Frequency of Failure

The quality performance of a stream from a distillation column can be evaluated by the average impurity concentration in the stream and the distance from the nearest specification limit (DNS) compared to the standard deviation (Equation 7.1). The value of DNS is three times the process capability index, Cpk. The DNS value is easy to communicate in the number of sigma units  

DNS = distance from nearest specification limit USL = upper specification limit 

When the concentration of impurity follows a normal distribution in samples, the frequency of failure rate can be calculated (Table 7.1). These values are taken from a single side of the normal Gaussian error distribution, which can be found in statistics books such as the one by Montgomery and Runger.i 

When samples of distillate and bottoms are taken once every 8-hour shift, there are 21 samples per week and 1,095 samples per year. If the samples follow a normal distribution and the average impurity concentration is 2g, that is, DNS = two standard deviations, below the upper specification limit (USL) there would be one shift sample out of spec about every 2 weeks. If the average were 3cr below the upper specification limit, there would be one shift sample out of spec about every 9 months from common cause variability. If the average were 4a below the upper specification limit, there would be one shift sample out of spec about every 27 years. 

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EPRI NP-2433 addresses diesel generator reliability at nuclear power plants. The sources include plant records, utility records, and LERs. The report gives frequency of failure to start, failure. o continue running, and mean repair times. 

Protect Workers and the Public. The reasons may not be eniirely altruistic because worker injury is detrimental to production. Furthermore, we are the workers and wish a safe working environment free of immediate or latent injury. This requires detailed analysis of the process systems to estimate frequency of failure and the consequences that could result. Generally if the workers are safe, the public is safe. 

This article presents an overview of the causes and frequency of failures for submarine and cross-country pipelines handling oil and natural gas. It gives several tables and charts which include information on the type of pipeline, the cause of the failure, and the number of failures. Data from failures in the US and the North Sea are included. Failure rates based on the total length of piping are calculated. 

Seventeen event sequences resulted in a runaway reaction. These are listed in Table 21.5.2 (using Table 21.5.1 notation) along with tlie mean annual frequency of release produced by each sequence G stands for failure of the EIS on demand. The average aiuiual frequency of failure on demand is estimated as 0.592. 

The protection of vessels containing corrosive materials presents a special problem for the selection of bursting discs—a rapid rate of corrosion can lead to a high frequency of failures. In addition, the creep of a metal disc when under tension at elevated temperatures would tend to weaken it and result in premature failure. 

Age of facility. Older equipment, particularly equipment subject to frequent thermal or mechanical cycling, may have a higher frequency of failure. Additionally, newer equipment may incorporate improvements designed to reduce the potential for equipment failure. This consideration can be applied not only to individual pieces of equipment but to entire process units. 

In this context remember that the frequency of failures with time often follows a curve that initially decreases, then maintains a constant minimum level, and finally increases. Such behaviour is familiar to anyone who has purchased and used equipment, including... 

As evidence of light guide fiber stabilization and control through processing refinement, plot of frequency of failure against the tensile strength (in hundreds of thousands pounds per square inch) shows extraordinary uniformity for the control system compared to wide distribution of failures from surface defects and other variations in a conventional fiber... 

The frequency of failure (breakdown) of polymeric materials has decreased and will continue to decrease as polymer scientists and technologists recognize the importance of significant tests. In addition to knowing the glass transition temperature Tg and the melting point Tm, scientists must know the results of many other laboratory tests before a polymer can be recommended for a specific application. 

TABLE 4.33 Types and Frequency of Failure of Copper Plumbing in the United States in 1983... 

The lifetime of a population of units at the component, board, box, or system level can be divided into three distinct periods. This is most often defined by the so-called reliability bathtub curve (Fig. 6.16). The bathtub curve describes the cradle-to-grave failure rates or frequency of failures as a function of time. The curve is divided into three distinct areas early failure rate (also known as infant mortality), the useful life period, and the wearout failure period. The infant-mortality portion of the curve, also known as the early life period, is the initial steep slope from the start to... 

As an interim measure operational constraints were imposed as the frequency of failures could have invalidated the risk analysis in the safety report, and hence jeopardised the authorisation to operate the plant. Meanwhile the AHXs were heavily instrumented with strain gauges and thermocouples to identify the cause of the problem and indicate a solution. 

Frequency is not the same as probability. An item has a frequency of failure measured in inverse time units such as once in a 100 years. The consequences of that event may be mitigated by a safeguard, which has a (dimensionless) probability of occurrence. For example, high level in a tank may occur once every 2 years. However, the tank has level control instruments that detect high level and stop the flow of liquid into the tank. These instruments may have a probability of failure of 0.01 or 1%. Therefore, the likelihood of a system failure is 0.005 year , i.e., once in 200 years. 

If control system equipment failure can cause an initiating event, then quantitative analysis must be done for all components where failure might initiate a hazard. For those failures with no other protection layer, the frequency of failure will result directly in an incident. The detailed quantitative analysis must show that these failures will not increase risk beyond tolerable levels. 

Tables 8.2 and 8.3 present the expected frequencies of failure for vessels and pipework as used in risk-based analyses.

Release frequencies per process unit are needed for the calculations. They are estimated as follows. One assumes that a plant comprises on the average 50 process units, which implies an expected frequency of failure of 1 x 10 per process unit and year. This value is used below. Since this quantity is very uncertain a large error factor of K95 = 10 for a corresponding log-normal distribution (vid. Sect. 9.3.4) is assumed. The parameters of that distribution then are p = -14.795 and s = 1.3998. 

These rationales and assumptions are often not included in the FMEA report, but must be available for audit (by the Independent Safety Auditor) and must be kept for future reference. The customer needs to be aware of these data and may consider ensuring that its inclusion is captured in the contractual deliverable. For relative frequency of failure modes of electronic components, it is also possible to refer to Alessandro Brilini s Reliability Engineering Theory and Practice, 1997. If, however, failure rates cannot be apportioned in a justified way (i.e. from in-service experience of published data), then it should be justified by qualitative argument (see Table 3.3). 

Figure 7. Frequency of failure location. From left to right for batch A, B and C.

In Equations 12 and 13, the function k(i) represents the intensity of the non-homogeneous Poisson process, which can also be seen as the frequency of failures, that is the expected amount of failure events per time unit (at time t). When the intensity at which failures occur is sufficiently small, the following approximation can be used ... 

It is also possible to create several model outputs and use the information from Section 3.1. The risk in terms of safety is commonly defined as a combination between a frequency/probability and consequence. In this case the frequency is the failure rate and the consequence may be classified with a grade, e.g. 1-5, where the numbers are defined in ranges of e.g. people injured or killed. This should be sufficient to give a good overall risk picture. The frequency on system level will of course be the frequency of failures on any component which represents a safety hazard. It could also be helpful to calculate an average consequence on system level as the safety consequence for each failure/event weighted with the frequency of the event. 

The median of column sums X coi o Table 16 is 5 which indicates that, on average, five out of nine evaluated measurements are implemented ( 55.6%). The median of row sums Xlrow O which is equivalent of safeguard level III. Tlii s level is mapped with an expected frequency of failures F within [6 5] which follows the FMEA frequency rating as mentioned above. 

In such circumstances, new failure modes may occur, and the overall frequency of failures may increase. Corrective actions can be expensive or impractical. If the system continues to operate in the new environment, it will have an impact on the remaining usefiil hfe. 

Chapters 2, 3, and 4 deal with the distillation variables, and Chapter 5 covers distillation process control strategies. Chapter 6 describes some of the constraints on distillation variables and separation capabilities. Chapter 7 introduces the concepts that are critical to product quality and the measurements that evaluate performance criteria such as frequency of failure. Chapter 8 describes the concepts and nomenclature that are fundamental to PID control loops. Chapter 9 covers the concepts of tuning process controllers when they are operating in automatic output mode. Chapter 10 is about measuring the response of process variables when the controller is in manual output mode, that is, with no feedback from the process variable. 

Understand the measurements that are critical to product quality performance and the resultant frequency of failure... 

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