They follow what is known in engineering and risk assessment circles as the bathtub curve
. A high number of initial failures gives way to a period of steady status quo which then starts to see more failures again as pipelines age.
Burn-in testing (BIT) is supposed to detect and eliminate such "freaks," so that the final bathtub curve
of a product that underwent BIT does not contain the infant mortality portion.
A bathtub curve
is the corresponding cumulative distribution function (CDF) evaluated in two parts: one for the lower half of the PDF, integrated from left to right, and one for the upper half, integrated from right to left.
I call it the "Bathtub Curve
"--down hard at the beginning, fiat across the bottom with some fits and starts along the way, and a slow improvement when demand comes back.
The failure rate is historically modelled (Crowe & Feinberg, 2001; Moubray, 1997; Andrews & Moss, 1993) using the traditional bathtub curve
shown in Figure 1.
Wg Cdr Bromehead, in evidence, said: "The bathtub curve
is a general engineering principle that is when something gets old, it is more likely to break.
A lot of facilities equipment has failure characteristics that are shaped in a pattern like a bathtub curve
(see Figure 1), meaning that it begins with a high incidence of failure (known as infant mortality); is followed by a lower, constant probability of failure; and is then followed by a wear-out zone where failure probability is high again.
The behavior of a torque-limiting instrument population throughout each instrument's operating life can be characterized by a graph similar to that in Figure 2 (see page 53), which, due to its shape, reliability engineers describe as the "Bathtub Curve
The Q-Scale plot provides a visual representation of jitter breakdown, which is a more intuitive presentation of the nature of the jitter components than a traditional bathtub curve
He begins with an introduction to statistical functions, Weibull distribution functions and characteristics, Weibull relationships to the extreme value distribution, and the features of the "bathtub curve
." He describes parameter estimation, including using censored data, plotting hazards and probability, estimating maximum likelihood, comparing estimation methods and using modified moment estimators; calculating confidence intervals, including those for the shape parameter, scale parameter, location parameter, reliability and percentiles, figuring goodness-of-fit, performing reliability verification testing and Bayesian estimation, and using the software, including the graph control and report function.
If we experience a bathtub curve
, with a steep decline followed by a sustained period of low economic activity, then supply chain executives will face a challenge most have never faced before: how to manage supply chains in a no-growth or slow-growth economy efficiently and effectively.
Component failure rates have been shown to follow the traditional bathtub curve
[ILLUSTRATION FOR FIGURE 5 OMITTED] which depicts component life in three stages.