Bathtub curve failure This curve describes how the failure rate of many products and systems changes over time. Deterioration modeling The bathtub curve hazard function (blue, upper solid line) is a combination of a decreasing hazard of early failure (red dotted line) and an increasing hazard of wear-out failure (yellow dotted line), plus some constant hazard of random failure (green, lower solid line). Understanding the bathtub curve is helpful when planning maintenance May 6, 2021 · OPERATIONS MANAGEMENT BATHTUB CURVE The bathtub curve describes a particular form of a failure rate function which comprise three parts: early failure, random failure and wear out failure. What follows is a period where failures… In this video we go over the main ideas of the bathtub curve, and how it's actually a summation of the modes and components under the asset being studied. These are: The ‘Bathtub Curve’ timeline of failure Hazard function (black solid line) incorporates rates of early failure (blue dotted line) with end of life wear-out failure (yellow dotted line), and continuous, unchanging random failure rates (red dotted line) Jul 23, 2025 · Pre-requisites: Software Engineering In Software Engineering, the concept of a software failure curve is part of the hardware bathtub curve. It consists of three main periods: A viable explanation to the reliability bathtub curve is presented wherein failure rate is governed by a physical process of component strength decay over time due to a distributed applied stress. And, more importantly, hard drives are failing less and lasting longer. This graph is used in reliability engineering and deterioration modeling. We typically talk about a failure mode being placed in one of the three categories, Quality (infant Mortality), Use stress, or Wear-out. time, which we would see if we were to wait long enough and keep good records for a given lot of devices. May 15, 2025 · The maintenance bathtub curve is a graphical representation that plots failure rate against time for industrial assets. 1 is normally used to describe engineering systems’ failure rate. Figure 1. Illustra‐tive Figure 3-1 shows the bathtub curve, a classic representation of random hardware faults over three key periods of a semiconductor product’s lifetime. time. The initially very high failure rates due to ‘infant mortality’ are followed by very low failure rates typical within the useful or design life of a component. Most reliability engineers are familiar with the traditional failure profile represented by the bathtub curve, as shown below. But in fact any specific type of failure mode may have driving factors in multiple categories. 2 Failure Rate and Probability of Failure Bathtub curve The reciprocal value of the MTBF that is a measure for the reliability of a component is the failure rate λ. Nov 20, 2021 · The original concept of the P-F curve was to identify a detectable triggering event along the useful life portion of a bathtub curve (P) and the survival rate to a point of defined failure (F). This curve shows that hardware exhibits a relatively high failure rate early in its life (these failures are often design or manufacturing defects); defects are corrected, and Understanding Bathtub Curve in Electronics Reliability allows engineers to implement strategies to reduce failure rates. Operational Failure Rate As a visual representation of machinery or equipment failure, the bathtub curve describes the Oct 15, 2025 · After 13 years, the data is clear—the bathtub curve does not apply to hard drives. Illustrative examples are included. The bathtub curve is divided into three distinct phases: initial production defects, a period of relatively low failure rate Nov 6, 2025 · The “bathtub curve” is a graphical representation that the electric company uses to make equipment replacement decisions. During this phase, components or systems may experience Example 2. The Muth distribution follows a “bathtub” shape (in blue) for observed failure rates. Components, like people, have a life expectancy. the facility begins to function to its full performance Dec 10, 2019 · Explain Bathtub Curve and its utility in reliability engineering. It shows higher failure rates early and late in a system’s lifespan, with a more stable period in between. A team at the University of Stuttgart looked at failure data collected from 20 different A real bathtub curve would capture all the different types of failure modes, represented by each of these lines. Schematic deterioration of an asset over time. Nov 17, 2015 · Unlike the replacement steam generator tubes at San Onofre, the replacement condenser tubes successfully navigated through the left-hand side of the bathtub curve. Not all assets come to this end, as some are phased out before their wear-out stage. The ‘Bathtub Curve’ timeline of failure Hazard function (black solid line) incorporates rates of early failure (blue dotted line) with end of life wear-out failure (yellow dotted line), and continuous, unchanging random failure rates (red dotted line) You may have heard of the bathtub curve, a failure rate graph, which is often used for measuring the reliability of products during their lifetime. The three sections of the bathtub curve – early fail, useful life, and wear-out – often have different shapes for failure distributions, as illustrated in the figure. It gets its name from its distinctive shape that resembles a cross-section of a bathtub, high at both ends with a flat section in the middle. 4. In between, the curve shows a long sustained period with a low failure rate. This curve is modeled mathematically by exponential functions. Many consider it the most valuable graph for the reliability of assets, as it can help you better predict asset failure and identify the root cause. This is a failure data analysis site to support validation and decision making for reliability, maintenance and management. Aug 29, 2024 · In the world of product reliability, the bathtub curve is a familiar concept. Learn how to enhance efficiency and reduce costs by understanding failure curves. Usually, an equipment has, at the beginning of its useful life, a high failure rate, due to manufacturing problems, improper installation, defective components, incorrect assembly. The Weibull curve is called a "bathtub curve," because it descends in the beginning (infant mortality); flattens out in the middle and ascends toward the end of life. On the left in dark grey are failures due to infant mortality, early life fails. The bathtub curve has three phases, each of them representing a product life phase. Jun 14, 2025 · The bathtub curve is a fundamental concept in reliability engineering and maintenance practices. The bathtub curve can be a useful tool to plot and visualize the expected quality of the software product, system, or sub-module but tracking the failure rates over time and assessing whether the observed failure rates are in line with the expected failure rate. The 'bathtub' refers to the shape of a line that curves up at both ends, similar in shape to a bathtub. The bathtub curve, named for its shape and shown in Fig. The bathtub-shaped distribution is used in survival analysis and reliability engineering to describe a product or system’s’s failure rate over its lifespan. Divided into three parts, the bathtub curve shows how the likelihood of failure changes with time. In manufacturing plants and industrial facilities, using the bathtub curve can greatly improve maintenance programs and efficiency. According to the diagram, the failure rate is a function of time for Hardware. Mar 22, 2019 · Bathtub Curve profiles the failure rate of a large sample of components (or a large sample of systems) as they age. Knowing what the bathtub What is the bathtub curve?The concept of the bathtub curve is derived from the human life experience involving infant mortality, chance failures, plus a wear out period of life since data for births and deaths is accumulated by government agencies. A common graphical interpretation of the failure rate is shown in Figure 2-5. Wear Out: Probability for failure increases due to expiration of design lifetime The 'Bathtub Curve' timeline of failure Hazard function (black solid line) incorporates rates of early failure (blue dotted line) with end of life wear-out failure (yellow dotted line), and continuous, unchanging random failure rates (red dotted line) RELIABILITY Explained! Failure Rate, MTTF, MTBF, Bathtub Curve, Exponential and Weibull Distribution CQE Academy 52. Divided into three sections the bathtub curb describes the hazard function and how failures are experienced; • the first part is a decreasing failure rate, known as early failures (infant mortality), • the second phase is a constant failure rate, known as random failures, • the third part is The Bathtub Curve is a graphical representation of the failure rate of a component or system over time, characterized by three distinct phases: "infant mortality" with a high failure rate from defects; "useful life" with a low failure rate; and "wear out" with a high failure rate as the component reaches end of life. The Bathtub curve The “bathtub curve” describes the hypothetical failure rate of a device versus time. For example, the random charts include the so-called infant mortality curve, which also makes up part of the bathtub curve, and it does indicate a higher risk of early life failure on a time line. It shows the typical trend of failure rate over time (Figure 1). The fallacy of the bathtub curve seems to derive from the fact that so many failures follow the infant mortality curve, which is indiscernible from a bathtub curve until or unless the item is allowed to run to failure to collect the additional age-related data. A bathtub curve is a statistical depiction of the failure rate over the lifetime of a population of products and is related to a failure-distribution curve: they can be combined to form a continuous curve. Introducing the “Bath Tub” curve concept In the Reliability and Maintenance world, we often refer to what is known as the “bathtub” curve and ask the question: “What is the bathtub curve for this equipment?” The name “bathtub” comes from the equipment failure rate curve resembling a sanitary bathtub’s longitudinal section. An experienced electricity accident lawyer Oct 20, 2025 · Backblaze disk drive failure stats suggest the “bathtub curve” effect may be imaginary. Weibull distribution is a versatile mathematical function that can represent all three sections of the bathtub curve, typically using only two adjustable parameters – β and η. A bathtub curve ismis a statistical depiction of the failure rate over the lifetime of a population of products and is related to a failure-distribution curve: they can be combined to form a continuous curve. The Bathtub Curve The life of a population of units can be divided into three distinct periods. As they get fixed Oct 31, 2024 · The break-in curve, which represents the initial phase of the bathtub curve, depicts a high initial failure rate that decreases over time. Companies leverage bathtub curve analysis to set performance expectations of assets throughout their life cycle. A detailed discussion about the curve can be found in the topic Traditional Reliability. For simple reasons of Product Stabilization 1) The Early stage failures would be high. Oct 26, 2021 · Hard drive failure rates tend to follow the “bathtub curve. Download scientific diagram | Bathtub curve of typical failure rate for components. In the early life of an asset, failures often occur more frequently due to initial May 12, 2023 · The failure rate increases gradually and the bathtub curve function has a positive slope. It has been touted as a dependable and accurate representation of various products, including hardware and other technology products. On the right in light gray are failures due to wear-out, or end of life. Lambda = failure rate = 1/MTBF, and t = time. The MEW model is designed to provide a more accurate description of failure time data resulting from a system with one or more May 23, 2024 · Explore the concept of the Bathtub Reliability Curve, which illustrates the lifecycle of product failures and its importance in maintenance planning. The bathtub curve is a graph of failure rate versus time that illustrates the failure rate tendencies of an item over its life span. In this comprehensive guide, we will explore the theoretical In this article, we explore the bath-tub curve, its significance in various industries, and how it relates to product reliability and performance over time. Mar 15, 2023 · The bathtub curve is a visual way to understand how machines, products and components fail with time. Apr 1, 2003 · The bathtub curve is an important tool for hardware reliability assessment (HWRA), as it allows manufacturers to analyze the failure rate of hardware over time and take steps to minimize the 1. The bathtub curve occupies a place of considerable impor-tance in reliability practice, particularly in justifying burn-in strategies for improving system reliability. It is called the normal life. The first period is called Infant Mortality period. This model is known as the "bathtub" curve and was initially developed to model the failure rates of mechanical equipment. The early stage of facility failure is called the initial failure period. The failure rate function is increasing and approaches 1 when t → ∞. For example, you can use this curve to eliminate the initial failure and get rid of ‘dead on arrival’ products. Why should IT decision makers be concerned with the Bathtub Curve? The bathtub curve is one of the most famous graphical representations in reliability. Histogram of Exponential Data The Exponential models the flat portion of the "bathtub" curve - where most systems spend most of their "lives" Uses of the Exponential Distribution Model Because of its constant failure rate property, the exponential distribution is an excellent model for the long flat "intrinsic failure" portion of the Bathtub Curve. Figure 1 shows the reliability “bathtub curve” which models the cradle to grave instantaneous failure rates vs. A bathtub curve graphically relates three types of failure: early, random, and wear out. Jun 15, 2023 · The bathtub curve is a fundamental concept in maintenance and reliability engineering. The first phase, or "infant mortality," is characterized by a higher failure rate Bathtub Hazard Rate Curve The bathtub hazard rate curve shown in Figure 3. The bathtub curve for Software Reliability Over time, hardware exhibits the failure characteristics shown in Figure 1, known as the bathtub curve. According to the theory Oct 11, 2023 · Importance of Bathtub Curve The Bathtub Curve is an important concept in technology as it represents the failure rates of a product over time, illustrating the three distinct phases of a product’s life cycle: infant mortality, normal life, and wear-out phase. It has three stage: Infant mortality period, normal life period, and wear-out period. 8. The Bathtub curve is a reliability model well matched to the Semiconductor industry, it is not one curve but the consequence of 3 Explore the intricacies of the product life failure curve to optimize durability and predict system reliability in engineering and design. Jun 11, 2025 · The upward curve – an increasing failure rate due to late failures as products wear out and hit their end-of-life point. Failure rate begins at a relatively high value starting at time zero due to defects in manufacture. Aug 2, 2018 · The theory behind the bathtub curve and its shape is generated by tracking the number of early failures during the commissioning and startup process, the number of random failures relative to constant failures during the equipment’s useful life period and the rate of normal wear failures as the product reaches or exceeds its design lifetime. Imagine the shape of a bathtub – it starts with a steep slope, flattens out in the middle, and then ends with another steep slope. This article introduces a new flexible four parameter distribution by convolution of the exponential and Weibull distribution using the odd function transformation, which offers greater flexibility in terms of fit, its called the modified exponential-Weibull (MEW). Plotted is the failure rate, h (t), versus time. Bathtub curve is usually considered to be one of most useful and essential graphical representations of reliability of assets. 15-11, is perhaps the most famous graphical representation in the field of reliability. Nov 30, 2017 · A curve that (a) is shaped like the longitudinal cross-sectional profile of an old-fashioned bathtub, (b) characterizes failure rates as a function of time for large populations of components, such as are used in communications, computer, data processing, and control systems, and (c) shows (i) an early failure-rate period with a high failure rate that weeds out defective items, (ii) followed The "bathtub curve" is an engineering term that refers to the reliability of a product or system. 2 Consider an item with failure rate function z(t) = t/(t + 1). Attention is paid to the useful-life period, where the failure rate is con‐stant and the distribution of times to failure (or between failures) is exponential. It presents a graphical representation of the failure rate of an asset throughout its entire lifecycle, providing a quick view into performance and reliability and helping inform key decisions. The bathtub curve is a particular shape of a failure rate graph. High but decreasing failure rate in the first part of the curve (1) indicates products defective or prone to fail due to manufacturing Changing the parameters changes the shape of the distribution: The classic “bathtub curve” to describe failure rate over time is a mix of three Weibull distributions fit the different subpopulations of parts. As shown in figure the curve is divided into three parts: burn-in period, useful-life period, and wear-out period. It is an important concept in engineering and risk management because it helps identify points in the cycle where maintenance and repair are most likely to be necessary. The reason for the name is pretty obvious. The term “bathtub” comes from the shape of the hazard function when plotted over time. Feb 28, 2024 · The bathtub curve illustrates the typical failure pattern of an automation system. It is called a bathtub curve because the average graph matches the shape of a bathtub. This graphical representation illustrates the failure rate of a product over its lifetime, typically divided into Feb 8, 2023 · The bathtub curve is a visual representation of a product’s life cycle, from production to failure. The third period begins at the point where the slope begins to increase and extends to the end of the graph. The three distinct regions are infant mortality, random failures, and wear out. Understanding the bathtub curve is crucial for optimizing maintenance strategies, reducing downtime, and improving overall reliability. Revisiting the Bathtub Curve In our popular 2020 article The Bathtub Curve and Data Center Equipment Reliability, Jake Blough, Chief Technology Officer for Service Express, dispels several myths about new and aging hardware. In this proposed alternate approach to studying reliability, interdisciplinary boundaries are crossed as links between the fields of reliability engineering, quality control and fracture mechanics Jan 4, 2016 · Bath-tube curve The frequency of facility failures is higher at the beginning stage and at the later stage of its life cycle. from publication: Reliability Evaluation of Underground Power Cables with Probabilistic Models | Underground The bathtub curve is a concept used in reliability engineering to describe the varying failure rates of a system over time. See full list on qualitygurus. The bathtub curve refers to a graphical representation of the failure rate of a product over its lifetime, which consists of three distinct periods: an initial period of high failure rate due to handling, storage, and installation errors, a normal life period with a constant failure rate, and a wear-out period with an increasing failure rate. Definition This curve describes the typical equipment failure rate against time since fit and takes the shape of a bath tub cross section. Later. Apr 16, 2025 · The bathtub curve is an engineering concept that illustrates potential failure rates for underground systems over time. If you plot the frequency of facility failures over time the chart looks like a bathtub. The Bathtub Curve theory suggests that equipment failure rates are high when a product is released, then decrease over the next two to three years. com Jul 21, 2025 · A bathtub curve visually represents the failure rate of one or more assets by plotting their failure occurrences over time. Aug 21, 2023 · What is the purpose of a bathtub curve? A bathtub curve is key to eliminating asset failure. 1. Assets are usually equipment, components Jun 18, 2024 · The ‘bathtub curve’ (blue, upper solid line) for Semiconductor Reliability is a combination of a decreasing Early Failure (red dotted line) and an increasing Wear-out Failure (yellow dotted line), plus some Constant (Random) Failure (green, lower solid line). Attention is paid to the useful-life period, where the failure rate is constant and the distribution of times to failure (or between failures) is exponential. In reliability context, the so called bathtub curve is an idealized representation of the failure rate (or MTBF) of a population of items over time. Period A, B and C stands for burn-in phase, useful life phase and end-of-life phase. This article provides an overview of how infant mortality, normal life failures and wear-out modes combine to create the overall product failure distributions. In the case of components, the terms service life or design life better indicate that a component’s life expectancy is how long it was designed to last. 1K subscribers Subscribe Apr 25, 2025 · The curve that demonstrates this probability of failure over time is known as the bathtub curve (or failure rate curve). The corresponding survivor R(t) MTTF function is. The Famous Bathtub Curve Figure 1 shows the reliability “bathtub curve” which models the cradle to grave instantaneous failure rate vs. The next period is the flat portion of the graph. The resulting curve describes not only the behavior of engineering components, but also the lifetimes of human populations. However, it has now been adopted by the semiconductor industry and has become an integral part of semiconductor reliability theory. It shows how equipment failure rates are highest when the equipment is new and then later when the equipment has “worn out” due to age and use. This data helps manufacturers predict when failures happen and hopefully identify root causes and prevent them. In short, it is the idea that when a product is new, there is a brief "burn-in" period, where the rate of failure is relatively high. Apr 21, 2020 · The Bathtub Curve Here's a bathtub curve. Thus the shape is called the bathtub curve. Electronic component and circuit failures follow a trend, commonly referred to the bathtub curve. If we follow the slope from the start to where it begins to flatten out this can be considered the first period. The fundamental approach of this service is to present field data in a form of a bathtub curve and MTBF values, and use characteristic performance properties obtained from the data as a basis to reach engineering and/or management decisions. 2. Time goes from left to right as usual, and the vertical access measures the failure rate. This curve simply represents overall life cycle of assets and failure rate of overall population of assets over time. Not all products work to the Bathtub Curve, but many items of IT hardware do – as indeed, do many electronic consumer products. The same failure mode may have a sensitivity to Apr 13, 2016 · Typical time course of failure rate of unrepaired objects, called bathtub curve, is shown and its main stages are explained: period of early failures, useful life, and period of aging and deterioration. What is the Bath-Tub Curve? H2: Definition and Overview The bath-tub curve is a graphical representation that illustrates the failure rate of products over their lifetime. When you plot failures over time, the bathtub curve will Jul 20, 2016 · Why do assets fail? Understanding the pattern of asset failure is the first step towards defining effective strategies to improve their reliability and availability. Bathtub curve The 'bathtub curve' hazard function (blue, upper solid line) is a combination of a decreasing hazard of early failure (red dotted line) and an increasing hazard of wear-out failure (yellow dotted line), plus some constant hazard of random failure (green, lower solid line). While there The bathtub curve is a concept used in reliability engineering to describe the failure rate of a system or component over time. Apr 7, 2022 · The Bathtub Curve The failure rate of components follows a trend called a “bathtub curve” where the failure rate starts high and quickly drops (the burn-in period), followed by a low, constant failure rate period, and ending in the wear-out period where the failure rate steadily increases with time. The first period is characterized by a decreasing failure rate We’ve all heard from reliability experts that the “bathtub curve” – the poor, misunderstood bathtub curve – fails to accurately reflect a machine’s failure rate as a function of time. It describes methods to reduce failures at each stage of product life and shows how burn-in, when appropriate, can significantly reduce operational failure rate. It is named for its resemblance to the shape of a bathtub. 10) describes the failure rate: Shape < 1 is a decreasing failure rate (infant mortality) Shape > 1 is an increasing failure rate (wear-out failures) The Bathtub Curve is graph model made to represent the failure rate of a group of products over a period of time. The idea is that disk drives fail either early on in their life or after many years, and a plot of failure rate over time shows a U-shaped curve with higher rates at the start and end of working life and few or no failures between these points. The Shape parameter (slope = 2. Hardware reliability and the bathtub curve The bathtub curve reliability theory suggests equipment failure rates are higher when the hardware is new to the market, decreases in the middle of the product’s life cycle and increase again toward the End of Service Life (EOSL). Nov 30, 2022 · Bathtub Curve is generally graph that is used to graphically demonstrate run-to-failure maintenance strategy. It provides a graphical representation of the failure rate of a product or system over its lifetime. Most equipment lacks the birth/death recording by g Jun 9, 2023 · The bathtub failure refers to a particular type of insulation failure characterized by a bathtub-shaped curve when plotting the failure rate against time. The bathtub curve is only for the Hazard function as it shows how a variety of failure modes throughout the life of a population can shape the hazard into a bathtub shape. Abstract Typical time course of failure rate of unrepaired objects, called bathtub curve, is shown and its main stages are explained: period of early failures, useful life, and period of aging and deterioration. It consists of three phases. A bathtub curve is a graphic representation of the failure rate of an asset over its life cycle. This curve can be divided into three parts corresponding to decreasing, constant and increasing failure rate. Plotting of the statistical failure rate λ over time t gives the bathtub function shown below (bathtub curve). More on this later. Is this concept applicable for all products? My interpretation : Mostly used in New Product to the Market offerings : Eg : Air Purifiers, Hotel Baking Industry machine new model or a simple NEW to market Coffee Maker. Uncover the 6 patterns of failure every maintenance engineer should know. As a final example, we will create a bathtub curve by creating and layering several distributions. With increasing time, this is followed by a period of progressively increasing failure rates Aug 9, 2021 · Failure to compute: Why we fall into the first 90 days of the Bathtub Curve Reliability engineers know this kind of failure as the beginning of what’s known as the Bathtub Curve — the life cycle curve that graphically illustrates the rate of failure of a product over time. The bathtub curve has 3 regions: Named because the primary curve resembles a tub, the bathtub curve is particularly useful in reliability engineering and deterioration modeling. ” What is this curve, and how does it indicate the drive failure rates at Backblaze? Jun 16, 2020 · Failure Pattern A is known as the bathtub curve and has a high probability of failure when the equipment is new (infant mortality), then a long period of low probability random failures over time and then sharply increasing at the wear-out point. It’s a good news, bad news situation—the high failure rate on the left-hand side was avoided only to approach the high failure rate on the right-hand side of the bathtub curve. "Bathtub" curve A plot of the failure rate over time for most products yields a curve that looks like a drawing of a bathtub If enough units from a given population are observed operating and failing over time, it is relatively easy to compute week-by-week (or month-by-month) estimates of the failure rate h (t). Apr 10, 2025 · The Bathtub Curve, with its initial decreasing failure rate followed by a constant and then increasing rate, captures the typical life stages of a product: early failure, random failure, and wear-out failure. Oct 26, 2023 · Updated on September 25th, 2024 The bathtub curve is a useful tool for data center executives and operators to visualize the reliability of their assets over a period of time. bjmd ltjox bzjrhbmw fbn gypx kmes oadln sbfo zoyx rkix rrdlmzwz fozd vqlddd uagbtt reoe