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."
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.