Blog Archives

Cumulative hazard function and average failure rate

Posted by on 19/ 11/ 15

Similar to the cumulative distribution function (CDF), the cumulative hazard function can be obtained from integrating the instantaneous hazard function h(t) over time as

Подпись: (5.5)Подпись: (5.6)H(t) = f h(t) dt

J0

Referring to Eq. (5.3), the hazard function can be written as

1 d [pf (t)] 1 d [ps(t)]

Ps (t) dt ps(t) dt

Подпись: H(t)
Cumulative hazard function and average failure rate Подпись: Ґ -d [ps(t)] 0 ps(t) Подпись: ln[ ps (t )]0 = ln[ ps (t)] Подпись: (5.7)

Multiplying dt on both sides of Eq. (5.6) and integrating them over time yields

under the initial condition of ps(0) = 1.

Unlike the CDF, interpretation of the cumulative hazard function is not sim­ple and intuitive. However, Eq. (5.7) shows that the cumulative hazard function is equal to ln[1/ps(t)]. This identity relationship is especially useful in the sta­tistical analysis of reliability data because the plot of the sample estimation
of 1/ps(t) versus time on semi-log pape...

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Manual Placement

Posted by on 19/ 11/ 15

In general, most regulations and guidelines do not permit manually placing SMA mixtures; however, there are places where there is no other option but to place the mixture manually (e. g., small and irregular pieces of a roadway) (Figure 10.10). In such cases one should remember not to scatter the mixture with shovels but to carry and lay it down. Compaction should be carried out imme­diately after laying and alignment. Unfortunately such surfaces will differ in structure from adjacent areas spread mechanically, and usually they will be more porous and permeable.

10.2 COMPACTION

Bearing in mind the unique philosophy of designing an SMA aggregate skeleton (see Chapters 2 and 6), SMA compaction may be regarded as the process of form­ing a structure made up of appropriately arranged and inter...

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Extraction Through Leaching and Percolation Methods

Posted by on 19/ 11/ 15

Leaching can be defined as the process by which soluble constituents are dissolved and filtered through the soil by a percolating fluid, while percolation can be de­scribed as the movement of water downward and radially through subsurface soil layers, continuing downward to groundwater (US EPA, 1997 in ADEME, 1999). This led Tas & Van Leeuwen (1995) to define leachate as water or wastewater that has percolated through a column of soil or solid waste in the environment (in ADEME, 1999). The laboratory terminology describes the leaching test as a technique of leaching of solid products by an appropriate solvent in order to ex­tract its soluble fraction (ADEME, 1999). Leaching tests are a kind of extraction technique.

Extraction may be achieved in a number of ways that may be usefully class...

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Vinyl Siding

Posted by on 19/ 11/ 15

It’s not difficult to understand the popularity of vinyl siding. It’s affordable, widely available, fairly easy to install, and maintenance-free.

A drawback is that it takes time to learn how to install the vinyl trim pieces that go around doors, windows, and under eaves. Another disadvantage is that in some areas, like the Northwest, vinyl siding needs to be pressure washed yearly to remove fungal growth.

Vinyl windows, vents, soffit material, and other components are designed to be compat­ible with vinyl siding, and there are plenty of
colors, surface textures, and styles from which to choose. You’ll find vinyl siding on compact, affordable houses like the one featured in this book, as well as on expensive custom – built homes.

Horizontal siding is the most popular type of vinyl si...

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Failure rate and hazard function

Posted by on 19/ 11/ 15

The failure rate is defined as the number of failures occurring per unit time in a time interval (t, t + At ] per unit of the remaining population in operation at

Failure rate and hazard function
TABLE 5.1 Selected Time-to-Failure Probability Distributions and Their Properties

time t. Consider that a system consists of N identical components. The number of failed components in (t, t + At ], NF (At), is

NF ( At) = N x pf (t + At) — N x pf (t) = N [pf (t + At) — pf (t)]

and the remaining number of operational components at time t is

N(t) = N x ps(t)

Then, according to the preceding definition of the failure rate, the instantaneous failure rate h(t) can be obtained as

h(t) = limA<^0

‘Nf (At )/A t

= limA<^0

N x pf (t + At) — N x pf (t)"

[ N (t) J

N(t) x At

= —^lim

ps(t)

"pf (t + At) — pf (t)

At^...

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Shotcrete Lining

Posted by on 18/ 11/ 15

Welded wire fabric may be used in conjunction with shotcrete to rehabilitate deteriorated portions of either metal or concrete culverts. The welded wire should be anchored to the in-place pipe either through the use of drilled dowels, if the pipe is concrete, or by welding to either the corrugations (of metal pipe) or to previously welded studs. The shotcrete can then be placed by the use of high-pressure hoses. The repair can be designed to restore structural integrity, with little loss of hydraulic capacity.

5.12.1 Grouting Soil Voids

Regardless of the method of repair or rehabilitation chosen, the possible need for grouting potential voids in the soil envelope surrounding the pipe should be addressed...

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Fiberglass Insulation

Posted by on 18/ 11/ 15

Ninety percent of the homes in the United States are insulated with fiberglass insulation. There has been much debate as to whether or not fiberglass is a human carcinogen, and for a period of time fiberglass insulation was labeled with the warning “probable human carcinogen.” Although the material did not change in any way, the labeling was dropped. Whatever the case may be, fiberglass is by no means a healthful substance. Fiberglass insu­lation can release both particulate matter and gaseous contaminants into the air from form­aldehyde binders in the fibers and asphalt in the backing. There are numerous reports link­ing fiberglass to pulmonary disease in pro­duction workers and installers...

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Relining

Posted by on 18/ 11/ 15

Relining of either rigid or flexible culverts may be done either by slip lining or by installing a flexible liner. Slip lining is merely the insertion of a prefabricated pipe inside an existing pipe. The most common insertion pipes are either corrugated metal or plastic. Obviously, the cross-sectional area of the pipe will be reduced. This will likely affect the hydraulic capacity of the culvert. If a smooth plastic pipe is utilized, the velocity of the flow may be increased, in part offsetting the reduction in the capacity due to the decreased area. Should this be the case, the downstream end of the culvert should be investigated to prevent additional erosion...

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Scale

Posted by on 18/ 11/ 15

Always design a thing by considering it in its next larger context—a chair in a room, a room in a house, a house in an environment. – Eliel Saarinen

Again, the scale of our homes should be determined by the true needs of their occupant(s). Few of us would go into a restaurant and seek out a table in the large, open space at the center of the dining room. Most of us pre­fer the comfort and security of the corner booth. Ideally, every room in our homes will offer the same sense of enclosure without confinement.

To be sure that a minimized space does not feel confining, its designer has to consider ergonomics and any pertinent anthropometric data. Understand­ing exactly how much space we occupy when we sit, stand or lie down is absolutely essential to the subtractive process...

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Rehabilitation of Flexible Structures

Posted by on 18/ 11/ 15

Flexible metal pipes may need rehabilitation wherever there is a loss of section or where large deflections (greater than 5 percent) are present. Where the culvert has
undergone a loss of its structural section due to corrosion or erosion, the amount of loss should be noted and a determination made whether the culvert needs to be strengthened or only protected. The loss of section in metal culverts usually occurs at the invert due to the abrasive conditions of the water flow and/or the corrosive effects of the water. If the loss of section is not significant, it may be adequate to protect the invert with a coating to prevent future erosion or corrosion. The reason for the loss of section should be determined...

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