Key Reliability Metrics
Reliability metrics provide the quantitative foundation for measuring, predicting, and improving the dependability of electronic systems. These metrics enable engineers to set meaningful requirements, compare design alternatives, and communicate reliability performance to stakeholders. Understanding the precise definitions, relationships, and appropriate applications of reliability metrics is essential for effective reliability engineering practice.
The metrics discussed in this article range from fundamental time-based measures such as mean time between failures to sophisticated availability calculations that account for system maintenance and repair. Each metric captures different aspects of reliability performance, and selecting the appropriate metrics for a given application requires understanding what each metric represents and how it relates to customer needs and business objectives.
This comprehensive guide covers the essential reliability metrics used throughout the electronics industry, including their mathematical definitions, practical interpretations, calculation methods, and common applications. The content addresses both repairable systems where failed units are restored to service and non-repairable items where failure ends the useful life. Throughout, the focus is on providing practical guidance for applying these metrics in real engineering situations.
Mean Time Between Failures
Definition and Interpretation of MTBF
Mean time between failures (MTBF) is one of the most widely used reliability metrics in the electronics industry. MTBF represents the average time between successive failures of a repairable system operating under specified conditions. For a system that fails and is repaired multiple times, MTBF provides a single number that characterizes the typical interval between failures, enabling comparisons between different designs and tracking of reliability improvement over time.
The mathematical definition of MTBF is straightforward: total operating time divided by the number of failures observed during that time. If a system operates for 10,000 hours and experiences 5 failures during that period, the observed MTBF is 2,000 hours. This calculation can be applied to individual units tracked over their service life or to populations of units where the total operating time is the sum of individual operating times.
MTBF is appropriately applied to repairable systems where failed units are restored to operation. After repair, the system continues accumulating operating time that counts toward the MTBF calculation. This distinguishes MTBF from mean time to failure (MTTF), which applies to non-repairable items. The repairable system assumption underlies MTBF calculations and interpretations, and applying MTBF to non-repairable items leads to conceptual confusion.
A common misconception about MTBF is interpreting it as the expected lifetime of a system before failure. An MTBF of 10,000 hours does not mean that all units will operate for 10,000 hours before failing. Due to the statistical nature of failure, some units will fail much sooner and some much later than the MTBF. For exponentially distributed failures, approximately 63 percent of units will have failed by the time they reach one MTBF of operation. Understanding this probabilistic interpretation is essential for correctly applying MTBF in decision-making.
MTBF Calculation Methods
Calculating MTBF from field data requires careful tracking of operating time and failure events. For systems with usage meters or operating hour counters, the accumulated operating time can be read directly. For systems without such instrumentation, operating time must be estimated from deployment records, usage patterns, or duty cycle information. Accurate operating time data is essential because errors in time estimation directly affect the calculated MTBF.
The basic MTBF calculation sums the operating time of all units and divides by the total number of failures. When some units are still operating without failure at the end of the observation period, their operating time is included in the total, making the data right-censored. Statistical methods for censored data should be applied to obtain proper MTBF estimates, though simple calculations ignoring censoring provide reasonable approximations when the number of failures is large relative to the number of unfailed units.
Confidence intervals quantify the uncertainty in MTBF estimates due to limited sample sizes. With few observed failures, the true MTBF could be substantially higher or lower than the calculated value. The chi-square distribution is commonly used to construct confidence intervals for MTBF under the assumption of exponentially distributed failures. A two-sided 90 percent confidence interval, for example, defines the range within which the true MTBF lies with 90 percent confidence based on the observed data.
MTBF prediction during the design phase relies on component failure rate data and system reliability models. Prediction handbooks such as MIL-HDBK-217 and Telcordia SR-332 provide failure rate data for electronic components under various operating conditions. The system MTBF is calculated by combining component failure rates according to the system architecture, with series components adding failure rates and parallel redundant configurations providing failure rate reduction. Predicted MTBF provides early reliability estimates but typically requires adjustment based on test and field data.
MTBF Applications and Limitations
MTBF serves multiple purposes in reliability engineering and product development. During design, MTBF targets establish reliability goals that guide component selection, derating decisions, and architecture choices. During testing, demonstrated MTBF provides evidence of achieved reliability. In field support, MTBF enables spare parts planning, maintenance scheduling, and warranty cost estimation. Contractually, MTBF requirements define acceptance criteria and may trigger financial penalties or incentives.
Comparing MTBF values across products or manufacturers requires caution because different definitions and calculation methods can produce different results for the same underlying reliability. The operating environment significantly affects failure rates, so an MTBF achieved in benign conditions may not apply to more stressful environments. The definition of failure also matters: some organizations count only critical failures while others count all failures including those with minor consequences. Understanding these factors is essential when using MTBF for comparisons or decisions.
MTBF has limitations that engineers must understand to avoid misapplication. The metric assumes a constant failure rate, which is accurate for many electronic systems during their useful life but does not account for infant mortality or wear-out phases. MTBF also provides no information about the distribution of time between failures or the consequences of failures. A system with high MTBF but severe failure consequences may be less desirable than one with lower MTBF but benign failure modes. Supplementary metrics address these limitations.
For systems with multiple failure modes, composite MTBF combines the contributions of all failure modes into a single number. While convenient for overall reliability assessment, composite MTBF can mask important differences between failure modes. A system might achieve acceptable composite MTBF while having an unacceptably high rate of a particular critical failure mode. Reliability analysis should examine individual failure modes, not just composite metrics, especially when failure consequences vary significantly.
Mean Time to Failure
MTTF for Non-Repairable Items
Mean time to failure (MTTF) is the reliability metric appropriate for non-repairable items where failure ends the useful life of the item. Unlike MTBF, which applies to systems that are repaired and returned to service, MTTF characterizes items that are discarded or replaced upon failure. Examples include light bulbs, semiconductor components, batteries, and other items where repair is not economically feasible or technically possible.
Mathematically, MTTF is the expected value of the time to failure random variable. For a population of identical items, MTTF represents the average lifetime across all items in the population. The calculation is analogous to MTBF: total operating time accumulated by all items divided by the number of failures. However, the interpretation differs because each item contributes only its time to first failure, not time between multiple failures.
The relationship between MTTF and the reliability function provides important insights. The reliability function R(t) gives the probability that an item survives beyond time t. MTTF equals the integral of the reliability function from zero to infinity, representing the area under the survival probability curve. This relationship connects MTTF to the underlying failure time distribution and enables MTTF calculation from known distribution parameters.
For exponentially distributed failure times, MTTF equals the reciprocal of the failure rate. If the failure rate is 0.001 per hour (0.1 percent per hour), the MTTF is 1,000 hours. This simple relationship is commonly used in reliability calculations and provides quick conversions between failure rate and MTTF. However, the relationship only holds for the exponential distribution; other distributions have more complex relationships between MTTF and failure rate.
MTTF Testing and Demonstration
Demonstrating MTTF through testing presents challenges because accumulating sufficient operating time and failures to achieve statistically meaningful results can be time-consuming and expensive. A product with an MTTF requirement of 100,000 hours cannot practically be tested for 100,000 hours per unit. Accelerated life testing addresses this challenge by applying elevated stresses to increase failure rates, then using acceleration models to extrapolate results to normal operating conditions.
The test time required to demonstrate a specified MTTF depends on the desired confidence level and the number of failures allowed during testing. Zero-failure test plans require less total test time but provide lower confidence in the MTTF estimate. Test plans that allow failures require more test time but provide tighter confidence bounds. The choice of test plan involves tradeoffs between test cost, schedule, and the precision of the reliability estimate.
Reliability demonstration tests often use the exponential distribution assumption, which simplifies test planning and data analysis. Under this assumption, the test can be designed to demonstrate a specified lower confidence bound on MTTF. The total test time required depends on the confidence level and the discrimination ratio, which is the ratio of the true MTTF to the minimum acceptable MTTF. Standard test plans are available in military standards and industry guidelines.
When accelerated testing is used to demonstrate MTTF, the acceleration factor relates test conditions to normal operating conditions. Common acceleration models include the Arrhenius equation for temperature acceleration, inverse power law for voltage and current stress, and Eyring model for combined stresses. Proper acceleration modeling is critical because errors in the acceleration factor directly affect the extrapolated MTTF. Validation of acceleration models through testing at multiple stress levels improves confidence in the results.
MTTF versus MTBF: Proper Usage
Confusion between MTTF and MTBF is common in the electronics industry, with the terms sometimes used interchangeably despite their distinct meanings. MTTF applies to non-repairable items while MTBF applies to repairable systems. Using the wrong metric can lead to incorrect reliability predictions and inappropriate decisions. Engineers should carefully consider whether the item under analysis is repairable or non-repairable and select the appropriate metric.
For repairable systems in the useful life phase with constant failure rate, the numerical values of MTTF and MTBF are equivalent. This equivalence sometimes leads to the terms being used interchangeably, but the conceptual distinction remains important. A system with MTBF of 10,000 hours experiences failures throughout its service life with average spacing of 10,000 hours between failures. A component with MTTF of 10,000 hours fails once on average after 10,000 hours of operation and is then replaced.
System-level reliability analysis often combines MTTF data for components with MTBF analysis for the repairable system. Component failure rates derived from MTTF data are used to calculate system failure rates, which are then converted to system MTBF. This approach is valid when components are replaced upon failure and the system continues operating. The analysis should clearly distinguish between component-level and system-level metrics.
Specifications and contracts should clearly define which metric applies and how it will be measured. Ambiguity about whether a requirement refers to MTTF or MTBF can lead to disputes about compliance. The specification should also define what constitutes a failure, as this definition significantly affects the metric value. Clear definitions established at the outset prevent misunderstandings and ensure that all parties have consistent expectations.
Mean Time to Repair
Understanding MTTR
Mean time to repair (MTTR) measures the average time required to restore a failed system to operating condition. This metric is essential for availability calculations and maintenance planning because it captures how long systems remain out of service when failures occur. MTTR encompasses the complete repair process including fault detection, diagnosis, obtaining replacement parts, performing the repair, and verifying successful restoration.
The components of MTTR vary depending on the repair environment and support infrastructure. Administrative delay time includes the time from failure occurrence to the start of repair activities, which may involve notification, scheduling, and obtaining authorization. Logistics delay time covers the time spent waiting for spare parts or special tools. Active repair time is the hands-on time technicians spend diagnosing and correcting the fault. Each component contributes to total MTTR and may be targeted for improvement.
MTTR is calculated by summing the repair times for all repair events and dividing by the number of repairs. Like MTBF, MTTR is an average that masks variation in individual repair times. Some repairs may be completed quickly while others take much longer. Understanding the distribution of repair times, not just the mean, is important for support planning and availability analysis. Highly variable repair times may require different planning approaches than consistent repair times.
Design decisions significantly impact MTTR. Built-in test capabilities reduce diagnosis time by quickly identifying failed components. Modular designs enable rapid replacement of failed modules rather than component-level troubleshooting. Accessible layouts reduce the time required to reach and replace failed components. Design for maintainability explicitly considers these factors and establishes MTTR targets that drive design decisions. Trading off MTTR improvements against cost and other design objectives is part of the reliability engineering process.
MTTR Measurement and Estimation
Measuring MTTR in the field requires tracking repair events and recording the time required for each repair. The starting point of repair time must be clearly defined: some organizations measure from failure occurrence while others measure from the start of active repair. The ending point is typically when the system is verified as operational. Consistent definitions ensure that MTTR data is comparable across different time periods and repair locations.
Estimating MTTR during design relies on task analysis and comparison to similar products. The repair process is decomposed into individual tasks, and time estimates are developed for each task. These estimates may come from historical data on similar repairs, time-motion studies, or engineering judgment. Task times are summed and combined with estimates of administrative and logistics delays to produce the MTTR estimate. Uncertainty in these estimates should be acknowledged and may be expressed as a range or confidence interval.
Maintainability demonstration testing verifies that MTTR requirements are achieved. Test technicians representative of field maintenance personnel perform repairs on failed or faulted systems while being timed. The demonstration may use actual failures or simulated failures introduced for the test. Statistical analysis of the repair times determines whether the MTTR requirement is met with the specified confidence. These demonstrations typically occur during product qualification.
MTTR improvement initiatives often yield significant returns because repair time directly affects operational availability. Root cause analysis of long repair times identifies opportunities for improvement. Common findings include inadequate documentation, difficulty obtaining spare parts, poor accessibility, and excessive diagnostic time. Addressing these issues through design changes, improved logistics, or better training can substantially reduce MTTR and improve overall system availability.
Related Maintainability Metrics
Mean time to restore (MTTR, also) encompasses the complete time from failure to system restoration, including all delays. This broader definition includes administrative, logistics, and other delays that may not be captured in repair time alone. Some organizations use MTTR specifically for active repair time and mean time to restore for total downtime. The terminology varies, making it important to verify definitions when comparing MTTR values from different sources.
Mean active maintenance time (MAMT) measures the average time spent actively performing maintenance, whether corrective or preventive. This metric focuses on technician hands-on time and excludes delays. MAMT is useful for maintenance workforce planning and for evaluating design features that affect maintenance task time. Preventive maintenance time should be tracked separately from corrective maintenance time to understand the relative contributions of each.
Maximum time to repair (MaxTTR) specifies an upper limit on repair time, ensuring that no repair exceeds a specified duration. While MTTR addresses average performance, MaxTTR addresses worst-case scenarios. Requirements may specify that 95 percent or 99 percent of repairs must be completed within the MaxTTR limit. This metric is important for applications where extended downtime has severe consequences and average performance alone is insufficient.
Maintenance ratio compares maintenance time to operating time, indicating the maintenance burden imposed by a system. A maintenance ratio of 0.01 means that one hour of maintenance is required for every 100 hours of operation. This metric captures both the frequency and duration of maintenance events, providing a comprehensive view of maintainability. Low maintenance ratios indicate systems that require minimal support, while high ratios indicate maintenance-intensive systems.
Failure Rate and Hazard Functions
Instantaneous Failure Rate
The failure rate, also called the hazard rate or hazard function, is a fundamental reliability metric that expresses the probability of failure per unit time for items that have survived to a given point in time. Unlike MTBF, which provides a single average value, the failure rate can vary with time, capturing patterns such as infant mortality, constant failure rate, and wear-out. This time-varying behavior makes the failure rate a more general and informative metric than MTBF alone.
Mathematically, the instantaneous failure rate h(t) is defined as the limit of the probability of failure in a small interval divided by the interval length, given survival to the start of the interval. This conditional probability distinguishes the failure rate from the probability density function, which is unconditional. The failure rate applies to items that have already survived to time t and asks about their probability of failure in the next instant.
For the exponential distribution, the failure rate is constant over time, denoted by the parameter lambda. This constant failure rate implies that the probability of failure in the next instant is the same whether the item is new or has been operating for thousands of hours. The constant failure rate assumption underlies many reliability calculations and is often a reasonable approximation for electronic systems during their useful life phase. When the failure rate equals lambda, MTBF equals one divided by lambda.
The Weibull distribution allows the failure rate to increase or decrease over time, capturing infant mortality and wear-out behavior. The shape parameter beta determines whether the failure rate decreases (beta less than one), remains constant (beta equals one), or increases (beta greater than one). This flexibility makes the Weibull distribution widely used in reliability engineering. The scale parameter eta relates to the characteristic life and determines when failures are most likely to occur.
Cumulative Failure Rate
The cumulative hazard function H(t) is the integral of the instantaneous failure rate from zero to time t. This function accumulates the instantaneous failure rates over time and provides another way to characterize failure behavior. The cumulative hazard has useful properties for statistical analysis, particularly for graphical methods and non-parametric estimation.
The relationship between the cumulative hazard and the reliability function is: R(t) equals e to the power of negative H(t). This exponential relationship means that the cumulative hazard directly determines survival probability. A cumulative hazard of 1 corresponds to a reliability of approximately 0.368, meaning about 63 percent of items have failed. A cumulative hazard of 2 corresponds to reliability of approximately 0.135, or about 87 percent failed.
For the exponential distribution with constant failure rate lambda, the cumulative hazard equals lambda times t, a straight line through the origin. Deviations from this linear behavior on a plot of cumulative hazard versus time indicate that the failure rate is not constant. This graphical approach provides a simple way to assess whether the constant failure rate assumption is appropriate for a given data set.
The Nelson-Aalen estimator is a non-parametric method for estimating the cumulative hazard function from censored data. At each observed failure time, the cumulative hazard increases by one divided by the number of items at risk at that time. This estimator makes no assumptions about the underlying distribution and provides a starting point for more detailed analysis. Confidence intervals for the Nelson-Aalen estimator quantify the uncertainty in the cumulative hazard estimate.
Failure Rate Units and Conversions
Failure rates are expressed in various units depending on the application and industry convention. Failures per hour is the fundamental unit, but for components with very low failure rates, derived units are more convenient. Failures per million hours and failures per billion hours (FIT, for Failures In Time) are commonly used for semiconductor components. Conversions between units require careful attention to the powers of ten involved.
One FIT equals one failure per billion device-hours, or 10 to the minus 9 failures per hour. A component with a failure rate of 100 FIT has an MTBF of 10 million hours, illustrating the extremely low failure rates achieved by modern semiconductor devices. FIT rates enable meaningful comparison of component reliability because the numbers fall in a convenient range, typically from single digits to thousands.
Percent failures per thousand hours is another common unit, particularly for higher-failure-rate items. One percent per thousand hours equals 10 to the minus 5 failures per hour, or 10,000 FIT. This unit is convenient for items with MTBF in the range of thousands to tens of thousands of hours, where expressing failure rate in FIT would yield awkwardly large numbers.
Converting between failure rate and MTBF requires the assumption of exponential distribution. MTBF in hours equals one divided by failure rate in failures per hour. MTBF in hours also equals one billion divided by failure rate in FIT. These conversions are straightforward but apply only when the constant failure rate assumption is valid. For non-exponential distributions, the relationship between MTTF and failure rate is more complex and depends on the specific distribution parameters.
Reliability Function and Survival Probability
The Reliability Function
The reliability function R(t) gives the probability that an item survives beyond time t without failure. This fundamental function completely characterizes the reliability behavior of an item and forms the basis for calculating other reliability metrics. The reliability function always starts at one when t equals zero, since all items are assumed functional at the start, and decreases toward zero as time increases.
The relationship between the reliability function and the failure time cumulative distribution function F(t) is complementary: R(t) equals one minus F(t). While F(t) gives the probability of failure by time t, R(t) gives the probability of survival beyond time t. Either function completely specifies the failure time distribution, and one can be calculated from the other.
For the exponential distribution, the reliability function takes the form R(t) equals e to the power of negative lambda t, where lambda is the constant failure rate. This exponentially decreasing function drops to 0.368 at t equals one MTBF and to 0.135 at t equals two MTBF. The exponential reliability function is memoryless, meaning that the conditional probability of surviving an additional time interval is independent of how long the item has already survived.
For the Weibull distribution, the reliability function is R(t) equals e to the power of negative quantity t over eta, raised to the power beta. The shape parameter beta determines the shape of the reliability curve, and the scale parameter eta determines its position along the time axis. When beta equals one, the Weibull reduces to the exponential distribution. Other values of beta produce S-shaped curves that better represent infant mortality or wear-out behavior.
Survival Probability Calculations
Calculating the probability of survival to a specified time is a common reliability engineering task. Given the reliability function parameters, the calculation is straightforward substitution. For example, with an exponential distribution having MTBF of 10,000 hours, the probability of surviving 1,000 hours is e to the negative 0.1, approximately 0.905 or 90.5 percent. Such calculations support mission planning, warranty analysis, and risk assessment.
For systems composed of multiple components, system survival probability depends on the system structure. For series systems where all components must survive for the system to survive, system reliability equals the product of component reliabilities. For parallel systems where only one component must survive, system reliability equals one minus the product of component unreliabilities. More complex configurations require reliability block diagram analysis or other system modeling techniques.
Conditional survival probability, also called residual life probability, gives the probability of surviving an additional time interval given survival to a specified time. For the memoryless exponential distribution, conditional survival probability equals unconditional survival probability for the additional time. For other distributions, conditional survival probability depends on the current age and captures how reliability changes as items age. This metric is important for decisions about replacement timing and remaining useful life.
Survival probability estimates from test or field data incorporate statistical uncertainty that should be reflected in confidence intervals. The Kaplan-Meier estimator is the standard non-parametric method for estimating the survival function from censored data. Greenwood's formula provides confidence intervals for the Kaplan-Meier estimate. Parametric estimates assume a specific distribution form and may provide narrower confidence intervals when the distributional assumption is valid.
Reliability versus Time Trade-offs
Understanding the relationship between reliability and time enables informed trade-offs in system design and operation. Higher reliability requirements for a given time period demand lower failure rates, which typically require more robust designs, higher-quality components, or redundancy. The exponential relationship between reliability and time means that modest increases in the required survival time can significantly increase the reliability challenge.
Mission reliability requirements specify the probability of successful operation for a defined mission duration. A requirement of 0.99 reliability for a 100-hour mission implies different design constraints than 0.99 reliability for a 1,000-hour mission. The longer mission requires a lower failure rate by a factor of ten to achieve the same reliability. Mission duration is thus a critical parameter in reliability requirements.
Redundancy provides a way to achieve high reliability without requiring extremely low component failure rates. A system with two parallel components, each having 0.90 reliability, achieves system reliability of 0.99. Adding a third parallel component increases system reliability to 0.999. This dramatic improvement in reliability through redundancy is a fundamental tool in high-reliability system design, though it comes with cost, weight, and complexity penalties.
Reliability growth over the product development cycle reflects improvements achieved through design iteration and test-fix-test activities. Initial prototypes typically have lower reliability than mature production units. Planning for reliability growth allows realistic scheduling and resource allocation. Reliability growth models such as the Duane model and AMSAA model provide quantitative frameworks for tracking and projecting reliability improvement.
Availability Metrics
Inherent Availability
Inherent availability (Ai) measures the proportion of time that a system is operational, considering only the effects of corrective maintenance. This metric excludes the effects of preventive maintenance, supply delays, and administrative delays, focusing on the fundamental design characteristics that determine how often a system fails and how long repairs take. The formula for inherent availability is MTBF divided by the quantity MTBF plus MTTR.
Inherent availability represents an upper bound on operational availability because it excludes delays and preventive maintenance that reduce actual availability. A system with inherent availability of 0.99 would achieve 99 percent availability if repairs could be performed instantly upon failure with no delays or preventive maintenance. Real-world availability is always lower than inherent availability due to these practical factors.
The relationship between MTBF, MTTR, and inherent availability illustrates important design trade-offs. Increasing MTBF improves availability by reducing the frequency of failures. Decreasing MTTR improves availability by reducing the duration of repair outages. Either approach can be used to achieve a target availability, and the optimal balance depends on the relative costs and feasibility of reliability versus maintainability improvements.
Calculating inherent availability requires compatible MTBF and MTTR values. Both metrics should reflect the same failure definition, operating environment, and maintenance approach. Mixing MTBF from one context with MTTR from another context produces misleading availability estimates. Careful attention to metric definitions ensures meaningful availability calculations.
Achieved Availability
Achieved availability (Aa) extends the availability calculation to include both corrective and preventive maintenance. This metric accounts for scheduled maintenance events that take the system out of service even when it has not failed. The formula for achieved availability uses mean time between maintenance (MTBM) and mean maintenance time (MMT), where MTBM includes both failure events and preventive maintenance events.
Preventive maintenance reduces failure rates by replacing or servicing components before they fail, but the maintenance events themselves reduce availability. The optimal preventive maintenance interval balances these effects, minimizing total downtime from both failures and maintenance. Achieved availability captures this balance and reflects the combined impact of the maintenance strategy.
MTBM is calculated as the reciprocal of the sum of the failure rate and the preventive maintenance rate. If a system has MTBF of 1,000 hours and undergoes preventive maintenance every 200 hours, MTBM is approximately 167 hours. The system is taken out of service more frequently than failures alone would require, but each outage may be shorter and total availability may be higher than without preventive maintenance.
Comparing inherent and achieved availability reveals the impact of the preventive maintenance program. If achieved availability is lower than inherent availability, preventive maintenance is reducing availability more than it is improving reliability. This situation suggests that the preventive maintenance interval may be too frequent or that preventive maintenance tasks are taking too long. Optimizing the maintenance program to maximize achieved availability is an important maintenance engineering task.
Operational Availability
Operational availability (Ao) is the most comprehensive availability metric, including all factors that affect the proportion of time a system is operationally capable. In addition to corrective and preventive maintenance time, operational availability includes supply delays, administrative delays, and any other factors that prevent operation. This metric reflects real-world operational conditions and is the appropriate measure for assessing actual system performance.
The formula for operational availability replaces repair time with mean downtime (MDT), which includes all time from failure to return to service. MDT encompasses administrative time to recognize and report the failure, logistics time to obtain spare parts and tools, active repair time, and any delays in returning the system to operation. MDT is typically significantly longer than MTTR, especially for systems with complex supply chains or administrative procedures.
Operational availability is strongly influenced by the support infrastructure and operating environment. The same system may have different operational availability in different locations or organizations depending on spare parts availability, technician skill, and management procedures. Achieving high operational availability requires attention to the entire support system, not just the equipment design.
Improving operational availability may require investments in logistics, training, or procedures rather than equipment redesign. Reducing supply delays by pre-positioning spare parts, reducing administrative delays by streamlining procedures, and reducing diagnosis time by improving documentation may be more cost-effective than increasing MTBF. Analysis of MDT components identifies the largest contributors to downtime and guides improvement investments.
Steady-State versus Instantaneous Availability
Steady-state availability, also called limiting availability, represents the long-term average proportion of time a system is operational. After initial transients, the system settles into a pattern where the long-term fraction of uptime converges to the steady-state availability. The availability formulas presented above calculate steady-state availability, which is appropriate for systems that operate over extended periods.
Instantaneous availability A(t) is the probability that a system is operational at a specific point in time t. This metric varies over time, starting at one when the system is known to be operational and generally decreasing as uncertainty about system state increases. Instantaneous availability eventually converges to steady-state availability as time approaches infinity, assuming the system undergoes repair upon failure.
Point availability is instantaneous availability evaluated at specific times of interest. For example, the probability that a system is operational at the start of a mission or at a specific calendar time may be of interest. Point availability calculations require detailed modeling of the failure and repair processes and their timing relative to the time of interest.
Interval availability is the expected fraction of a specified time interval during which the system is operational. This metric is useful when operation during a particular period is important, such as a production shift or a mission window. Interval availability depends on the system state at the start of the interval, the failure and repair rates, and the interval duration. For short intervals relative to MTBF and MTTR, the starting state dominates; for long intervals, interval availability approaches steady-state availability.
Percentile Life and Warranty Analysis
B-Life and Percentile Life
Percentile life metrics specify the time by which a given percentage of a population will have failed. B10 life, for example, is the time by which 10 percent of units will have failed, or equivalently, the time at which reliability equals 0.90. These metrics provide more specific information than MTTF alone because they characterize the early portion of the failure distribution where warranty claims and customer dissatisfaction are most likely.
The B-life nomenclature originated in the bearing industry where B10 life became a standard specification. The notation indicates the percentage failed: B1 is the time to 1 percent failures, B50 is median life (50 percent failures), and so on. This convention has spread to other industries and components, providing a standardized way to specify early-life reliability requirements.
Calculating B-life requires knowledge of the failure time distribution. For the Weibull distribution, B-life can be calculated directly from the distribution parameters. B10 equals eta times the quantity negative natural log of 0.90, raised to the power one over beta. The scale parameter eta strongly influences B-life, while the shape parameter beta affects how B-life relates to median life and MTTF.
B-life requirements are common in automotive and other industries with warranty obligations. A requirement that B1 life exceeds the warranty period ensures that less than 1 percent of units will fail during warranty, limiting warranty costs. More stringent requirements such as B0.1 life exceeding the warranty period further reduce warranty failures but require higher reliability. These requirements drive design decisions and quality improvements.
Warranty Period Analysis
Warranty period analysis predicts the number of failures and associated costs during the warranty period. The analysis combines the failure time distribution with production quantities and warranty terms to estimate total warranty claims. This information supports warranty pricing, reserve setting, and design decisions that affect warranty exposure.
The basic warranty analysis calculates the expected number of failures during the warranty period by integrating the failure density function from zero to the warranty duration and multiplying by the number of units. For the exponential distribution, this calculation is particularly simple: expected failures equal the number of units times one minus e to the power negative lambda times warranty period. More complex distributions require numerical integration.
Time-in-service distributions affect warranty analysis when usage rates vary across the population. A product with a one-year warranty experiences different exposure depending on whether customers use it one hour per day or ten hours per day. Accounting for the distribution of usage rates across the customer population improves warranty prediction accuracy. Usage-based warranty terms, where warranty coverage depends on operating time rather than calendar time, simplify this analysis.
Warranty cost estimation multiplies expected failures by the cost per warranty claim. Claim costs include parts, labor, shipping, and administrative expenses. Some failures may result in product replacement rather than repair, with different cost implications. Extended warranties and service contracts introduce additional complexity because they extend coverage beyond the standard warranty period and may cover different failure modes or have different terms.
Field Return Rate Predictions
Field return rate is the fraction of shipped units that are returned due to failure within a specified time period. This metric directly reflects customer experience and is a key indicator of product quality. Field return rate depends on the underlying failure distribution, the time period considered, and any selection effects that cause certain customers to be more likely to return failed units.
Predicting field return rate during design requires estimating the failure distribution and accounting for the population of units in the field. As more units are shipped and accumulate operating time, the number of returns generally increases before reaching a steady state. The time pattern of returns depends on shipping rate, failure distribution, and usage patterns. Early shipments to lead customers may have different usage patterns than later mainstream customers.
Monthly return rate normalizes returns by the number of units that could potentially be returned, providing a rate that can be tracked over time. This metric typically starts low when few units are in the field, increases as the installed base grows and accumulates operating time, and may stabilize or decline as the production ramp completes and early failures are cleared. Tracking monthly return rate reveals trends and enables early identification of reliability problems.
Annualized failure rate (AFR) expresses the failure rate as an annual percentage, facilitating comparison across products with different shipping patterns and observation periods. AFR equals total failures divided by total unit-years of exposure. This metric is widely used in the data storage industry and provides a standardized way to report field reliability. Conversion between AFR and other failure rate units enables comparison with reliability predictions expressed in different units.
Early Life and Infant Mortality
Early Life Failure Rate
Early life failure rate characterizes the elevated failure rate that many products experience during their initial operating period. This phenomenon, often called infant mortality, results from manufacturing defects, weak components, and assembly errors that cause early failures but do not affect properly manufactured units. Understanding and controlling early life failure rate is essential for customer satisfaction and warranty cost management.
The bathtub curve illustrates how failure rate varies over product life, with elevated early life failure rate, followed by a constant useful life failure rate, and finally increasing wear-out failure rate. The early life region may last from hours to thousands of hours depending on the product and its screening processes. Products that have survived the early life period have lower failure rates than newly manufactured products.
Early life failures often have different causes than useful life failures. Manufacturing defects such as solder voids, contamination, and weak wire bonds cause early failures when stressed during initial operation. These defects may be latent, meaning the product passes initial testing but fails during customer use. Understanding the dominant early failure mechanisms guides process improvements and screening strategies.
Quantifying early life failure rate requires separating early failures from useful life failures, which can be challenging when both occur simultaneously. The Weibull distribution with shape parameter less than one models decreasing failure rate, enabling estimation of early life failure rate from field data. Mixed distributions that combine early life and useful life populations may provide better fits when both failure modes are significant.
Burn-In and Screening
Burn-in subjects products to elevated stress, typically temperature, for a period intended to precipitate early failures before products reach customers. Units that fail during burn-in are removed from the population, ideally leaving only robust units for shipment. Effective burn-in reduces field failure rate by eliminating weak units that would otherwise fail in customer hands.
The effectiveness of burn-in depends on the acceleration factor between burn-in conditions and field conditions and on the proportion of the population susceptible to early failure. If early failures have strong temperature acceleration, high-temperature burn-in efficiently precipitates them. If only a small fraction of units are weak, burn-in may not be cost-effective because most units survive without defects being present.
Burn-in duration involves trade-offs between screening effectiveness and cost. Longer burn-in precipitates more potential early failures but increases manufacturing cost and cycle time. Optimal burn-in duration depends on the early life failure distribution, the cost of burn-in, and the cost of field failures. Analysis methods exist to optimize burn-in duration based on these factors.
Environmental stress screening (ESS) extends screening beyond simple burn-in by applying multiple stresses including temperature cycling and vibration. ESS aims to precipitate latent defects that would not be revealed by constant-temperature burn-in. The more aggressive stress profiles can be more effective at finding defects but must be carefully designed to avoid damaging good units. ESS is common for high-reliability and military applications.
No-Fault-Found Returns
No-fault-found (NFF) returns are products returned as defective but found to operate correctly when tested. NFF returns complicate reliability analysis because they may represent intermittent failures, customer misuse, or simply customer perception that the product is not working correctly. High NFF rates waste support resources and may mask real reliability issues.
Intermittent failures are a common cause of NFF returns. A product may fail under specific conditions in the customer's environment but operate correctly under different test conditions. Temperature, humidity, vibration, and electrical noise can all trigger intermittent failures. Replicating field conditions during failure analysis improves the detection of intermittent failure modes.
Customer-induced failures from misuse, overstress, or incorrect installation may appear as product failures even though the product operated correctly within specifications. Training customers on proper use and installation reduces customer-induced failures. Design features that prevent misuse or protect against overstress can also reduce this category of returns.
Tracking NFF rates and investigating NFF returns provides valuable information for reliability improvement. Patterns in NFF returns may reveal intermittent failure modes, inadequate test coverage, or customer education needs. Reducing NFF rates improves both customer satisfaction and support efficiency. Advanced test methods and more comprehensive test coverage can convert some NFF returns to fault-found, enabling proper root cause analysis.
Practical Applications of Reliability Metrics
Setting Reliability Requirements
Effective reliability requirements translate customer needs into measurable engineering targets. The requirements should specify the metric (MTBF, reliability for a stated mission time, availability), the required value, the confidence level for demonstration, and the conditions under which the requirement applies. Vague requirements lead to disputes and may not adequately address customer needs.
Selecting appropriate metrics depends on the application and what aspects of reliability are most important. For single-use or non-repairable items, MTTF or reliability for a specified time is appropriate. For repairable systems, MTBF and availability capture different aspects of reliability performance. Safety-critical applications may require additional metrics such as probability of dangerous failure or safety integrity level.
Requirement values should be achievable and verifiable within the program constraints. Setting requirements too high may be impossible to achieve or demonstrate within the available budget and schedule. Setting requirements too low may result in products that fail to meet customer expectations. Benchmarking against similar products, analyzing customer needs, and understanding the state of the art inform appropriate requirement levels.
Requirements should include the operating environment and conditions because reliability performance varies with operating conditions. A product may have different MTBF at different temperatures, humidity levels, or vibration environments. The requirement should specify the conditions that represent intended use or define multiple requirements for different operating scenarios. Environmental profiles derived from field measurements or standards provide a basis for specifying operating conditions.
Reliability Allocation and Apportionment
Reliability allocation divides a system-level reliability requirement among subsystems and components. The allocation establishes reliability targets that, when achieved by all lower-level elements, will result in the system meeting its overall requirement. Allocation enables parallel development of subsystems with clear reliability targets and identifies areas requiring focused reliability improvement.
Equal allocation assigns the same failure rate to each component or subsystem, regardless of complexity or inherent reliability characteristics. While simple to implement, equal allocation may result in impossible targets for some components while setting easily achievable targets for others. Equal allocation is most appropriate when little is known about the relative reliability of subsystems.
Allocation based on complexity weights assigns higher failure rate allocations to more complex subsystems that inherently tend to have higher failure rates. Complexity can be measured by part count, function count, or engineering judgment. This approach produces more achievable allocations than equal allocation but still may not reflect actual subsystem reliability characteristics.
Allocation based on historical data or similar system performance assigns failure rate allocations proportional to observed failure rates for similar subsystems. This approach produces realistic allocations that reflect actual experience. When historical data is limited, allocation can combine historical data, complexity weighting, and engineering judgment. The allocation should be revisited as design matures and better information becomes available.
Reliability Tracking and Reporting
Tracking reliability throughout product development and field service enables assessment of progress toward requirements and early identification of problems. Tracking metrics should be reported regularly and compared against targets and historical performance. Trends in reliability metrics reveal whether improvement efforts are succeeding or whether problems are developing.
Development phase tracking uses reliability predictions, test results, and failure reports to assess current reliability status. Early predictions establish a baseline that is refined as design matures and test data becomes available. Each test phase provides data to update reliability estimates. Tracking the evolution of reliability estimates reveals progress and identifies areas needing additional attention.
Field reliability tracking uses field failure data to monitor reliability performance of products in service. Data collection systems capture failure events, failure modes, operating conditions, and time in service. Statistical analysis of this data produces field reliability estimates that can be compared to predictions and requirements. Discrepancies between field reliability and predictions indicate modeling errors or unanticipated failure modes.
Reliability reporting communicates reliability status to management and stakeholders. Reports should present key metrics clearly, with context to support interpretation. Comparisons to requirements and historical performance highlight whether reliability is acceptable or requires action. Failure analysis results and corrective action status demonstrate that problems are being addressed. Effective reporting supports informed decision-making about product development and support.
Conclusion
Reliability metrics provide the quantitative foundation for measuring, predicting, and improving the dependability of electronic systems. From fundamental time-based measures like MTBF and MTTF to comprehensive availability calculations, these metrics enable engineers to set meaningful requirements, compare design alternatives, and communicate reliability performance to stakeholders.
Proper application of reliability metrics requires understanding their precise definitions, underlying assumptions, and appropriate use cases. MTBF applies to repairable systems while MTTF applies to non-repairable items. Availability metrics range from inherent availability that considers only design characteristics to operational availability that reflects real-world support conditions. Failure rate can be constant or time-varying, and the appropriate model depends on the failure mechanism being characterized.
The metrics discussed in this article support the full range of reliability engineering activities from early design through field support. During design, reliability requirements and allocations establish targets that guide design decisions. During testing, demonstrated reliability values provide evidence of achieved performance. In field service, tracking of field reliability enables continuous improvement and early identification of emerging problems.
Mastery of reliability metrics is essential for effective reliability engineering practice. These metrics form the common language used by reliability engineers, designers, managers, and customers to discuss and specify reliability requirements. Understanding the metrics, their relationships, and their proper application enables engineers to make informed decisions that result in products meeting customer expectations for dependability and longevity.