Reliability Demonstration Testing
Reliability demonstration testing provides statistical evidence that a product meets its specified reliability requirements. Unlike development testing that seeks to find and fix problems, demonstration testing formally proves to customers, regulators, and internal stakeholders that reliability targets have been achieved with quantified confidence levels.
These tests transform reliability claims from engineering estimates into statistically validated statements. The methods covered in this article enable engineers to design efficient test programs that balance the need for conclusive evidence against practical constraints of time, cost, and available test units.
Test Planning and Design
Effective reliability demonstration begins with thorough test planning that aligns testing objectives with contractual requirements and available resources. Test planning establishes the statistical framework, defines success criteria, and ensures that results will be accepted by all stakeholders.
Requirements Analysis
Test planning starts with a clear understanding of the reliability requirements to be demonstrated. These requirements typically specify a reliability metric such as mean time between failures, failure rate, or probability of survival along with a confidence level. For example, a requirement might state that the product must demonstrate a mean time between failures of 10,000 hours with 90% confidence.
Requirements analysis also identifies the operational conditions under which reliability must be demonstrated. Environmental parameters, duty cycles, and stress levels define the test conditions. Misalignment between test conditions and actual field conditions can invalidate demonstration results, making careful requirements interpretation essential.
Test Strategy Selection
Several testing strategies can demonstrate the same reliability requirement, each with different implications for test duration, sample size, and risk. Fixed-time tests run for a predetermined duration and count failures. Fixed-failure tests continue until a specified number of failures occur. Sequential tests make accept or reject decisions based on accumulating evidence and can terminate earlier than fixed designs when evidence strongly supports either conclusion.
The choice of strategy depends on factors including available test time, number of test units, cost of failures, and whether interim decisions are valuable. Programs with tight schedules often favor sequential methods that offer the possibility of early acceptance, while programs requiring definitive evidence may prefer fixed designs with predetermined test durations.
Sample Size Determination
Sample size calculations balance statistical power against practical constraints. Larger samples provide stronger evidence and higher confidence but increase cost and require more test units. The relationship between sample size, test duration, confidence level, and reliability target determines the minimum resources needed for valid demonstration.
For time-based reliability metrics, the total test time accumulation across all units matters more than the specific combination of units and time per unit. Ten units tested for 1,000 hours each provide the same statistical power as twenty units tested for 500 hours, assuming failures follow an exponential distribution. This equivalence allows flexibility in test design to accommodate unit availability and facility constraints.
Success Run Testing
Success run testing, also called zero-failure testing, demonstrates reliability by testing a calculated number of units for a specified duration without observing any failures. This approach provides a simple pass-fail outcome that is easily understood by non-statistical audiences while offering efficient demonstration when reliability is high.
Theoretical Foundation
Success run testing relies on the relationship between observed success and underlying reliability. If the true reliability equals or exceeds the requirement, the probability of observing zero failures in the test equals or exceeds the specified confidence level. Conversely, if the true reliability falls below the requirement, failures become increasingly likely as sample size grows.
The mathematical basis derives from the binomial distribution for discrete success and failure outcomes or the exponential distribution for continuous operating time. For a reliability requirement expressed as probability of survival R with confidence C, the required sample size n follows from the relationship (1-C) = (1-R) raised to the power n, yielding n = ln(1-C) / ln(R).
Test Duration Calculation
For time-based reliability parameters like mean time between failures, the required total test time depends on the reliability target and confidence level. Demonstrating an MTBF of theta with confidence C requires total test time T given by T = -theta times ln(1-C) for zero-failure demonstration assuming exponential failure distribution.
Higher confidence levels demand substantially more test time. Demonstrating 90% confidence requires 2.3 times the MTBF in total test time, while 95% confidence requires 3.0 times and 99% confidence requires 4.6 times. These multipliers apply whether the test time accumulates on one unit or is distributed across many.
Advantages and Limitations
Success run testing offers simplicity in both execution and interpretation. The binary pass-fail outcome eliminates complex statistical analysis, and zero failures provides a psychologically compelling demonstration of quality. Test termination criteria are unambiguous since any failure before reaching the required test time results in failure to demonstrate.
However, this simplicity comes with limitations. Success run tests provide no information about actual reliability beyond the demonstration threshold, unlike tests that observe and analyze failures. A single early failure invalidates the entire test regardless of subsequent performance, which can be frustrating when failures occur near test completion. Additionally, success run testing becomes impractical for demonstrating very high reliability levels due to exponentially increasing sample size requirements.
Sequential Probability Ratio Test
The Sequential Probability Ratio Test provides a statistically rigorous framework for making accept or reject decisions as evidence accumulates during testing. Unlike fixed-sample tests that require predetermined test durations, sequential tests can terminate as soon as sufficient evidence exists for a decision, often resulting in shorter average test times.
SPRT Principles
Sequential testing compares the likelihood of observed results under two hypotheses: that the true reliability equals an acceptable level versus that it equals an unacceptable level. As testing proceeds, each observation updates the likelihood ratio. Testing continues until this ratio crosses a threshold indicating strong evidence for acceptance or rejection.
The test boundaries form parallel lines on a plot of cumulative failures versus cumulative test time. Results falling above the upper boundary lead to rejection, while results below the lower boundary lead to acceptance. Results between the boundaries require continued testing. The slope and intercepts of these boundaries derive from the reliability parameters and risk levels specified in the test plan.
Boundary Calculations
SPRT boundaries depend on four parameters: the acceptable reliability level (producer's quality), the unacceptable reliability level (consumer's quality), the producer's risk alpha (probability of rejecting acceptable product), and the consumer's risk beta (probability of accepting unacceptable product). From these, the acceptance boundary A and rejection boundary B calculate as functions of accumulated test time and failures observed.
The discrimination ratio, defined as the ratio of acceptable to unacceptable reliability, influences test efficiency. Wider discrimination ratios lead to faster decisions but provide less precise reliability estimates. Narrower ratios require more testing but distinguish between closer reliability levels. Typical discrimination ratios range from 1.5 to 3.0 depending on the consequence of incorrect decisions.
Truncation Procedures
While sequential tests theoretically can continue indefinitely when evidence remains inconclusive, practical tests include truncation rules that force a decision after specified maximum test time or failures. Truncation prevents open-ended testing while maintaining statistical validity through modified acceptance criteria at truncation points.
Common truncation approaches include time truncation at a multiple of the expected test duration and failure truncation at a maximum number of observed failures. The truncation boundaries modify the risks slightly from nominal values, requiring careful analysis to ensure contractual requirements remain satisfied.
Bayesian Demonstration Methods
Bayesian methods incorporate prior knowledge about product reliability into demonstration test analysis. This approach proves particularly valuable when substantial historical data exists from similar products, development testing, or field experience. By crediting prior evidence, Bayesian methods can significantly reduce demonstration test requirements while maintaining statistical rigor.
Prior Distribution Development
Bayesian analysis requires specifying a prior distribution that represents knowledge about reliability before demonstration testing begins. Prior distributions typically follow gamma or beta distributions, chosen for mathematical convenience and their ability to represent diverse states of knowledge. Non-informative priors represent minimal prior knowledge, while informative priors encode specific historical evidence.
Prior distribution parameters derive from historical data analysis, physics-based reliability predictions, or expert judgment. The strength of the prior, quantified by its effective sample size, determines how much influence prior knowledge has relative to new test data. Strong priors based on extensive heritage data substantially reduce test requirements, while weak priors provide minimal credit.
Posterior Analysis
Demonstration test results combine with the prior distribution to produce a posterior distribution representing updated reliability knowledge. For gamma priors with exponential failure data, the posterior is also gamma distributed with parameters that combine prior parameters and test results. This mathematical tractability allows straightforward calculation of confidence bounds and reliability estimates.
The posterior distribution provides richer information than classical methods, including the full probability distribution of reliability rather than just point estimates or confidence bounds. This enables assessment of the probability that reliability falls within any specified range and supports decision-making under uncertainty.
Test Requirements with Prior Credit
Bayesian demonstration tests determine required test time by finding the test duration that, combined with the prior, yields a posterior distribution meeting the reliability requirement at the specified confidence level. Strong priors reduce required test time, sometimes dramatically, compared to classical methods that ignore prior information.
However, customers and regulators may scrutinize or reject prior credit claims, particularly when prior data comes from different operating environments or product variants. Test plans using Bayesian methods must document the prior basis thoroughly and may require stakeholder approval before execution. Conservative prior selection or sensitivity analysis demonstrating robustness to prior assumptions helps build acceptance.
Zero Failure Testing
Zero failure testing represents a specialized approach to reliability demonstration that plans for and expects no failures during the test period. This methodology recognizes that many high-reliability products rarely fail during testing, making failure-based statistical methods impractical. Zero failure methods extract meaningful reliability conclusions from successful test completions.
Applicability Assessment
Zero failure testing applies when expected failure rates during practical test durations are very low. Products designed for extended life, safety-critical applications, or high-reliability markets often fall into this category. The approach requires confidence that observed zero failures genuinely indicates high reliability rather than insufficient test severity or duration.
Before committing to zero failure testing, engineers should verify that test conditions adequately stress failure mechanisms, that test duration provides meaningful exposure, and that failure detection methods would identify failures if they occurred. Test validation through accelerated stress testing or physics-of-failure analysis helps establish test adequacy.
Statistical Methods for Zero Failures
Several statistical approaches enable reliability inference from zero failure data. The chi-square method provides confidence bounds on failure rate from total test time when failures follow exponential distribution. The Poisson approximation applies when testing discrete units for pass-fail outcomes. Bayesian methods with appropriate priors yield posterior distributions even with zero observed failures.
The key relationship for exponential data states that upper confidence bound on failure rate lambda equals chi-square value for specified confidence with two degrees of freedom divided by twice the total test time. For zero failures, this simplifies to lambda equals minus natural log of one minus confidence divided by total test time.
Handling Test Failures
Despite the name, zero failure tests must define procedures for handling failures that occur. A single failure typically invalidates demonstration of the planned reliability level, but the test program must specify next steps. Options include extending test time to demonstrate lower reliability, implementing corrective action and restarting, or analyzing whether the failure mode falls within the demonstration scope.
Failure analysis during zero failure tests requires particular rigor since each failure significantly impacts demonstration success. Distinguishing relevant failures from those outside test scope, such as test equipment failures or conditions exceeding specification, requires clear failure definition criteria established before test start.
Confidence Level Selection
Confidence level expresses the probability that demonstrated reliability equals or exceeds the stated value given the test results. Selecting appropriate confidence levels requires balancing the cost of testing against the consequences of incorrect reliability claims and stakeholder expectations.
Standard Confidence Levels
Industry conventions establish common confidence levels for different applications. Many commercial applications use 90% confidence, which provides reasonable assurance while keeping test requirements practical. Safety-critical applications often require 95% or 99% confidence. Military and aerospace programs frequently specify 90% confidence for general reliability and higher levels for safety-critical functions.
Contractual requirements often dictate confidence levels, leaving little room for engineering optimization. When flexibility exists, engineers should consider the cost implications since moving from 90% to 95% confidence increases required test time by approximately 30% for zero failure tests, while 99% confidence doubles the requirement compared to 90%.
Economic Optimization
When contractual flexibility exists, economic analysis can optimize confidence level selection. The analysis balances testing costs against expected warranty, liability, and reputation costs from field failures. Higher confidence levels increase testing cost but reduce the probability of releasing inadequate products.
Products with high consequence of failure, whether measured in safety impact, warranty cost, or reputation damage, justify higher confidence levels despite increased test cost. Conversely, products with limited failure consequences and tight development budgets may appropriately use lower confidence levels.
Confidence vs. Reliability Trade-offs
For fixed test resources, a trade-off exists between demonstrated reliability level and confidence level. The same test results might demonstrate 10,000 hour MTBF with 90% confidence or 8,000 hour MTBF with 95% confidence. Understanding this trade-off helps in negotiating requirements and interpreting results.
Requirements should avoid specifying both very high reliability and very high confidence unless the program can support the resulting test burden. Unrealistic requirements lead to either inadequate testing or program delays and cost overruns.
Consumer and Producer Risks
Statistical testing cannot eliminate uncertainty, so demonstration tests carry inherent risks of incorrect decisions. Understanding and quantifying these risks ensures that test designs appropriately balance the interests of both producers and consumers.
Risk Definitions
Producer's risk, typically denoted alpha, is the probability of rejecting a product that actually meets reliability requirements. This risk leads to unnecessary redesign, retest, or program delays when the product is truly acceptable. Consumer's risk, typically denoted beta, is the probability of accepting a product that actually fails to meet reliability requirements. This risk results in field problems, warranty costs, and potential safety issues.
Neither risk can be eliminated entirely since any finite test has some probability of yielding misleading results. The test design determines the balance between these risks, with more stringent tests reducing consumer risk at the cost of increased producer risk and vice versa.
Operating Characteristic Curves
Operating characteristic curves graphically display test performance across a range of true reliability values. The horizontal axis represents true product reliability, while the vertical axis shows the probability of passing the demonstration test. Ideal tests would show a sharp transition between rejection at low reliability and acceptance at high reliability, but practical tests show gradual transitions.
OC curves reveal the discrimination power of a test design. Steeper curves indicate better discrimination between acceptable and unacceptable reliability levels. Test parameters can be adjusted to steepen the curve, typically at the cost of increased sample size or test duration.
Risk Allocation Strategies
Different applications warrant different risk balances. Consumer products with low individual failure consequence but high volume may tolerate higher consumer risk in favor of reduced testing cost. Safety-critical products demand minimal consumer risk regardless of testing expense. Military contracts often specify equal producer and consumer risks, commonly 10% each.
Test plan negotiations should explicitly address risk allocation rather than assuming default values. Both parties benefit from understanding what risks they assume and how the test design reflects their interests.
Test Time Determination
Test time determination translates reliability requirements and statistical parameters into practical test durations. The calculations must account for the number of available test units, desired confidence level, and the mathematical relationship between test accumulation and demonstrated reliability.
Total Test Time Calculations
For exponential failure distributions, total test time T required to demonstrate MTBF theta at confidence level C with r failures allowed follows from chi-square statistics: T equals chi-square for confidence C with 2(r+1) degrees of freedom times theta divided by 2. For zero-failure tests, this simplifies to T equals theta times the natural log of 1 divided by 1 minus C.
Test time distributes across available test units based on program constraints. More units tested for shorter duration generally reduces calendar time but increases unit and facility costs. Fewer units tested longer reduces handling overhead but extends program duration. The total test time requirement remains constant regardless of distribution.
Acceleration Factor Application
Accelerated testing reduces calendar time by applying elevated stresses that speed failure mechanisms. The acceleration factor relates accelerated test time to equivalent operating time, allowing conversion between test conditions and field conditions. Valid acceleration requires maintaining the same failure mechanisms at elevated stress.
When acceleration factors apply, required test time at accelerated conditions equals required equivalent time divided by the acceleration factor. An acceleration factor of 10 reduces a 10,000 hour test requirement to 1,000 hours at accelerated conditions. However, acceleration factor uncertainty should be reflected in test planning through conservative factor values or additional margin.
Schedule Integration
Test time determination must integrate with program schedules, recognizing that demonstration testing typically occurs late in development when schedule pressure is highest. Test planning should identify the critical path and ensure adequate time allocation including allowance for potential retest if initial results are unfavorable.
Parallel testing strategies can reduce calendar time by distributing test time across multiple units and test facilities. However, parallel testing requires more resources and introduces logistics complexity. Trade studies between serial and parallel approaches help optimize the test program within schedule and budget constraints.
Failure Definition Criteria
Clear failure definition criteria ensure consistent test interpretation and prevent disputes about whether observed anomalies constitute failures. The failure definition establishes what performance degradation or malfunction counts against demonstration requirements and what conditions fall outside the test scope.
Functional Failure Criteria
Functional failure criteria define the performance thresholds below which the product fails to meet its intended function. These criteria should align with product specifications and customer expectations. Overly strict criteria inflate failure counts and make demonstration harder, while overly lenient criteria mask genuine reliability problems.
Performance parameters requiring monitoring during test should be identified along with their acceptable limits. Some parameters may have hard limits where any exceedance constitutes failure, while others may allow temporary excursions or gradual degradation within defined bounds.
Relevant vs. Non-Relevant Failures
Not all failures observed during testing necessarily count against reliability demonstration. Failures caused by test equipment malfunction, operator error, conditions exceeding test specifications, or design changes implemented after test start may be classified as non-relevant and excluded from statistical analysis.
Non-relevant failure criteria must be defined before testing begins to prevent post-hoc rationalization of failures. The criteria should be specific and objective, with clear procedures for documenting and adjudicating non-relevance claims. A failure review board or similar governance structure provides independent assessment of failure classification.
Failure Classification Procedures
Documented procedures ensure consistent failure classification throughout testing. Each potential failure event triggers an investigation to determine the failure mechanism, root cause, and appropriate classification. Evidence supporting classification decisions must be preserved for review by stakeholders and auditors.
Classification disputes should be resolved through predefined escalation procedures rather than ad hoc negotiation. Timely resolution is important since unresolved failures create uncertainty about test status and can delay program decisions.
Test Monitoring Procedures
Continuous test monitoring ensures that demonstration tests proceed according to plan and that anomalies are detected promptly. Monitoring procedures define what parameters to observe, how frequently to check, and what actions to take when deviations occur.
Parameter Monitoring
Demonstration tests monitor both unit under test parameters and test condition parameters. Unit parameters include functional performance metrics and any indicators that might predict impending failure. Test condition parameters ensure that environmental stresses remain within specification and that test equipment operates correctly.
Monitoring frequency balances detection speed against data handling burden. Critical parameters may require continuous monitoring with automated alarm systems, while less critical parameters might be checked at regular intervals. The monitoring plan should justify frequency choices based on parameter criticality and expected rate of change.
Anomaly Response
Anomaly response procedures define actions when monitoring detects unexpected conditions. Minor anomalies might require only documentation and continued observation, while significant anomalies may trigger test interruption for investigation. The procedures should clearly define thresholds between response levels.
Test interruptions affect demonstrated reliability accumulation and must be handled consistently. Time during interruptions may or may not count toward test duration depending on the interruption cause and test plan provisions. Clear rules prevent disputes about how interruption time affects demonstration results.
Data Recording and Backup
Test data represents significant investment and must be protected against loss. Monitoring systems should include redundant data recording and regular backups. Data integrity checks verify that recorded data accurately reflects actual conditions without corruption or gaps.
Raw data retention enables later reanalysis if questions arise about test validity or failure classification. The test plan should specify data retention requirements consistent with program needs and applicable quality standards.
Data Collection Protocols
Systematic data collection protocols ensure that demonstration tests generate the information needed for statistical analysis and qualification decisions. Protocols specify what data to collect, when to collect it, how to record and store it, and who has access and responsibility.
Required Data Elements
Minimum required data includes unit identification and configuration, test start and end times, environmental conditions throughout testing, functional test results at prescribed intervals, and detailed documentation of any failures or anomalies. Additional data may be required depending on the product type, customer requirements, or applicable standards.
Time accumulation data requires particular care since demonstrated reliability derives directly from recorded test hours. Time recording systems should be calibrated and verified, with procedures to handle system outages or malfunctions. Any time accumulation adjustments must be documented and justified.
Documentation Standards
Documentation standards ensure data quality and traceability. Laboratory notebooks, electronic records, or formal data packages may be appropriate depending on program requirements. Whatever format is used, documentation should allow reconstruction of test history and support audit verification.
Data corrections must follow documented procedures that preserve the original entry while clearly identifying the correction and its justification. Undocumented changes to test records undermine data credibility and may invalidate demonstration results.
Chain of Custody
Chain of custody procedures track data from collection through analysis and archival. Responsibilities for data at each stage should be clearly assigned. Access controls prevent unauthorized modification while ensuring that authorized personnel can retrieve data when needed.
Electronic data systems should include audit trails that record access and modifications. These trails support data integrity verification and help investigate any anomalies discovered during analysis or audit.
Results Analysis Methods
Results analysis transforms raw test data into reliability conclusions suitable for qualification decisions. The analysis methods must align with the statistical framework established in the test plan and produce results that satisfy stakeholder requirements.
Statistical Calculations
Basic statistical calculations include total test time accumulation, failure count by category, demonstrated reliability point estimate, and confidence bounds. For Bayesian analysis, posterior distribution parameters and credible intervals replace classical confidence bounds. All calculations should be documented with sufficient detail to allow independent verification.
Software tools for reliability calculations should be validated for the specific methods employed. Spreadsheet implementations require particular scrutiny since formula errors can propagate undetected. Cross-checking results with independent calculations or published examples helps verify correctness.
Distributional Assumptions
Statistical analysis relies on assumptions about the underlying failure distribution. The exponential distribution, implying constant failure rate, is commonly assumed for demonstration testing due to mathematical convenience. However, this assumption should be verified through goodness-of-fit testing when sufficient failure data exists.
When data suggests non-exponential behavior, alternative distributions such as Weibull may be more appropriate. Weibull analysis can identify whether failure rate increases, decreases, or remains constant with time, with implications for both reliability estimates and failure mechanism understanding.
Sensitivity Analysis
Sensitivity analysis explores how results depend on analysis assumptions and input uncertainties. Key sensitivities include acceleration factor uncertainty, failure classification decisions, and prior distribution parameters for Bayesian analysis. Understanding sensitivities helps assess result robustness and identify areas needing additional attention.
Results that are highly sensitive to questionable assumptions warrant additional scrutiny or conservative interpretation. Conversely, robust results that remain favorable across reasonable assumption ranges provide stronger confidence in demonstrated reliability.
Qualification Report Generation
The qualification report documents demonstration test results and provides the formal basis for qualification decisions. A well-structured report presents evidence clearly, addresses stakeholder concerns, and supports timely decision-making.
Report Structure
Effective qualification reports typically include an executive summary with key conclusions, test objectives and requirements, test article description and configuration, test plan summary, environmental and test conditions, chronological test narrative, failure summary and analysis, statistical analysis results, conclusions and recommendations, and supporting appendices.
The report should stand alone, providing sufficient background for readers unfamiliar with the program. Cross-references to supporting documents, test procedures, and raw data packages enable detailed verification without cluttering the main report.
Evidence Presentation
Evidence presentation should clearly link test results to demonstration requirements. Tables summarizing test time accumulation, failures observed, and statistical results provide quick access to key information. Graphs showing test progress, operating characteristic curves, and confidence bound calculations help readers understand the basis for conclusions.
Failure documentation deserves particular attention since failures are typically the most scrutinized aspect of demonstration results. Each failure should be fully described including time of occurrence, symptoms observed, investigation results, root cause determination, and relevance classification with justification.
Conclusion Statements
Conclusion statements must clearly state whether demonstration requirements have been met. Qualified conclusions that identify caveats or limitations are preferable to unqualified statements that may be misleading. If demonstration was not fully successful, the report should identify what was demonstrated and what gaps remain.
Recommendations for follow-on action may include suggestions for design improvement, additional testing, or field monitoring. These recommendations help ensure that demonstration results translate into appropriate product qualification and release decisions.
Customer Acceptance Criteria
Customer acceptance criteria define what evidence customers require before accepting that reliability has been demonstrated. Understanding and documenting these criteria early in the program prevents surprises during qualification review and ensures that test programs generate acceptable evidence.
Contractual Requirements
Contractual requirements establish the baseline acceptance criteria. These typically specify the reliability parameter to be demonstrated, the required value, and the confidence level. Additional requirements may address test methods, failure classification procedures, reporting formats, and customer witness or approval rights.
Ambiguous contractual requirements should be clarified before test execution. Questions about interpretation are better resolved during planning than during qualification review when program pressure is highest and positions may have hardened.
Witness and Audit Requirements
Many customers require witness of critical test events or audit of test facilities and procedures. Witness requirements might include test start, functional tests, failure investigations, and test completion. Audit requirements might cover calibration records, data handling procedures, and analysis methods.
Test planning should accommodate witness and audit requirements, including scheduling coordination and facility access arrangements. Failure to provide required access can delay or invalidate qualification even when test results are otherwise acceptable.
Approval Processes
Formal approval processes define how customers review and accept qualification evidence. Understanding the approval process helps in preparing appropriate documentation and anticipating review questions. Key aspects include who has approval authority, what review meetings or boards are required, and what the typical review duration is.
Proactive engagement with customer reviewers can smooth the approval process. Pre-submission reviews, draft report discussions, and early escalation of potential issues help ensure that the formal review focuses on genuine technical concerns rather than documentation deficiencies or surprises.
Summary
Reliability demonstration testing provides the statistical evidence that transforms reliability predictions into validated performance claims. Through careful test planning, appropriate method selection, rigorous execution, and thorough documentation, engineers can efficiently demonstrate that products meet reliability requirements with quantified confidence.
Success in demonstration testing requires attention to both statistical rigor and practical execution. Test plans must align statistical methods with program constraints while ensuring that results will satisfy stakeholder requirements. Test execution must maintain the controlled conditions and accurate data collection that underpin valid conclusions. And qualification reports must present evidence compellingly while honestly acknowledging limitations.
The methods covered in this article, from success run testing to sequential probability ratio tests to Bayesian approaches, provide a toolkit for addressing diverse demonstration requirements. Selecting the appropriate method for each situation, understanding its assumptions and limitations, and executing it rigorously enables engineers to prove reliability with confidence.