Mean time to failure

Mean time to failure of an item/system can be obtained by using any of the following three formulas [6,24]  

MTTF is the mean time to failure of an item/system. 

Using Equation 3.3, prove that Equations 3.13 and 3.14 yield the same result for the mean time to failure of the oil and gas industry system. 

MTTF = mean time to failure s = Laplace transform variable 

R s) = Laplace transform of the reliability function R f) Elf) = expected value 

Prove by using Equation (3.3) that Equations (3.12) and (3.14) yieid the same resuit for the transportation system mean time to faiiure. By substituting Equation (3.3) into Equation (3.12), we obtain 

MTTEj = transportation system mean time to faiiure By taking the Lapiace transform of Equation (3.3), we get 

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Early failures may occur almost immediately, and the failure rate is determined by manufacturing faults or poor repairs. Random failures are due to mechanical or human failure, while wear failure occurs mainly due to mechanical faults as the equipment becomes old. One of the techniques used by maintenance engineers is to record the mean time to failure (MTF) of equipment items to find out in which period a piece of equipment is likely to fail. This provides some of the information required to determine an appropriate maintenance strategy tor each equipment item. 

The mean time to failure of various instrumentation and equipment parts would be known from the manufacturer s data or the employer s experience with the parts, which then influence inspection and testing frequency and associated procedures. Also, applicable codes and standards—such as the National Board Inspection Code, or those from the American Society for Testing and Materials, American Petroleum Institute, National Fire Protection Association, American National Standards Institute, American Society of Mechanical Engineers, and other groups—provide information to help establish an effective testing and inspection frequency, as well as appropriate methodologies. 

Equation 2.5-43 is a definition of availability." Since 1/p = MTTR (mean time to repair) and 1/A, = MTTF (mean time to failure) A more conventional definition is given by 2.5-44. 

Equipment used to process, store, or handle highly hazardous chemicals must be designed constructed, installed and maintained to minimize the risk of release. A systematic, scheduled, test and maintenance program is preferred over "breakdown" maintenance " that could compromise safety. Elements of a mechanical integrity program include 1) identification and categorization of equipment and instrumentation, 2) documentation of manufacturer data on mean time to failure, 3 ) test and inspection frequencies, 4) maintenance procedures, 5) training of maintenance personnel, 6) test criteria, and 7) documentation of test and inspection results. 

With the Industrial Revolution, life became more complex but it was not until World War II that reliability engineering was needed to keep the complex airplanes, tanks, vehicles and ships operating. Of particular concern was the reliability of radar. Prior to this time equipment was known qualitatively to be reliable or unreliable. To quantify reliability requires collecting statistics on part failures in order to calculate the mean time to failure and the mean time to repair. Since then, NASA and the military has included reliability specifications in procurements thereby sustaining the collection and evaluation of data build statistical accuracy although it adds to the cost. 

Since dependency analysis is not needed, we can go on to the BUILD program. Go to FTAPSUIT and select 5 "Run Build." It asks you for the input file name including extender. Type "pv.pch," It asks you for name and extender of the input file for IMPORTANCE. Type, for examle, "pv.ii . It next asks for the input option. Type "5" for ba.sic event failure probabilities. This means that any failure rates must be multiplied by their mission times as shown in Table 7.4-1. (FTAPlus was written only for option 5 which uses probabilities and error factors. Other options will require hand editing of the pvn.ii file. The switch 1 is for failure rate and repair time, switch 2 is failure rate, 0 repair time, switch 3 is proportional hazard rate and 0 repair time, and switch 4 is mean time to failure and repair time.)... 

The practice of using actual operating conditions of plant equipment and systems to optimize total plant operation. Relies on direct equipment monitoring to determine the actual mean-time-to-failure or loss of efficiency for each machine-train and system in a plant. This technique is used in place of traditional run-to-failure programs. 

Sample frequency is a function of the mean time to failure from the onset of an abnormal wear mode to catastrophic failure. For machines in critical service, sampling every 25 hours of operation is appropriate. However, for most industrial equipment in continuous service, monthly sampling is adequate. The exceptions to monthly sampling are machines with extreme loads. In this instance, weekly sampling is recommended. 

For the purpose of showing how to obtain from an exponential hazard plot an estimate of the exponential mean time to failure, assume that the straight line on Figure 62.9 is the one fitted to the data. Enter the plot at the 100 per cent point on the horizontal cumulative hazard scale at the bottom of the paper. Go up to the fitted line and then across horizontally to the vertical time scale where the estimate of the mean time to failure is read and is 1000 hours. The corresponding estimate of the failure rate is the reciprocal of the mean time to failure and is 1/100 = 0.001 failures per hour. 

The behavior of the failure rate as a function of time can be gaged from a hazard plot. If data are plotted on exponential hazard paper, the derivative of the cumulative hazard function at some time is the instantaneous failure rate at that time. Since time to failure is plotted as a function of the cumulative hazard, the instantaneous failure rate is actually the reciprocal of the slope of the plotted data, and the slope of the plotted data corresponds to the instantaneous mean time to failure. For the data that are plotted on one of the other hazard papers and that give a curved plot, one can determine from examining the changing slope of the plot whether the tme failure rate is increasing or decreasing relative to the failure rate of the theoretical distribution for the paper. Such information on the behavior of the failure rate cannot be obtained from probability plots. 

In an earlier section, we acquainted ourselves with commonly used reliability terms mean time between repairs (MTBR), mean time between failures (MTBF), etc. We saw that these terms have similar meanings but often include minor deviations. To avoid confusion, mean time to failure (MTTF) will be used in the following discussion. It can be expressed in terms of any time periods, i,e, days, months, years, etc. ... 

The incorporation of associated alpha particle detection in a sealed tube neutron generator (STNG) appears to severely aggravate the concerns over the limited neutron flux and tube lifetime previously detailed for STNG FNA approaches. A mean time to failure of some APSTNGs at a neutron flux of lO n/s is about 200 h [24]. Work is continuing to improve this mean time to failure. 

Imide passivated linear devices was determined from I-V characteristics of statistically significant numbers of devices following severe PTHB test (i.e., 15 psi, 120°C, 100% relative hvimidity, and 30 V bias). Two coat (3 p) polyimide passivation provided almost twice the mean time to failure of 1 p thick PSG passivation. Polyimide protection against high humidity (13,14) and Na" " diffusion (15) has been reported previously. 

Bills (7) has applied an adaptation of this law to solid propellants and propellant-liner bonds for discrete, constantly imposed stress levels considering U to be the time at the ith stress level and tfi the mean time to failure at the ith stress level. A probability distribution function P was included to account for the statistical distribution of failures. For cyclic stress tests the time is the number of cycles divided by the frequency, and the ith loading is the amplitude. The empirical relationship... 

Mean-Time-to-Failure The most common metric for reliability is the mean-time-to-failure or MTTF where... 

TABLE 8.3 Increase in Mean-Time-to-Failure with an Increasing Number of Electrodes... 

Performance response times (e.g., screen refresh rates, cycle times, and critical control response times), Mean-Time-To-Failure (MTTF), system remedial action, power failure recovery, startup, shutdown... 

The phosphoric acid does not change the physical ESC behaviour significantly when compared to water, but it does accelerate the chemical ESC. This leads to a decrease of the mean time to failure from a factor of 1.25 at 0.6 MPa to a factor of 10 at 5 MPa compared to water. 

Some of the criteria that have been used for evaluation are mean time to failure or system or component durability. A related issue is the ease and cost of component replacement. System or component obsolescence should also be taken into consideration. Obsolescence is related to the adaptability of the overall system to changes in some of the components or changes in protection requirements. 

When the probability density function fit) is known (or R(t) or F(t)), the mean time to failure MTTF, which is the characteristic lifetime, can easily be calculated as... 

The Weibull distribution is completely described by the shape parameter / and the characteristic time T. We should mention that T is related to but not identical to the mean time to failure (MTTF). T is actually the time by which 63% of the original population fails. Figure 5.9.8 shows how the time dependence of the failure rate changes with the shape parameter at constant T. 

For an exponential distribution function, the mean time to failure and the characteristic time T are identical. When / = 1 the Weibull distribution represents the region of the working life. For fS > 1 the failure rate increases with time, as when the product is wearing out... 

The reliability parameters, such as the mean time to failure, have to be determined in experiments under well defined conditions. Failure rates of microsystems for automotive applications are typically in the range of a few ppm (parts per million). This may sound negligible, but due to the large number of sensors sold every year and their increasing numbers in each car, even this failure rate must be decreased further. However, the engineer who tries to investigate failure mechanisms is confronted with the problem of lack of failures in the sense that he finds too few defective samples for a thorough failure analysis. Thus, due to the lack of a statistical basis, the quality of lifetime predictions under normal in-use conditions would be poor. 

Thermal Modeling A key stumbling block in the roadmap of 2.5-D integration is excessive heat generation in the 2.5-D stack and the rather limited ability for heat removal. Thus analysis tools have to be developed to precisely quantify the thermal effects in 2.5-D ICs. With these tools, designers could derive a temperature profile at different abstractions levels. The thermal distribution information would enable calculation of the mean time to failure (MTTF) and the self-heating effect... 

Although worldwide production of heat pipes designed for applications involving the thermal control of electronic components or devices was in excess of 1,000,000 per year in 1992, it is difficult to calculate a mean time to failure (MTTF) for heat pipes, thermosyphons, and other similar devices due to the relatively small amount of data that exists on actual products in operation. Experience with a wide variety of applications ranging from consumer electronics to industrial equipment has demonstrated that mechanical cleaning of the case and wick-... 

IEC60085 and IEC60034 part 1 describe the limitations placed on materials used inside motors (and other electrical equipment). Most electrical machines with air or gas as the cooling medium use Class B or F solid insulation material. Where the environment is harsh, and high ambient temperatures occur, then it is advisable to specify Class F insulation materials but with a restriction of Class B temperature rise. Such a specification will inherently increase the mean time to failure of the materials since they will be less stressed. 

Then we derived a set of equations describing electromigration, using Hooke s law for the stress tensor, and by approximation, compared the results with previous work. We found that the mean-time-to-failure is approximately proportional to the square of the conductivity, and to the viscosity of the metal. 

Suppose the station can fail even when they are idling. Let the mean time to failure, and repair times of stage i, be and D, respectively, for i = 1, 2,. . . , m. With no inventory bank, all stations in the line stop as soon as any station fails. Then it follows that... 

Quality of pmduct pertains to product reliability, value, functionality, and dependability. End users also utilize mean-time-to-failure, mean-time-to-repair, and maintenance cycle time and costs to evaluate the quality of products. 

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