What Is Failure Rate?

Failure rate is a measure of the frequency at which engineered items fail, expressed as the number of failures per unit time for a given population of items operating under specified conditions. It is the fundamental quantity in reliability engineering, used to predict how long a component or system will function before failure, to specify maintenance intervals, to compare the reliability of competing designs, and to estimate the probability that a system will complete a given mission without failure. Failure rate is often denoted by the Greek letter lambda (λ) and expressed in units such as failures per million hours (FIT, Failures In Time, where 1 FIT equals 10⁻⁹ failures per hour) for electronic components, or failures per operating cycle for mechanical items.

The reciprocal of failure rate, for items with a constant failure rate, is Mean Time Between Failures (MTBF) for repairable systems or Mean Time to Failure (MTTF) for non-repairable items. These quantities are widely used in system reliability prediction and in contractual reliability requirements.

The Bathtub Curve and Failure Rate Phases

Most hardware populations exhibit a failure rate that varies over the product's lifetime in a pattern described by the bathtub curve. In the early-life phase, failure rate is elevated because manufacturing defects, assembly errors, and material anomalies cause a disproportionate number of units to fail shortly after entering service. This infant mortality region is characterized by a decreasing failure rate over time as weak units are removed from the population.

The middle region of the bathtub curve shows an approximately constant failure rate corresponding to random failures from external stresses and unanticipated events rather than intrinsic degradation. In the final wear-out phase, failure rate increases as accumulating fatigue, corrosion, and material degradation bring increasing fractions of the population to end of life. NIST's engineering statistics handbook describes the mathematical basis for the bathtub curve model and the Weibull distribution parameters that characterize each phase.

Statistical Models and Weibull Analysis

The Weibull distribution is the most widely used statistical model for failure time data because its shape parameter directly encodes which phase of the bathtub curve the data represents. A shape parameter below 1 indicates decreasing failure rate (infant mortality), a shape parameter equal to 1 indicates constant failure rate (the exponential distribution, appropriate for the random failure phase), and a shape parameter above 1 indicates increasing failure rate (wear-out). Fitting a Weibull distribution to failure time data from accelerated life tests or field returns yields an estimate of the failure rate at any operating time and under any stress condition for which an acceleration model exists.

Corrosion, degradation, endurance, and fatigue are among the mechanisms that drive increasing failure rates in the wear-out phase of fielded hardware. Physics of failure models, developed through programs at NASA and defense laboratories, provide mechanistic equations that relate temperature, humidity, voltage, and mechanical stress to the acceleration of these degradation mechanisms. NASA's physics of failure methodology provides the quantitative foundation for computing failure rates from first principles rather than relying solely on handbook averages.

Failure Rate in System Reliability Analysis

Component-level failure rates combine to produce system-level reliability predictions through reliability block diagram models, fault trees, or Markov analysis, depending on the complexity of the system architecture. FMEA and FMECA use failure rate data to compute occurrence ratings and criticality numbers for individual failure modes. Field failure data, collected through FRACAS or warranty return analysis, provides empirically observed failure rates that can be compared against design predictions and used to update reliability models as products age in service.

Applications

Failure rate analysis and prediction have applications across a wide range of technical disciplines, including:

• Electronic component and assembly qualification and life prediction
• Military and aerospace system reliability requirements and verification
• Power grid equipment maintenance scheduling and spare parts planning
• Medical device post-market surveillance and corrective action programs
• Industrial process equipment preventive maintenance interval optimization