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,“5A7¾- ŁThe Risk Analysis Correspondence Course
This information is presented to Federal Aviation Administration (FAA) engineers and other interested individuals for aid in the understanding of the risk assessment process used by the FAAs Engine and Propeller Directorate. It also has applicability to risk analysis in general.
Contents:
Probabilistic failure modes
Weibulls and other distributions
Risk analysis techniques - Inputs and outputs
Risk analysis techniques - How the simulation works
Risk analysis techniques - Calibration
Assumptions used in the risk analysis
Prioritization of multiple safety problems
Risk factor guidelines
Miscellaneous topics
Probabilistic failure modes
In this first installment:
Introduction to failure modes
Hours vs. cycles for tracking failure probability
Introduction to failure modes
The probabilistic failure mode of a given piece of engine hardware is a reflection of its relative probability of failure versus its age. There are three categories of failure mode - wearout, infant mortality and random. Wearout is the most common of the three - parts are increasingly likely to fail as they age. Conversely, infant mortality describes those situations where parts are more likely to fail early in their life. Parts are usually considered safe from this mode once they pass a certain age. Maintenance errors typically result in infant mortality failures; for example, if a bearing was installed incorrectly, it would be expected to fail within its first 100 hours of operation. After that point, it is assumed that the bearing was correctly installed and will not fail in normal operation.
In a random failure mode, parts or engines are equally likely to fail whatever their age. For example, fan blade failures due to birdstrikes are a random event, as birds dont selectively aim for older or newer blades (and blade leading edge damage and polishing occurs fairly continuously). Having a random failure situation allows for a simplified risk assessment through the use of the Mean Time Between Failure (MTBF). To calculate MTBF, divide the total cycles (or hours) by the number of events. The future risk (the expected number of additional failures) is estimated by multiplying the average number of cycles each part will be expected to run until repair or replacement by the total number of parts, and dividing by the MTBF. Using the birdstrike example, if we had 4 fan blade fractures due to birds over 2,000,000 cycles of operation, we would have a 500,000-cycle MTBF (2,000,000 / 4). If we were to then introduce a bird-proof blade, the future risk until that new blade was completely incorporated can be calculated: for example, lets say we have 1,000 engines which will run an additional 500 cycles, on average, with the old blades. The expected number of additional failures until all engines have been retrofit with the new blades is
1,000 x 500 / 500,000 = 1.0 additional failures
When multiple failure causes are combined (for example, all causes of inflight shutdowns), the resultant distribution tends to be random due to the mixture of wearout, infant mortality, and random modes.
The Weibull distribution (probability of failure versus age) is often used to model failure data; for wearout problems, the Weibull distribution will have a slope (beta) greater than 1. Typical values for the slope are in the area of 3 to 5, but may vary. A Weibull distribution with a slope equal or close to 1 reflects a random failure mode, and a slope of less than 1 is indicative of infant mortality. A more complete discussion of the Weibull and other distributions follows in the next installment.
Hours vs. cycles for tracking failure probability
Parts installed in turbine engines are typically only highly stressed during takeoff. The hours spent at cruise have little impact on their life. Each flight, no matter how short or long, basically puts the same amount of stress on the part. Therefore, the likelihood of failure is best addressed as a function of the number of cycles on each part. There are exceptions to this general rule:
Bearings
Oil system components
Fuel nozzles
Tubes, etc.
(In general, any parts that operate in a continuous and consistent manner throughout the flight.)
In addition, failure causes such as high-cycle (high-frequency) fatigue are typically a function of the time spent in the excitation area. If this area occurs at a particular airspeed during descent, for example, it may still be best to look at part cycles, since each part will spend the same amount of time passing through that region during descent. However, if the excitation occurs during cruise, hours would be considered a better method to track the likelihood of failure.
2. Weibulls and Other Distributions
The Weibull distribution is commonly used in industry to model failure data. The main advantages of the Weibull distribution are:
It can model a variety of data.
It handles suspensions (non-failure points) easily.
It provides a simple graphical solution and description of the data.
The Weibull distribution plots time or other such measure on the X axis versus cumulative percent failing on the Y axis. The Weibull is defined by two parameters: the shape parameter, called the slope or Beta, and the characteristic life, Theta or Eta (it goes by either Greek letter, depending on who you talk to). These parameters define the specific distribution, as the mean and standard deviation define a Normal distribution. Therefore, note that -3 sigma has no meaning against a Weibull distribution. The correct term is Bx.x life, where x.x is the percent of the distribution failing. A commonly used value for minimum life from a Weibull is the B0.1, which is the 1/1000 failure life (0.1% of the population).
As in any distribution, confidence limits can be calculated around the parameters. In general, confidence limits are a measure of how different the true distribution may reasonably be from the sample of data being plotted. The true distribution is what the result would be if we knew the failure time for every part in the population. In reality, we have only a few failures (most of the parts have not failed), and less than every part (whether failed or not).
The true distribution is just as likely to be better than the sample as it is to be worse. However, it is usually the latter case that is of interest - how bad might the situation reasonably be? Note that the sample distribution as plotted (not the confidence limit) is usually used to estimate future risk, for the reason that it represents the average expectation and calibrates with the experience to date.
Confidence limits are a function of the amount of the data (and the amount of variability in the population). The more data, the tighter the confidence limits will be. Also, confidence limits tail off - i.e., the true distribution is more likely to be closer to the sample plot line than out at the limit.
Weibulls are often performed with limited failure information (after all, we dont want to wait until there are lots of failures!) In fact, Weibulls can be performed without any failures by assuming a slope and assuming that one failure has occurred. This provides a picture of how good the experience has proven so far. This type of Weibull is called a Weibest or Weibayes. Weibests can also be used with multiple failures; the difference between a Weibull and a Weibest is that the Weibull plots the best fit through the actual failure data, whereas the Weibest plots what the distribution should look like given the number of failures and the times on all the parts (simplistically, it picks the most likely failures rather than the actual failures). How close the Weibull plots to the Weibest is a measure of whether the actual failures are outliers or indicative of multiple populations in the data.
Take with a grain of salt any slope derived from a Weibull with just a few failure points. In these cases, sometimes its better to use an assumed slope (Weibest) based on the knowledge of similar failure situations.
The failure points should plot in a straight line, or near to it, on Weibull probability paper. If they do not, either there are multiple populations, or a Weibull distribution is not appropriate to describe the data. An exception to this is the use of curved Weibulls (Curbulls) to fit data which requires a minimum incubation time t(0).
For Weibulls with crack rather than failure data, the Weibull represents a crack discovery distribution rather than a pure initiation distribution. In other words, the part is inspected at some age and found to be cracked. The actual crack initiation occurred at some point prior to the inspection. Sometimes fracture mechanics is used to back up the crack to estimated initiation.
Instantaneous failure probability is the probability that the part will fail in the next cycle given that it hasnt failed yet. The equation is the probability of failure in the next cycle minus the probability of failure in the current cycle divided by 1 minus the probability of failure in the current cycle.
[P(t+1) - P(t)] / [1 - P(t)]
Other distributions are sometimes used to model failure data. For example, the log-normal distribution is used extensively by Airbus - they prefer it to the Weibull. A log-normal distribution converts failure data to a normal distribution by taking the log of each point and plotting the transformed data. No particular distribution is inherently better than the other - it simply a question of which best fits the data. Often, adequate results can be achieved with several different distributions, especially those in the same general family (such as Weibulls, log-normals, exponentials, etc. Note that a Weibull collapses to an exponential distribution when the Weibull slope is equal to 1 - a random failure mode, youll remember from the earlier discussion.) A non-transformed normal distribution is usually not a good descriptor of failure data. Normal data is evenly distributed about the average value, whereas failure data tends to extend much higher above the average value than it does below. A Weibull can be used to model normally-distributed data; the slope comes out to be 3.44.
Other distributions of note include the binomial and the Poisson. A binomial distribution models an either/or situation - for example, a coin toss (heads/tails). It has applicability in manufacturing situations as well (defective/not defective). It is important to remember that either/or does not necessarily imply a 50-50 chance of the two different outcomes!
The Poisson distribution is used to model such types of data as the number of defects or inclusions in a part, the number of accidents in a year, the number of cars passing through a tollbooth every minute, etc. The two important factors are: the possible number of occurrences is a great deal larger than the average, and the events are independent of each other. The Poisson distribution has applicability to the risk analysis process in that it is used to calculate the probability of 0, 1, 2, or more additional events for a predicted average outcome (called the risk factor in the risk analysis process). For example, a risk factor of 0.5 predicted additional events translates to a 61% probability of no events, a 30% chance of 1 (and only 1) event, an 8% chance of 2 events, a 1% chance of 3 events, etc.
For that matter, I realize that I should define risk analysis. Therefore, a couple of definitions:
Risk analysis is the qualitative or quantitative analysis of information to establish an expected loss from events based on their estimated probabilities of occurrence.
The risk analysis procedure used within the Engine and Propeller Directorate is a numeric method based on computer simulations which quantify the expected number of future events (risk factor) for specific problems as a function of specific operational and maintenance constraints.
3. Risk analysis techniques
In this installment:
An overview of risk analysis
Inputs and outputs
Overview
As was defined last week, the risk analysis procedure used within the Engine and Propeller Directorate is a numeric method based on computer simulations which quantify the expected number of future events (risk factor) for specific problems as a function of specific operational and maintenance constraints.
Risk analyses are performed to control risk while optimizing the inspection and modification programs aimed at addressing unsafe conditions which are uncovered during service. Their aim is to achieve the desired risk factor goal (more about that in future installments) while minimizing operational impact. The analysis will also output the number of spare parts, shop visits and inspections which will be required, allowing for timely provisioning.
The centerpiece of the risk analysis is the simulation model. This simulation builds an computerized model of the field. Once the simulation has been developed, various future inspection, repair, and replacement scenarios can be analyzed to determine their effects on the simulated fleet. Essentially, the program can run the simulated fleet through many possible futures. The different futures evaluated often include the one in which no action is taken, to establish a standard for comparison.
Inputs and Outputs
Obviously, we desire to have the best possible correlation between the actual fleet and the simulation. Various input distributions are required to help define the simulation model. These include:
Part time/cycles - the current age of the affected fleet
Crack initiation and propagation - Weibull or similar distributions
Shop visit distribution - based on recent experience with the applicable fleet
Inspection reliability - crack POD (probability of detection)
Any changes to the above based on new operational or maintenance procedures
These inputs should represent the sum of knowledge about the safety problem:
Realistic assessment of known conditions (based on service experience, test results, etc.)
Conservative assessment of unknowns
Engineering judgment
The main question that the risk analysis answers is this: based on the current age of my parts, and the intervals at which I plan to inspect, repair, and/or replace them, how many more events are expected until the program is complete? Note that I used the term events rather than failures. One of the other inputs to the risk analysis is the definition of an event. For example, consider the case of a fan blade fracture. The event could be defined as:
blade fracture
uncontained failure (a subset of all fractures)
uncontained failure which causes damage to the aircraft (a subset of uncontainments)
Actually, the risk analysis is usually set up to output the base event (in this case, fractures), which is then corrected for the probability of uncontainment, etc. So, the outputs can include the expected number of fractures (the risk factor for fractures), uncontainments (the risk factor for uncontainments), and so on.
The risk factor(s) can be calculated versus calendar time. This enables us to graphically plot the cumulative risk against time. Most of the risk of additional events during any correction program usually occurs early on, before many parts have been inspected; the plot of cumulative risk vs. time thus shows an asymptotic approach to the total risk factor for the program. It is often of interest to plot the risk factor if no action is taken along with the planned or possible inspection/modification scenario(s).
Additional outputs from the risk analysis are possible, including:
the number of cracks found
the number of replacement parts required
the number of inspections
These can also be listed on a month-by-month basis; thus, the risk analysis can establish how many parts will be needed and when they will be needed. The predicted number of cracks found vs. time is especially important, as it allows us to track whether the results in the actual future corresponded to the predicted results of the simulated future.
4. Risk analysis techniques (continued)
In this installment:
How the simulation works
How the simulation works
Basically, there are two techniques to use in arriving at the risk factor - calculating it directly, or using Monte Carlo techniques. The first involves calculating the instantaneous probability of failure on a cycle-by-cycle basis for each part until it is inspected or replaced, and adding up all the answers to get the total expected number of failures. (Remember that the instantaneous failure probability was defined in installment 2 as [P(t+1) - P(t)] / [1 - P(t)]. ) The probability of missing a crack must also be factored into the equation, along with inspection and replacement intervals and all the other input variables. You can see how this might get a little complicated, especially if you want the results on a month-by-month basis.
The other method uses many iterations (repeat analyses within the computer program) to simulate the behavior of the different parts and sums the results of each of those iterations. The behavior of a particular part during a particular iteration is randomly selected from the distributions associated with the different inputs. This process is called Monte Carlo simulation (after the gambling resort). Monte Carlo simulation assigns random numbers to the outcomes of a statistical distribution. The probability of a given value is determined by the random numbers assigned to that value. The random numbers are assigned based on the percent of the population failing vs. time. Let me provide an example from a Weibull distribution of crack initiation, which we want to be able to simulate using the Monte Carlo technique. Remember that the Bx.x life is the age at which x.x% of the population will fail (or, in this case, initiate a crack).
Weibull distribution Random number
B0.01 initiation life 2,000 cycles 0.000
B0.1 3,000 cycles 0.001
B1.0 7,000 cycles 0.010
B6.0 11,000 cycles 0.060
etc.
B99.9 35,000 cycles 0.999
B99.99 50,000 cycles 1.000
Now, lets see what this means. The program uses a random number generator to randomly select a number between 0 and 1. Lets say our random number for part #1 in iteration #1 is 0.045. The program looks at the distribution weve input, as above, sees that 0.045 falls between 7,000 and 11,000 cycles initiation life, and interpolates between those two lives with the same ratio as between their respective random numbers - in this case,
[(0.045 - 0.010) / (0.060 - 0.010)] = [( X - 7000) / (11000 - 7000)]
Solving for X, we get an initiation life of 9,800 cycles.
The set of corresponding lives and random number probabilities is sometimes called pairwise points.
This process is repeated to calculate an initiation life for each part in the fleet. What we end up with is a distribution of initiation lives. A similar process is performed for crack propagation, age at inspection, etc., all based on their respective distributions. For each individual part, we end up with an assumed initiation life, propagation life, inspection interval(s), and replacement age. The question of whether that particular part fails is then simply a matter of looking at whether it is replaced, or its crack is found, prior to the sum of its initiation and propagation. For example:
Part #1, currently 7,000 cycles old
Crack initiation life 9,800 cycles
Propagation life 2,500 cycles (so, part fractures at 12,300 cycles)
On-wing inspections: 8,000 cycles - no crack found (none there yet)
10,115 cycles - crack not found (based on inspection
reliability distribution)
Shop visit at 12,000 cycles; part replaced - therefore, part does not fail, as it is scrapped prior to the point at which it fractures.
Part #2, currently 11,254 cycles old
Crack initiation life 7,714 cycles
Propagation life 4,400 cycles (part fractures at 12,114 cycles)
On-wing inspections: 13,000 cycles
Part fails prior to first inspection.
Part #3, currently 6,050 cycles old
Crack initiation life 5,507 cycles
Propagation life 4,216 cycles (part fractures at 9,723 cycles)
On-wing inspections: 9,013 cycles - crack found
Engine removed - part does not fail.
The number of failures is summed for each iteration. In the case above, we had only 3 parts, of which 1 failed. In reality, of course, we have many more parts. The process is the same - simulate the experience for each part, and count how many fail. The process is iterated many times (100 or more) to ensure that the simulated distributions correspond to the actual distributions (remember how we discussed sample size vs. the true distribution back in the confidence limits topic?) The average number of failures is then obtained by dividing the total number of failures for all iterations by the number of iterations. This gives us the risk factor.
For example: 1000 parts - 100 iterations
40 iterations had 0 failures
53 iterations had 1 failure
6 iterations had 2 failures
1 iteration had 3 failures
total number of failures = (40 x 0) + (53 x 1) + (6 x 2) + (1 x 3) = 68
average number of failures = 68 / 100 iterations = 0.68
The risk factor for the inspection/modification scenario used in this simulation is thus 0.68
You can see how we can also arrive at the number of cracks, inspections, etc.
5. Risk analysis techniques (continued)
In this installment:
Calibration
Summary: Steps in the risk analysis process
Calibration
Before a risk analysis can be used to predict future behavior, it must be calibrated against the experience to date. This means, if we back the simulated fleet back up in time, and let the program run forward to the present, does it give the same results as have occurred in real life? This should hold true for both failures (fractures, or whatever the relevant event) as well as cracks (if applicable). If the simulated results do not match reality within a reasonable amount, the assumptions and distributions which have been input into the program must be examined and revised until calibration occurs. Remember that the simulation may predict that, say, 2.4 failures have occurred to date. Since we cannot have .4 of a failure, this result is reasonable for either 2 or 3 actual failures. Depending on the degree of confidence in the assumptions, we may wish to revise them until the simulation predicts exactly 2.0 (or 3.0, whichever applies) failures.
Another important aspect of calibration looks at the predicted and actual results versus calendar time. If the simulation predicts 2 failures, and we have had 2 in reality, does the timing match? In other words, if the reality is 6 years of successful operation and 2 failures within the past year, the simulation programs 2 failures should be within the same time frame.
As was stated at the beginning of this section, calibration of the risk analysis simulation is vitally important. Unless we have a program that predicts the experience to date, we cannot have any confidence in its ability to predict fleet behavior in the future.
Summary: Steps in the risk analysis process
Define event of interest
Establish upper limit for risk factor (more on this in later installments)
Define simulation model characteristics
Define relevant distributions
Part life (initiation/propagation)
Shop visits
Define operational and maintenance constraints (what can and cant be done)
Create computer model
Define inspection/modification scenarios
Calibrate model
Should predict experience to date
Output information
Risk factor
Sensitivity analyses
Parts requirements
6. Assumptions used in the risk analysis
In this installment:
Assumptions and validations
Sensitivity analyses
Assumptions and validations
Many assumptions are made in the process of performing a risk analysis. It is important that all concerned parties buy in to those assumptions. Therefore, any presentation of results from a risk analysis should begin with a thorough review of the assumptions made, and what supporting evidence exists to support them. Each of the assumptions may be based on data, engineering judgment, or both. Where data are lacking, some element of conservatism is called for.
A word here about engineering judgment and data. First and foremost, it is not a case of either/or. Engineering judgment is informed opinion. It is based on a knowledge of the parts, processes and physics involved, as well as the ability to relate new situations to experience. Engineering judgment should reflect the consensus view among the knowledgeable experts. Data is the engines judgment - and the engine (or aircraft) is usually the best expert of all! The engineer should always be interested in what the engine has to say, and develop his or her informed opinion in light of that evidence. Conversely, engineering judgment is often required to interpret the data.
That being said, recognize that some assumptions in a risk analysis will by definition rely more heavily on judgment than others. Other assumptions are relatively straightforward. For example, the OEMs (Original Equipment Manufacturers) have very good data on shop visit and utilization rates. The only things to be concerned about when reviewing these distributions are whether theyre based on recent data for the proper models and whether there are any major operational or maintenance changes forecast that would affect either usage or shop visit scheduling.
Likewise, initiation and propagation distributions are usually very heavily data-based, relying on a combination of test data and field experience. The question always arises as to whether there are enough data to perform an analysis. The answer to this is to recognize that the available data are never perfect, but represent the best estimate of the situation as it is currently known. The presence of incomplete data should not be seen as justification to ignore the data (see paragraph 2, above). Furthermore, the necessity of calibrating the risk analysis with the past experience helps to ensure that the future prediction is reasonable, assuming that operational parameters (derate schedules, etc.) remain constant. Remember that an important consideration is whether the failure mode is a function of cycles or hours.
The assumed availability of spare or replacement parts can be validated by the raw material and finished part production schedules. Future fleet growth, if involved, is determined by orders and projections.
An important assumption that is often not readily apparent is the extent of the affected population. What is the justification for excluding certain models? Has an analysis of the failures versus production date been performed to identify possible manufacturing-related problems? Are the failures limited to a particular segment of the fleet or type of operation? Bear in mind that a statistically-significant difference in the rate of occurrence between two different populations does not necessarily mean that the better population will never have the problem, only that it is not as prevalent. This is a prime example of the use of engineering judgment to interpret results.
Inspection reliability
Inspection reliability is an important assumption. Usually, the only data available on the probability of crack or defect detection (POD) come from the laboratory. Judgment must be applied to translate those carefully-controlled results to what is achievable in practice. An on-wing inspection is probably inherently not as reliable as an in-shop inspection due to accessibility and environmental factors. (Of course, the on-wing inspection has the benefits of convenience and availability.) For situations where the POD does not vary significantly versus crack size, a single value for POD may be used. In other cases, the POD curve (probability of detection vs. crack length or defect size) is input as a series of pairwise points, as in the initiation and propagation distributions. Another factor in the assumed inspection reliability is whether multiple cracking or defect sites exist. Everything else being equal, a part with two cracks is more likely to fail the inspection than a part with only one crack.
There may also be human factor considerations. For example, if many parts are expected to be cracked, the inspection reliability is probably better than if only one or two parts in the entire fleet are cracked. The reason for this (and it can be considered a personal opinion) is one of expectations on the part of the inspector. If cracks are regularly found, the inspector may feel an increased level of vigilance. On the other hand, if many inspections are performed without rejects, the expectation may develop that the next part wont be cracked either. Needless to say, this is nearly impossible to quantify, but is something to factor into the judgment aspect of the situation.
The use of dual inspections to increase overall inspection reliability is a source of contention. If two inspections are truly independent, a single 90% inspection reliability translates to a dual 99% reliability (.10 x .10 chance of missing the crack twice). Once again, however, practice does not quite match theory. It is generally agreed that there is some improvement in the POD rate, but not the amount predicted by true independence. The justification of some improvement is the idea that whatever caused the crack to be missed the first time will not happen precisely the same way the second time. The justification for not taking the entire amount of predicted improvement is twofold: endemic problems associated with the inspection technique or process (the setup is inadequate, the part misses the inspection process entirely, etc.) and the possibility that some cracks, by nature of their geometry, may be inherently less detectable than others. Whenever a dual inspection is called for, it is important that the second inspector (note the requirement for two different inspectors) does not have knowledge of the results of the first inspection. This lack of foreknowledge helps to improve the independence of the inspections.
Sensitivity analyses
A sensitivity analysis involves running the risk analysis with a range of possible inputs for a given parameter to determine the sensitivity of the results to that parameter. An obvious use is to evaluate inspection reliability. If there is disagreement as to the expected reliability, the analysis can be performed with different PODs to determine the effect of reduced inspection reliability on the projected risk factor (remember that risk factor is the expected number of future events).
Monitoring
On-going field experience should be monitored to continue validation of the assumptions. For example, if cracks are projected to be found, but are not, the problem may be with the inspection reliability (i.e., its worse than assumed) or with the initiation distribution. The finding of any significant shortfalls in the assumptions calls for revision to the risk analysis.
7. Prioritization of multiple safety problems (the Continued Airworthiness Assessment Methodologies process)
In this installment:
The need for prioritization
CAAM hazard levels
Calculation of the hazard ratio
The need for prioritization
Prioritization is the recognition that we cannot solve multiple problems simultaneously due to the lack of infinite resources (of people, materials, shop capacity, etc.) Therefore, it is necessary to have a risk management system which appropriately assigns prioritizes to the variety of problems we face. The goal of establishing these priorities is to ensure that the available resources of all concerned parties - the FAA, the OEMs, and the operators - are applied to the areas of greatest safety threat.
This prioritization process by definition requires an assessment of an individual engine problem or event against the concept of safety. At the FAA, we usually address safety by managing its converse, the unsafe condition. An unsafe condition may be defined with various specific words, but, in general, it refers to any problem which has the potential to cause harm. A specific definition for the engine world might be: Any engine, propeller or APU malfunction, defect or failure which can directly or indirectly hazard the aircraft, its passengers and crew, or both.
CAAM hazard levels
We see, then, that we need an understanding of whether and how a particular problem might cause an unsafe condition, and how extensive this potential for harm. To this end, a standardized list of aircraft situations was developed to relate a particular result to a quantified level of harm. This list was developed by the joint FAA-industry committee known as the Continued Airworthiness Assessment Methodologies (CAAM) committee; the Engine and Propeller Directorate adopted the list as part of its risk assessment and prioritization process (also known as CAAM). The quantified level of harm is called the Hazard Level, and ranges from 1 through 4 (since expanded to 5 from the TAD-EPD-ARAC coordination activity, though only levels 3 and higher have been coordinated with TAD). The list of aircraft situations comprising those hazard levels is as follows:
CAAM Hazard Levels
LEVEL 1 - MINOR CONSEQUENCES
a. Uncontained nacelle damage confined to affected nacelle/APU area.
b. Uncommanded power increase, or decrease, at an airspeed above V1 and occurring at an altitude below 3,000 feet (includes inflight shutdowns (IFSD) below 3,000 feet).
c. Multiple propulsion system malfunctions or related events, temporary in nature, where normal functioning is restored on all propulsion systems and the propulsion systems function normally for the rest of the flight.
d. Separation of propeller/components which causes no other damage.
e. Uncommanded propeller feather.
f. Excess loads.
LEVEL 2 - SIGNIFICANT CONSEQUENCES
a. Nicks, dents and small penetrations in aircraft primary structure.
b. Slow depressurization.
c. Controlled fires (i.e., extinguished by on-board aircraft systems).
d. Fuel leaks in a fire zone or in the presence of an ignition source, which exceed the drainage capability of the compartment.
e. Minor injuries.
f. Multiple propulsion system/APU malfunctions, or related events, where one engine remains shutdown but continued safe flight at an altitude 1,000 feet above terrain along the intended route is possible.
g. High speed takeoff abort (usually 100 knots or greater).
h. Separation of propulsion system, inlet, reverser blocker door, translating sleeve inflight without significant aircraft damage.
i. Partial inflight reverser deployment or propeller pitch change malfunction(s) which does not result in loss of aircraft control or damage to aircraft primary structure.
j. Malfunctions or failures that result in smoke or toxic fumes, delivered through the ECS system, that cause minor impairment or minor injuries to crew and/or passengers.
LEVEL 3 - SERIOUS CONSEQUENCES
a. Substantial damage to the aircraft or second unrelated system.
b. Uncontrolled fires.
c. Rapid depressurization of the cabin.
d. Permanent loss of thrust or power greater than one propulsion system.
e. Temporary or permanent inability to climb and fly 1000 feet above terrain.
f. Any temporary or permanent impairment of aircraft controllability.
g. Malfunctions or failures that result in smoke or other fumes, delivered through the ECS system, that result in a serious impairment.
LEVEL 4 - SEVERE CONSEQUENCES
a. Forced landing.
b. Loss of aircraft (hull loss).
c. Serious injuries or fatalities.
LEVEL 5 - CATASTROPHIC CONSEQUENCES
Catastrophic outcome (reference Catastrophe as defined by draft AC 25.1309-B) - an occurrence resulting in multiple fatalities, usually with the loss of the airplane.
Levels 3, 4 and 5 represent the greatest area of safety concern. CAAM addresses this special concern by establishing the hazard ratio, or the conditional probability of serious or severe consequences (i.e., hazard level 3, 4 or 5) given that a particular engine, propeller, or APU event with at least some safety significance (at least level 1) occurs. The paragraphs below describe how to calculate the hazard ratio. First, let us return to the issue of prioritization.
Prioritization assumes that when we are faced with multiple problems, we devote the most attention and resources to those problems most likely to cause serious harm. Within the CAAM process, the prioritization is therefore undertaken against the risk of level 3 and higher events (assume from now on that level 3 means level 3 and higher). We previously discussed how the risk analysis could output a risk factor for the basic event (fracture, etc.), for uncontainments, and for other categories of outcomes. We can see now that we are probably most interested in the risk factor for level 3s. A problem with a high uncorrected level 3 risk factor (uncorrected being the risk factor if we were to let the situation continue without any corrective action) should receive a much higher portion of resources than a problem with low risk of progressing to a level 3 event. This allocation of resources means that we allow more time for the low-risk problem to be corrected compared to the high-risk problem. It does not mean we ignore the low-risk problem, only that we recognize that if we force a quick response to a problem with minor consequences, we may not have adequate resources available to react quickly to the next, more serious problem.
Calculation of the hazard ratio
Calculating the hazard ratio will require considerable engineering judgment. Since the hazard ratio is a strong influence on the prioritization process, it should either be based on validated data or be assessed conservatively. To this end, we can consider it another assumption within the risk analysis process. Specific data are often not available; historical hazard ratios, developed from past events on similar engine types, should be used cautiously. The hazard ratio is dependent on the installation (e.g., wing-mounted vs. tail-mounted engines), and the historical data may be skewed by the amount of information available for the affected aircraft installation. The following three methods of calculating the hazard ratio are offered, depending on whether specific data exist or not:
1. At least one level 3 event has occurred. Use the value obtained by dividing the number of level 3 events by the total number of safety events (i.e., at least a hazard level 1). For example, two level 3 events out of four total would be 2 / 4 = 0.50 hazard ratio. If the latest event used in the calculation was not level 3, add one additional level 3 event, and one additional safety event, to the totals to cover the possibility that the next event would be level 3. E.g., one level 3 out of four total events (1 / 4) becomes two out of five (2 / 5 = 0.40).
2. No level 3 or higher event has occurred. When no level 3 event has occurred, historical hazard ratios may be used, with care taken to ensure proper methods of comparison, including: similar aircraft installation, engine bypass ratio, and any other factors of possible significance.
3. No level 3 or higher event has occurred and no historical data are suitable. Where no level 3 event has occurred and no historical data are available or suitable, use the method in (1.) above by assuming the next event would be level 3 (e.g., 0 / 4 becomes 1 / 5 = 0.20). There may be cases where this method is overly conservative. In those instances, engineering analysis and/or coordination with the installer and operator(s) may be used to establish a more realistic hazard ratio.
It may also be desirable to establish the conditional probability of a level 4 event given that a level 3 event has occurred. Typically, coordination with the installer and operator(s) is necessary to establish a level 4 hazard ratio.
The information in this installment is included in the CAAM Advisory Circular, AC39-8. This AC also contains data for use in calculating historical hazard ratios for various types of engine, propeller, and APU events for the period 1992-2000; earlier data are contained in the FAAs Technical Report on Propulsion System and Auxiliary Power Unit (APU) Related Aircraft Safety Hazards, dated October 25, 1999.
8. Risk factor guidelines
In this installment:
Guidelines for allowable risk factors
Per-flight risk
Cumulative risk
Risk factor guidelines
The guidelines described below represent the short-term risk that can be reasonably allowed during the time period required to correct an unsafe condition. These guidelines are not targets or typical values; the risk factor should normally be lower than these guidelines unless a lower value would result in extreme resource difficulties. The goal of risk analysis is not to find the most lenient program that still squeaks under the risk factor upper limit. Any reasonable action which reduces the risk should be included as part of the correction program (keeping in mind the principles of prioritization discussed in the previous installment).
On the other hand, zero risk is unattainable without grounding the fleet. Also, the plot of risk factor versus impact on resources reveals an asymptotic relationship; in other words, at some point, any additional reduction in risk factor comes only at great increase in the required resources. That particular point varies from situation to situation. The engineer must decide if the additional burden on the fleet is worth the reduction in risk.
The risk factor for level 3 events during the correction action period should not exceed 1.0 except in rare cases. Remember that the level 3 events means those at least level 3 (i.e., level 3, 4 and 5 events). The risk factor for level 4 events (i.e., level 4 and 5 events) should not exceed 0.1 for the correction action period. In most instances, however, level 4 events should be managed to a much lower risk factor to minimize the cumulative effects of multiple unsafe conditions on overall risk. There is no guideline as yet for level 5 events.
Per-flight risk
Risk factor guidelines apply to the total number of expected events. However, we also need guidelines for per flight risk. This requirement recognizes that we must limit the additional risk posed by any one unsafe condition to any one plane during any one flight. The average risk per flight is calculated by dividing the risk factor by the total engine cycles (or hours, as the case may be), corrected for the number of engines per plane. For example, a risk factor of 0.5 for a correction period totaling 300,000 engine cycles for a twin-engine aircraft fleet equates to an average per-flight risk of [(0.5 / 300,000) x 2] = 3.3x10-6.
The per-flight guidelines for short-term risk are less than one level 3 event in 25,000 flights (4x10-5) and one level 4 event in 250,000 flights (4x10-6).
Once the problem has been corrected, the long-term average per-flight risk should not exceed one level 3 event per 100 million flights (1x10-8). The long-term level 4 guideline is less than one level 4 event per billion flights (1x10-9).
Cumulative risk
Back in installment 2, we discussed the Poisson distribution and how we use it to relate risk factor to the probability that more events will occur. Looking at the risk factor guidelines above, we find that a level 3 risk factor of 1.0 equates to a 70% probability that at least one level 3 event will occur during the correction program. A level 4 risk factor of 0.1 equates to a 10% probability that at least one level 4 event would occur. You can see why we want these guidelines to be treated as upper limits rather than as typical values; the cumulative effects of multiple unsafe conditions over the life of the fleet becomes a consideration. Allowing all problems to reach the upper limit could result in an undesirably high cumulative risk. If, for example, during the life of a fleet, there are seven different problems that are all allowed to reach a level 4 risk factor of 0.1 events, we would have a cumulative risk factor of 0.7 level 4 events. This equates to a 50% probability of at least one level 4 event, and a 16 percent probability of two or more over the life of the fleet. While there are currently no guidelines for cumulative risk, expecting to have a level 4 event at some point is not a desirable situation.
9. Miscellaneous risk analysis topics
In this installment:
The requirement for a consistent set of ground rules
Dual-event risk
Why limiting conditions arent enough
Specimen tests versus part tests
The requirement for a consistent set of ground rules
Prioritization requires comparing risk analysis results from multiple problems to ensure that they are being managed appropriately. A consistent set of ground rules for constructing these quantitative assessments is necessary to ensure valid comparisons, and that the risk factor guidelines are being properly applied. Examples of areas where consistent ground rules are necessary include: the determination of flight exposures; event hazard levels; hazard ratios; and per-flight risk. There may be differences in the ground rules used by different manufacturers in performing quantitative assessments; it is therefore important to refrain from directly comparing results from different manufacturers unless it can be verified that the analyses were performed using the same ground rules.
Dual-event risk
Most of the unsafe conditions weve discussed have arisen from a serious event, or sequence of events, on a single engine. However, we sometimes are faced with the situation of having benign single-engine failures (not in and of themselves unsafe) occur at a rate that raises concern over the risk of multiple engine failures within the same flight. The single-engine rate is used to estimate the multiple-engine risk. For all practical purposes, the risk does not go beyond dual-engine events for non-common cause problems. And, of course, common-cause problems - fuel contamination, runway ice ingestion, incorrect maintenance on multiple engines, etc. - are really single-event unsafe conditions affecting multiple engines.
The seriousness of the dual-engine event should be evaluated against the CAAM hazard levels. CAAM hazard level 3 includes permanent loss of thrust or power greater than one propulsion system. In addition, the loss of enough engine thrust to force a landing is an automatic CAAM level 4 event. For twin-engine aircraft, dual inflight shutdowns (if the engines cannot be restarted) are thus level 4 situations. Engine failures which result in the loss of the ability to produce sufficient thrust, even if the engines were not actually shutdown, must be considered in the analysis. For example, suppose we had blade fractures occurring in the high-pressure compressor. Four fractures resulted in inflight shutdowns (IFSDs), and, in two other cases, the engines were retarded to idle but not shutdown. The factor to consider when calculating the appropriate dual-engine risk is whether the failure condition (HPC blade fracture) renders an engine incapable of producing any significant amount of thrust. If so, not only are all the IFSDs to be counted, but the non-IFSD events (operational discrepancies) must be counted as well, since the engines could not produce thrust if called upon.
For random failure modes, or for fleets of aircraft with engines of differing ages (it is a fairly common practice for airlines to stagger their engines so that, on a given airplane, all engines are not of the same total hours or cycles), the dual-engine (d.e.) risk can be simply calculated from the single-engine (s.e.) rate, corrected for the number of total engines:
for a two-engine plane d.e. risk = (s.e. rate) x (s.e. rate)
for example, s.e. rate = 1x10-4 per engine cycle
d.e. risk = (1x10-4 x 1X10-4) = 1X10-8 per airplane flight
for a three-engine plane d.e. risk = 3 x [(s.e. rate) x (s.e. rate)]
the factor of 3 is needed because there are 3 ways to fail 2 engines
on a three-engine plane (engines 1 and 2, 1 and 3,
or 2 and 3)
for example, d.e. risk = 3 x (1x10-4 x 1X10-4) = 3X10-8
for a four-engine plane d.e. risk = 6 x [(s.e. rate) x (s.e. rate)]
the factor of 6 is needed because there are 6 ways to fail 2 engines
on a four-engine plane (1 and 2, 1 and 3, 1 and 4, 2 and 3,
2 and 4, or 3 and 4)
for example, d.e. risk = 6 x (1x10-4 x 1X10-4) = 6X10-8
Note how the risk is automatically higher on planes with more engines; however, permanently losing two engines is not automatically a level 4 (depending on the phase of flight) for a three- or four-engine aircraft.
For wearout or infant mortality probabilistic failure modes, with unstaggered engines, the risk must be calculated from the instantaneous failure probability for the given age of the engines or parts. In these cases, a summary table is usually produced to show the dual-engine risk versus the age (cycles or hours, as appropriate) of the engines. Resources can then be diverted to addressing the population of aircraft with engines at the greatest risk.
Why limiting conditions arent enough
Occasionally, we are faced with unsafe conditions where a variety of different parts may fail from the same basic event. For example, an engine overspeed can cause any of the disks to burst, or excessive loads can cause the engine mounts, pylon, or other structures to break. In these situations, an analysis may be presented against the limiting condition - the disk under highest stress, or the structure most likely to break. However, the aim of a risk analysis is to evaluate total risk. The limiting condition may represent the part most likely to fail, but it isnt the only part that could fail. Remember in the risk analysis process that we discussed how material properties (such as crack initiation and propagation) were simulated for each part. For any given engine, the limiting condition part may be actually be stronger than another part because of the difference in their respective material properties. The additional failure probabilities for each of the other parts, even though they amount to lower risk than the limiting condition part, must be considered to properly estimate the total risk exposure from the basic event (overspeed, etc.) The exception to this would be if the risk analysis assumed minimum material properties (rather than distributions) for the limiting condition.
Specimen tests versus part tests
To help define part failure distributions, material tests in a laboratory environment are often performed. Due to the costs involved, these tests are usually run with specimens rather than actual parts. The aim is to make these specimen tests as close to actual engine operation as is possible. Any available field data on cracking should be used to validate the testing.
In addition, if multiple parts are at risk in the engine (for example, 46 blades in a rotor) but only single blades or specimens are tested in the laboratory, a correction must be made to the test failure distribution to account for the multiple parts in an engine. For example, testing might show that 1 out of 100 blades fails within 5,000 cycles. However, roughly one out of every two engines will have a 1/100 blade somewhere in its rotor of 46 blades. If we have field experience, this effect sorts itself out - the engine fails when the weakest blade fails.
This concludes the discussion of the FAA Engine and Propeller Directorates risk analysis process. I hope the material has been useful. Please address any comments or questions to:
Ann Azevedo
Risk Analysis Specialist
781-238-7117
ann.azevedo@faa.gov
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