Reliability engineering analytics including Weibull distribution analysis, MTBF/MTTF/MTTR calculations, failure mode classification, and lifecycle cost modeling.
The Weibull distribution is the most widely used statistical model in reliability engineering because it can represent all three phases of the bathtub curve through a single two-parameter function. Reliatic fits failure event data to the Weibull distribution using maximum likelihood estimation (MLE), producing two parameters. Beta (shape parameter): Controls the shape of the failure distribution. When beta < 1, the hazard rate is decreasing (infant mortality or early-life failures). When beta = 1, the hazard rate is constant (random or memoryless failures, equivalent to the exponential distribution). When beta > 1, the hazard rate is increasing (wear-out or aging failures). The beta value has direct engineering significance — it tells you whether your equipment is failing due to manufacturing defects, random external events, or end-of-life degradation. Eta (scale parameter): The characteristic life, defined as the age at which 63.2% of the population will have failed. Eta is measured in the same units as the time-to-failure data (typically operating hours, calendar months, or number of cycles). Reliatic displays the fitted Weibull curve alongside the empirical failure data using median rank regression plotting, allowing engineers to visually assess goodness-of-fit and identify outliers that may represent distinct failure populations.
Reliatic calculates three fundamental reliability metrics from the asset event history. Mean Time Between Failures (MTBF): For repairable systems, MTBF is the average elapsed time between consecutive failures. It is calculated as the total operating time divided by the number of failures observed. MTBF is the primary reliability metric for equipment that is repaired and returned to service, such as pumps, compressors, and rotating machinery. Mean Time To Failure (MTTF): For non-repairable items or components that are replaced rather than repaired, MTTF is the average time from installation to failure. MTTF is appropriate for items like gaskets, seals, catalysts, and sacrificial anodes. In Weibull terms, MTTF = eta x Gamma(1 + 1/beta), where Gamma is the gamma function. Mean Time To Repair (MTTR): The average duration of a repair event, from the time the failure is detected to the time the equipment is returned to service. MTTR captures both diagnostic time and active repair time. It is a key input for availability calculations: Availability = MTBF / (MTBF + MTTR). Reliatic computes these metrics automatically from the reliability event log, which records failure events, repair events, and the associated timestamps. The calculations handle censored data (equipment still running without failure) using standard survival analysis techniques.
The Weibull beta parameter provides a natural classification of failure behavior into three categories that map directly to the bathtub curve. Infant Mortality (beta < 1): Failures are concentrated early in the equipment's life and the failure rate decreases over time. Root causes include manufacturing defects, installation errors, commissioning problems, and material quality issues. The engineering response is to improve quality control, commissioning procedures, and acceptance testing — not to increase inspection frequency, which would be ineffective against these causes. Random Failures (beta approximately 1): The failure rate is roughly constant over time, meaning the equipment is equally likely to fail in any given period regardless of age. This pattern is characteristic of externally-caused failures (impact damage, operator error, process upsets) and some electronic component failures. Age-based replacement is ineffective against random failures; condition monitoring and protective systems are the appropriate response. Wear-out (beta > 1): The failure rate increases with age, indicating a time-dependent degradation mechanism such as corrosion, erosion, fatigue, or creep. This is the only failure pattern where age-based preventive maintenance or time-based inspection is effective. The higher the beta value, the more predictable the failure timing — a beta of 3.5 or higher indicates a tight wear-out distribution where preventive replacement just before the characteristic life is highly effective.
B-life values (also called L-life in bearing engineering) express the age at which a given percentage of the population is expected to have failed. Reliatic calculates B-life from the fitted Weibull parameters using the formula: B_p = eta x (-ln(1 - p/100))^(1/beta). The most commonly used percentiles are: B1 (1% failure): The age at which 1 in 100 units is expected to have failed. B1 life is used for safety-critical applications where even a small probability of failure is unacceptable. B10 (10% failure): The standard warranty life metric and the basis for preventive replacement in many maintenance strategies. Replacing components at B10 life means accepting a 10% probability that the component will have already failed before replacement — an acceptable trade-off for non-safety-critical equipment. B50 (50% failure): The median life, the age at which half the population is expected to have failed. B50 is useful for spare parts planning: if you have 100 identical components, you should expect approximately 50 to need replacement by the B50 life. Reliatic displays B-life values on the Weibull plot and uses them in the reliability dashboard to flag equipment approaching its B10 or B50 life.
For complex maintenance optimization decisions, Reliatic provides Monte Carlo simulation that models thousands of possible futures for an asset or fleet. The simulation samples from the fitted Weibull distribution to generate random failure times, applies the maintenance policy (run-to-failure, time-based replacement, or condition-based replacement), and accumulates costs over the planning horizon. Each simulation run tracks: failure costs (repair labor, parts, production loss, and consequential damage), preventive maintenance costs (planned replacement labor and parts), inspection costs (NDE services, scaffolding, insulation removal), and inventory holding costs (spare parts stored on site). By running 10,000 or more iterations, the simulation produces a distribution of total lifecycle cost for each maintenance strategy. Engineers can compare strategies objectively: for example, replacing a pump seal every 18 months versus running to failure with a spare on the shelf. The simulation accounts for the stochastic nature of failures — unlike deterministic analysis, it reveals the range of possible outcomes and the probability of worst-case scenarios. This is particularly valuable for spare parts optimization: the simulation determines the minimum number of spares needed to achieve a target service level (e.g., 95% probability that a spare is available when needed).