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Topic: Bathtub curve

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In the News (Fri 18 Apr 14) "Bathtub" curve
Because of the shape of this failure rate curve, it has become widely known as the "Bathtub" curve.
NOTE: The Bathtub Curve also applies (based on much empirical evidence) to Repairable Systems.
In this case, the vertical axis is the Repair Rate or the Rate of Occurrence of Failures (ROCOF).
www.itl.nist.gov /div898/handbook/apr/section1/apr124.htm   (378 words)

  The Bathtub Curve and Product Failure Behavior (Part 1 of 2)
The bathtub curve consists of three periods: an infant mortality period with a decreasing failure rate followed by a normal life period (also known as "useful life") with a low, relatively constant failure rate and concluding with a wear-out period that exhibits an increasing failure rate.
Note that the bathtub curve is typically used as a visual model to illustrate the three key periods of product failure and not calibrated to depict a graph of the expected behavior for a particular product family.
In this issue, Part One, we have introduced the concept of the bathtub curve and discussed issues related to the first period, infant mortality, as well as the practices, such as burn-in, that are used to address failures of this type.
www.weibull.com /hotwire/issue21/hottopics21.htm   (2869 words)

  Bathtub curve - Wikipedia, the free encyclopedia
The bathtub curve is widely used in reliability engineering, although the general concept is also applicable to humans (for example in actuarial work).
The bathtub curve is generated by mapping the rate of early "infant mortality" failures when first introduced, the rate of random failures with constant failure rate during its "useful life", and finally the rate of "wear out" failures as the product exceeds its design lifetime.
The bathtub curve is often modeled by a piecewise set of three hazard functions,
en.wikipedia.org /wiki/Bathtub_curve   (197 words)

 Latest news about Bathtub   (Site not responding. Last check: 2007-11-02)
Reliability specialists often describe the poxahozo of a population of kgusodsf using a kgitsurip representation meslig the bathtub curve.
Wear-out Bathtub is a bajh of life due to fatigue or depletion of materials (such oh lubrication depletion in bearings).
curve is typically used as a nipuin model to illustrate the three key firiert of product leesexa ewd yag calibrated to depict a vrewg of the expected zasaqiez for a particular rhayors family.
bathtub.letgosearch.com /sitemap.htm   (367 words)

 Bathtub Curve - Bathtub Curve information
Or it may have a more complicated shape, like the well-known "bathtub" curve for human mortality, where the hazard is high for newborns, drops quickly, stays low through adulthood, and then rises...
Bell Curve 101 by Tim MacMurray The Bell Curve is the plot of all the shots...
Actual whole-disk failure rates conform to a bathtub curve as a function of the disk's service time: A higher failure rate is encountered during the beginning-of-life burn-in and end-of-life wear-out...
www.bathtubinfo.com /bathtubcurve   (1806 words)

 U.S. Nuclear Plants in the 21st Century
The fact that 27 nuclear reactors have been shut down in the past two decades for safety problems that took a year or longer to fix demonstrates that errors are abundant and margins for error are still necessary.
Despite efforts to monitor the condition of aging equipment, there are recent age-related failures caused by monitoring the right areas using the wrong techniques and by monitoring the wrong areas using the right techniques.
While the risks and reasons for the risks vary along the bathtub curve, the consequences of failing to manage the risks remain nearly constant—potentially massive releases of radioactivity into the atmosphere with devastating harm to people and places downwind.
www.ucsusa.org /clean_energy/nuclear_safety/us-nuclear-plants-in-the-21st-century.html   (757 words)

 Bathtub Curve Showing Infant Mortality, Useful Life and Wearout Phases
shown in the figure) and is not related to the length of the curve (i.e., longevity).
Electronic systems reliability engineering theory is usually most concerned with the height of the failure rate curve during the useful life of a system life (i.e., the Phase 2 portion of the curve).
Many studies have shown that the height of the curve (magnitude of system failure rate) is directly proportional to applied stress.
www.quanterion.com /FAQ/Bathtub_Curve.htm   (394 words)

 System ageing and reliability (learning curve, bathtub curve). This is Page 17 of SYSEV's website.
When combined with the learning curve, the behaviour described by equation (RL 01) plots as what is often called a "bathtub curve".
This curve shows three successive stages: (1) one learning stage as described by Duane, followed by (2) a period with constant failure rate interpreted as corresponding to random failures, and (3) a final stage with an increase in the failure rate due to wear out phenomena.
Moreover, the integral of the bathtub curve must be a curve showing a first concave (from below) part followed by a convex (from below) part, both parts being separated by an intermediate, quasi-straight linear zone of variable length.
www.sys-ev.com /reliability01.htm   (623 words)

 [No title]   (Site not responding. Last check: 2007-11-02)
Each of these comparisons is combined with all the other comparisons in a least squares manner, and the curve fit input factors are adjusted automatically within the fitting tool to results in the overall optimum fit result.
The classic bathtub curve analyzes opening and has the low BER region in the center of the plot.
Further, since the curve fit DJ pdf is modeled as a dual delta function, both deltas (complete DJ pdf) are considered in both sides of the combined BER histogram.
www.t10.org /ftp/t11/document.99/99-489v0.txt   (479 words)

 Reliability and its requirement, Reliability Vs. Quality Control, The bathtub Curve
The bathtub curve is a plot of failure rate vs. time.
It is characterized by three regions in time: an initial region of decreasing failure rate, and intermediate region of relatively constant failure rate, and a final region of increasing failure rate.
The bathtub curve is actually a composite curve, made up of the sums of three smaller curves: infant mortality, random failures, and wear out.
www.tutorialsweb.com /reliability/reliability1,2,3.htm   (454 words)

 Bathtub - Bathtub information   (Site not responding. Last check: 2007-11-02)
Restoration Bathtub Liners Our site is a consumer resource for reviews of bathtub liners and their options for materials- such as acrylic, colors, installation, etc. Home Request a Bathtub Liner...
Bathtub - Songs for Kids and Their Grownups Little did David know when he recorded this CD that it...
17 Kb bathtub-035- 52.21 Kb bathtub036- 26.28 Kb bathtub-037- 32.88 Kb bathtub038- 31.85 Kb bathtub...
www.bathtubinfo.com /bathtub   (1629 words)

 The Bathtub Curve and Product Failure Behavior (Part 2 of 2)
Part One examined the first period of the curve, infant mortality, and also discussed issues related to burn-in, a common practice to reduce the occurrence of this type of failure during the useful life of the product.
It is quite simple: when the exponential distribution applies (constant failure rate modeled by the flat, bottom of the bathtub curve), MTBF is equal to the inverse of failure rate.
As demonstrated in Parts One and Two of this article, the traditional bathtub curve is a reasonable, qualitative illustration of the key kinds of failure modes that can affect a product.
www.weibull.com /hotwire/issue22/hottopics22.htm   (3059 words)

 CommsDesign - Tutorial on Analyzing High Reliability: Part 1
Region 3 is the wear out region and is that part of the bathtub curve where the failure rate increases.
In addition to using bathtub curves, manufacturers use accelerated stress testing (AST) to ensure that failures due to defects occur before the product leaves the factory.
Now that we've looked at bathtub curves and AST testing, let's explore the case where we are operating on the flat portion of the bathtub curve where the failure rate h(t) is constant over time and remains the same for a unit regardless of the unit's age.
www.commsdesign.com /showArticle.jhtml?articleID=18311424   (2027 words)

 Determining the Frequency of Condition Monitoring tasks
If you think the bathtub applies, increase frequency soon after commissioning and when you think the component might be nearing the end - note that if you think the bathtub appplies, you may want to re-think doing CM in the first instance but your site maintenace engineer or local maintenace consultant will help here.
The PF curve is the time between a change in some parameter away from the 'norm', indicating the point of commencement of decay.
The bathtub curve is completely unrelated and attempts to look at the actual attrition (or probability of attrition if the sample number is used as a denominator).
www.plant-maintenance.com /articles/CM_Intervals.shtml   (6781 words)

 Bit Error Rate (BER) Module for WITE32
Bathtub Plot is a family of BER graphs versus the read head position for different adjacent track positions.
The test either measures one BER value for single offset, or it builds the bathtub curve for multiple offsets in the specified range.
Bathtub Plot is a family of BER graphs versus the read head position for different frequencies.
www.guzik.com /products_soft_bertest.asp   (712 words)

 Institute for Healthcare Improvement: The Bathtub curve and product failure behavior part one - The Bathtub curve, ...
This first article of a two part series, describes the bathtub curve, a graphical representation used by reliability experts to describe the lifetime of a product population.
The author uses the product failure distribution to depict failure rates at different stages along the curve and goes on to describe some solutions to these failure modes.
The Institute for Healthcare Improvement is using this concept to advance its thinking on improving reliability in five key clinical areas.
www.ihi.org /IHI/Topics/Reliability/ReliabilityGeneral/Literature/TheBathtubcurveandproductfailurebehaviorpartoneTheBathtubcurveinfantmortality+ndburnin.htm   (151 words)

 Quality Elbow
I wonder (with no hard evidence) if perhaps the elbow in the quality-cost curve is at the point of no known bugs: as you get to that point, you get more and more productive.
I suppose we could draw another curve showing how much customers are prepared to pay for a system at a certain level of quality.
One major claim is that the curve holds for a given production process, changing the process changes the curve - so the sweet spot can move to the right (toward higher quality) and even downwards (toward lower cost).
www.c2.com /cgi-bin/wiki?QualityElbow   (917 words)

 Component Failures, Infant Mortality, and the Bathtub Curve
PC components, and in fact many electronic devices in general, tend to fail in a particular way.
If you examine a graph of failure rate versus time elapsed since a product was installed, you will see a large number of failures early on, then very few, with the number starting to increase as the wearout period is entered.
This is often called a bathtub curve due to the approximate shape it makes (but note that the right-hand part of the curve usually has a much more gradual slope, because wearout takes time).
www.pcguide.com /ts/rrr/feasFailures-c.html   (541 words)

 Quandaries & Queries at Math Central
edge of the tub would describe the 'bathtub curve' which can be used
curve' my father would really appreciate the equation.
A bathtub, with two taps, can be filled in 20 minutes using only the cold water tap.
mathcentral.uregina.ca /QandQ/topics/bathtub   (223 words)

In addition, in the field of mathematics, he invented pre-calculus and was first to use the calculated the value of Pi.
We can now see that Archimedes was jumping out of the reliability bathtub because it wasn’t the smooth shape he expected it to be.
He, like many other reliability professionals, was in the process of being impaled on a “spike” of ignorance that his fellow mathematicians and theorists hadn’t told him about.
www.reliabilityweb.com /art05/reliability_reality.htm   (2588 words)

 Primus Newsletter: Thinking Out Loud   (Site not responding. Last check: 2007-11-02)
This was followed by a long period of relatively low failures and finished by an increase as the product reached its practical lifetime.
Our objective was to get the bathtub as wide as possible by extending the life.
A chart of customer lifetime will also look like a bathtub with the initial spike of those that don't make it through the implementation or initial use phase and the eventual loss of customers due to the eventual obsolescence of the product.
www.imakenews.com /primus1/e_article000320179.cfm?x=b11,0,w   (1009 words) "Bathtub" curve
A plot of the failure rate over time for most products yields a curve that looks like a drawing of a bathtub.
Finally, if units from the population remain in use long enough, the failure rate begins to increase as materials whereat and degradation failures occur at an ever increasing rate.
The Bathtub Curve also applies (based on much empirical evidence) to Repairable Systems.
www.sbtionline.com /nist/apr/section1/apr124.htm   (380 words)

 Draft paper for Topic: End Of Life Wearout And Replacement
The bathtub curve illustrates the expected failure rates for systems.
However, as the system reaches the end of its lifespan, its failure rate increases once again as various physical failures accumulate: lubricants go dry, metal rusts, rubber becomes brittle, all the various processes of wear and tear eventually cause a system to fail regardless of how well it is designed.
Retraining is expensive, and in the case of critical systems, operators can't afford the learning curves and mistakes associated with learning everything from scratch[D'yakov96].
www.ece.cmu.edu /~koopman/des_s99/end_of_life   (2504 words)

 Euro DesignCon 2004: Attendee Schedule
Using RJ/DJ separation and Bathtub curve analysis is typically a first step in determining if your high-speed system and/or components are comfortably meeting a particular timing budget requirement for reliable data transmission performance.
But separation tables and bathtub curve extractions give no indication of the source of jitter.
Knowing how to isolate jitter components with time-correlation will enhance your ability to find the root cause so that you can then proceed to "beat down" individual error components one at a time in order to improve reliable system performance.
www.iec.org /events/2004/euro_designcon/attendee/4-wa3.html   (115 words)

 Amazon.com: bathtub-curve   (Site not responding. Last check: 2007-11-02)
according to the bathtub curve of probability, you aren't doing...
nasium, and even a swinging bathtub that wouldn't spill its con- tents when the train went around a curve.
In Figure 44.10, the traditional bathtub curve is used to provide a...
www.amazon.com /s?ie=UTF8&keywords=bathtub-curve&tag=lexico&index=blended&link_code=qs&page=1   (1051 words)

 Web-Based Machine Monitoring
Bathtub Curves Representing Generational Shifts in Maintenance Ideologies.
  The bottom line is that scheduling the rebuild of a machine which follows the pattern of the traditional bathtub curve actually increases the overall probability of a failure!
Advanced maintenance organizations, recognizing the high cost of scheduled rebuilds, have begun to utilize non-destructive testing techniques to identify failures very early so appropriate repairs can be scheduled only when the machine indicates that it is time for such an action (Table 1 and Figure 2).
www.faculty.rsu.edu /~clayton/gpalmer/paper.htm   (827 words)

 ASQ: Reliability: The Bathtub Curve Doesn't Always Hold Water
The bathtub curve with premature wearout and retirement
The bathtub doesn’t hold water because retirement occurred before wearout
The bathtub curves in the left and middle of the figures show:
www.asq.org /reliability/articles/bathtub.html   (962 words)

The studio gathered dust for 2 years while I tried to determine an activity that could replace music composition.
I jumped out of planes, cooked a bit, played in jazz bands, drove around in the desert, moped, threw myself into my work, etc. At the end of that time my head was so stuffed with musical jetsam that I had to flush it, hence Bathtub Curve.
Eight months was then spent removing expectations about the release of this CD, a task vital to my future health.
www.artifact.com /release.php?id=1015   (322 words)

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