrhenius, S-N curve) to assess their impact. (Apply)
      4. Simulation techniques
        Describe the advantages and limitations of the Monte Carlo and Markov models. (Apply)
      5. Dynamic reliability
        Describe dynamic reliability as it relates to failure criteria that change over time or under different conditions. (Understand)
    2. Reliability predictions
      1. Part count predictions and part stress analysis
        Use parts failure rate data to estimate system- and subsystem-level reliability. (Apply)
      2. Reliability prediction methods
        Use various reliability prediction methods for both repairable and non-repairable components and systems, incorporating test and field reliability data when available (Apply)

     
  5. RELIABILITY TESTING (24 Questions)
    1. Reliability test planning
      1. Reliability test strategies
        Create and apply the appropriate test strategies (e.g., truncation, test–to-failure, degradation) for various product development phases. (Create)
      2. Test environment
        Evaluate the environment in terms of system location and operational conditions to determine the most appropriate reliability test. (Evaluate)
    2. Testing during development
      Describe the purpose, advantages, and limitations of each of the following types of tests, and use common models to develop test plans, evaluate risks, and interpret test results. (Evaluate)
      1. Accelerated life tests (e.g., single-stress, multiple-stress, sequential stress, step-stress)
      2. Discovery testing (e.g., HALT, margin tests, sample size of 1),
      3. Reliability growth testing (e.g., test, analyze, and fix (TAAF), Duane)
      4. Software testing (e.g., white-box, black-box, operational profile, and  fault-injection)
    3. Product testing
      Describe the purpose, advantages, and limitations of each of the following types of tests, and use common models to develop product test plans, evaluate risks, and interpret test results. (Evaluate)
      1. Qualification/demonstration testing (e.g., sequential tests, fixed-length tests)
      2. Product reliability acceptance testing (PRAT)
      3. Ongoing reliability testing (e.g., sequential probability ratio test [SPRT])
      4. Stress screening (e.g., ESS, HASS, burn-in tests)
      5. Attribute testing (e.g., binomial, hypergeometric)
      6. Degradation (wear–to-failure) testing

         
  6. MAINTAINABILITY AND AVAILABILITY (15 Questions)
    1. Management strategies
      1. Planning
        Develop plans for maintainability and availability that support reliability goals and objectives. (Create)
      2. Maintenance strategies
        Identify the advantages and limitations of various maintenance strategies (e.g., reliability-centered maintenance (RCM), predictive maintenance, repair or replace decision making), and determine which strategy to use in specific situations. (Apply).
      3. Availability tradeoffs
        Describe various types of availability (e.g., inherent, operational), and the tradeoffs in reliability and maintainability that might be required to achieve availability goals. (Apply)
    2. Maintenance and testing analysis
      1. Preventive maintenance (PM) analysis
        Define and use PM tasks, optimum PM intervals, and other elements of this analysis, and identify situations in which PM analysis is not appropriate. (Apply)
      2. Corrective maintenance analysis
        Describe the elements of corrective maintenance analysis (e.g., fault-isolation time, repair/replace time, skill level, crew hours) and apply them in specific situations. (Apply)
      3. Non-destructive evaluation
        Describe the types and uses of these tools (e.g., fatigue, delamination, vibration signature analysis) to look for potential defects. (Understand)
      4. Testability
        Use various testability requirements and methods (e.g., built in tests (BITs), false-alarm rates, diagnostics, error codes, fault tolerance) to achieve reliability goals (Apply)
      5. Spare parts analysis
        Describe the relationship between spare parts requirements and reliability, maintainability, and availability requirements. Forecast spare parts requirements using field data, production lead time data, inventory and other prediction tools, etc. (Analyze)

     
  7. DATA COLLECTION AND USE (18 Questions)
    1. Data collection
      1. Types of data
        Identify and distinguish between various types of data (e.g., attributes vs. variable, discrete vs. continuous, censored vs. complete, univariate vs. multivariate). Select appropriate data types to meet various analysis objectives. (Evaluate)
      2. Collection methods
        Identify appropriate methods and evaluate the results from surveys, automated tests, automated monitoring and reporting tools, etc., that are used to meet various data analysis objectives. (Evaluate)
      3. Data management
        Describe key characteristics of a database (e.g., accuracy, completeness, update frequency). Specify the requirements for reliability-driven measurement systems and database plans, including consideration of the data collectors and users, and their functional responsibilities. (Evaluate)
    2. Data use
      1. Data summary and reporting
        Examine collected data for accuracy and usefulness. Analyze, interpret, and summarize data for presentation using techniques such as trend analysis, Weibull, graphic representation, etc., based on data types, sources, and required output. (Create)
      2. Preventive and corrective action
        Select and use various root cause and failure analysis tools to determine the causes of degradation or failure, and identify appropriate preventive or corrective actions to take in specific situations. (Evaluate)
      3. Measures of effectiveness
        Use various data analysis tools to evaluate the effectiveness of preventive and corrective actions in improving reliability. (Evaluate)
    3. Failure analysis and correction
      1. Failure analysis methods
        Describe methods such as mechanical, materials, and physical analysis, scanning electron microscopy (SEM), etc., that are used to identify failure mechanisms. (Understand)
      2. Failure reporting, analysis, and corrective action system (FRACAS)
        Identify the elements necessary for a FRACAS to be effective, and demonstrate the importance of a closed-loop process that includes root cause investigation and follow up. (Apply)
 

NOTE: Approximately 20% of the CRE exam will require candidates to perform mathematical functions.

 

Levels of Cognition
based on Bloom’s Taxonomy – Revised (2001)

In addition to content specifics, the subtext for each topic in this BOK also indicates the intended complexity level of the test questions for that topic. These levels are based on “Levels of Cognition” (from Bloom’s Taxonomy – Revised, 2001) and are presented below in rank order, from least complex to most complex.

Remember
Recall or recognize terms, definitions, facts, ideas, materials, patterns, sequences, methods, principles, etc.

Understand
Read and understand descriptions, communications, reports, tables, diagrams, directions, regulations, etc.

Apply
Know when and how to use ideas, procedures, methods, formulas, principles, theories, etc.
 
Analyze
Break down information into its constituent parts and recognize their relationship to one another and how they are organized; identify sublevel factors or salient data from a complex scenario.

Evaluate
Make judgments about the value of proposed ideas, solutions, etc., by comparing the proposal to specific criteria or standards.

Create
Put parts or elements together in such a way as to reveal a pattern or structure not clearly there before; identify which data or information from a complex set is appropriate to examine further or from which supported conclusions can be drawn.

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Sample Questions

  1. Which of the following is best defined as the practice of using parallel components and subsystems?
    1. Maintainability
    2. Reliability
    3. Optimization
    4. Redundancy

  2. Balancing a reliability requirement against other design parameters such as performance, cost, or schedule, and then analyzing the consequences of placing special emphasis on one of these factors is called
    1. reliability allocation
    2. reliability predictions
    3. trade-off decisions
    4. system modeling


  3. Software reliability planning includes all of the following EXCEPT
    1. selecting models for data analysis and prediction
    2. modeling acquisition of computer software systems
    3. trade-offs of general purpose programs vs. commercially available programs
    4. trade-offs involving cost, schedule, and failure intensity of software products

  4. The lifetime of a mechanical lifter is normally distributed with a mean of 100 hours and a standard deviation of 3 hours. What is the reliability of the lifter at 106 hours?
    1. 0.0228
    2. 0.0570
    3. 0.9430
    4. 0.9772

  5. In an analysis of variance, which of the following distributions is the basis for determining whether the variance estimates are all from the same population?
    1. Chi square
    2. Student's t
    3. Normal
    4. F

  6. A full factorial design of experiments has four factors. The first factor has two levels, the second factor has three levels, the third factor has two levels, and the final factor has four levels. How many runs are are required for this analysis?
    1. 16
    2. 48
    3. 192
    4. 256

  7. In a certain application, two identical transducers are used to measure the vacuum in a system. The system is considered to have failed if either of the vacuums read by the transducers varies from the standard by more than 10 mm Hg. Which of the following is the correct reliability logic block diagram for the transducer assembly?

  8. On the basis of the fault tree below, what is the likelihood of the top event occurring?
    1. 0.0044
    2. 0.2600
    3. 0.3000
    4. 0.5200
  9. Assuming perfect switching and perfect starting, which of the following systems has the longest mean life if each system consisits of n units with identical reliability?
    1. A series system
    2. A parallel system
    3. A k out of n system
    4. A cold standby system

  10. Questions 10-12 refer to the following situation:

    A high incidence of failures has developed during aircraft acceptance testing over the last several months. The identified failure is that an instrument panel light has malfunctioned on 6 of the last 10 aircraft tested. This problem needs to be investigated and a Failure Reporting and Corrective Action System (FRACAS) needs to be completed without stopping aircraft production.

  11.   The first step of the investigation should be to
    1. collect additional data on similar events over the last two years
    2. conduct failure analysis to determine the failure mode and mechanism
    3. conduct surveillance testing on suspect components
    4. establish a cross-functional team to brainstorm on the cause and effect
  12.   If the cause of the failure is determined to be a faulty subassembly manufactured only by a single supplier, and this situation is threatening to shut down aircraft production, the next step should be to
    1. visit the supplier to assist in determining the root cause of the problem
    2. initiate a supplier corrective action and return all of the unsorted inventory
    3. issue a Government and Industry Data Exchange Program (GIDEP) alert
    4. update the inspection instruction and retrain receiving inspection

  13.   If a corrective action notice was sent to the supplier of a faulty subassembly, and the supplier's response states that the root cause is simply an operation error, the next step should be to
    1. accept the response and close the FRACAS
    2. visit the supplier to develop a better understanding of the root cause
    3. issue a Government and Industry Data Exchange Program (GIDEP) alert
    4. being looking for a new supplier

  14. Which of the following is an appropriate use for experimental design?
    1. Establishing product requirements
    2. Developing a fault-tree analysis
    3. Ensuring the robust design of a product
    4. Analyzing customer complaint reports

  15. Which of the following is NOT considered good practice in reliability design?
    1. Using proven parts
    2. Using series design
    3. Using failure mode and effects analysis (FMEA)
    4. Simplifying item configuration

  16. According to Taguchi, robustly designed experiments should employ all of the following techniques EXCEPT
    1. inner and outer arrays
    2. signal-to-noise ratios
    3. linear graphs
    4. fold-over capabilities

  17. Which of the following measures can be used to find a quick approximation of the availability of a system?
    1. Mean time to failure (MTTF) and mean time to repair (MTTR)
    2. Failure rate and failure mode
    3. Mission time and failure rate
    4. Downtime and time to repair

  18. The investment in automated test equipment is often justified under which of the following circumstances
    1. Numerous tests must be performed.
    2. Repair times must be short.
    3. Conformance records are required.
    4. Traceable records are required.

  19. For a company operating multiple units of production equipment, the observed failure rate is 42 x 10-6 failures per operating hour, and the preventive maintenance rate is 320 x 10-6 actions per hour. What is the mean time between corrective and preventive maintenance (MTBM)?
    1. 2,688.2 hr
    2. 2,762.4 hr
    3. 2,840.9 hr
    4. 26,935.0 hr

  20. All of the following are purposes of a production reliability assurance test (PRAT) EXCEPT
    1. detect significant shifts between the as-built reliability requirements and the as-assigned reliability requirements
    2. assess performance against reliability requirements
    3. assess actual product reliability against reliability requirements
    4. minimize the need for specific process controls

  21. The primary aim of sequential-life testing is to determine
    1. the probability density function of failures
    2. the mean time between failures (MTBF)
    3. whether a lot meets the reliability goal
    4. whether the stress-level variation is significant

  22. A small sample from a product population is subjected to multiple levels of elevated stress. Which of the following could be used to model the life of the product?
    1. Poisson process
    2. Pascal expansion
    3. Pareto rule
    4. Inverse power law

  23. Which of the following are important elements of the concept of risk?
    1. Frequency
    2. Schedule
    3. Damage

     

    1. I and II only
    2. I and III only
    3. II and III only
    4. I, II, and III

  24. Which of the following tools is used to analyze the safety of a system?
    1. Fault-tree analysis
    2. Failure reporting and corrective action system
    3. Reliability allocation
    4. Environmental stress screening

  25. System-safety analytical techniques included all EXCEPT
    1. hazards analyses
    2. fault tree analyses
    3. logic diagram analyses
    4. design readiness reviews

  26. A component fails on the average of once every 4 years with 75% of the failures observed to occur during stormy weather. If there are 12 hours of stormy weather to every 240 hours of good weather, what are the failure rates for stormy and good weather respectively?
  27. A go/no-go device is tested until it fails. If X is the number of tests to first failure with no wear out present, and the probability of success on each test is .99, then the probability that X is greater than 5 is:
    1. .9310
    2. .9410
    3. .9510
    4. .9610

  28. The best way to set an overall reliability goal is to
    1. write a specification calling for a product to have high realiability and incorporate it into a contract
    2. put down specific numerical requirements for reliability, statements of operating environments, and a definition of successful product performance
    3. insist that the goal be expressed in terms of mean-time-between-failures for all components and assemblies
    4. indicate who would be at fault if the desired reliability is not obtained during the warranty

  29. Weibull analysis is a way to quickly and easily analyze field data or interval test data. The limits of the use of this technique include having a good estimate for the:
    1. MTBF
    2. expected life
    3. shape parameter
    4. average quality of the production lots

  30. A system consists of 4 parallel units each having a reliability of 0.80. The system can still complete its mission with only 2 units functioning. If the failure rate is constant and failures are independent then the system reliability will be:
    1. 0.4096
    2. 0.5376
    3. 0.8192
    4. 0.9728

  31. Given a reliability growth test in progress having accumulated 4 failures during 5000 test hours. Assume a growth rate of 0.3, what is the expected MTBF at 25,000 hours?
    1. 1250 hrs
    2. 1895 hrs
    3. 2026 hrs
    4. 3856 hrs

  32. Successful operation of System S, illustrated below, requires that at least 1 out of 3 through paths be good. The 3 paths are ABC, AEF, and DEF.

    If A and D have predicted reliability of .95, and B, C, E, and F each have a predicted reliability of .99, find the predicted reliability (Rs) of the system.

    1. .996
    2. .997
    3. .998
    4. .999

  33. A Weibull distribution has been found to describe the reliability distribution with characteristic life= 12,000 hrs., and shape parameter If these are good parameters, at what time will reliability decrease to .85?
    1. 2204 hrs
    2. 3503 hrs
    3. 4838 hrs
    4. 5254 hrs

Answers:

1. d 6. b 11. a 16. a 21. d 26. c 31. a
2. c 7. a 12. b 17. a 22. b 27. b 32. d
3. b 8. a 13. c 18. b 23. a 28. c  
4. a 9. d 14. b 19. d 24. d 29. d
5. d 10. b 15. d 20. c 25. a 30. c

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