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1.3 The concepts of reliability and robust engineering in diesel engine system
1.3.6 The concept of reliability
on reducing variations in design and believed that it might be preferable to have a product that gives consistently good results than one that gives inconsistent results which are sometimes better but worse on average. The details of Taguchi’s concepts of quality, quality loss function, signal-to-noise ratio, and robust design were explained in detail by Fowlkes and Creveling (1995).
in the time domain. In general, reliability is defined as the fulfillment of quality requirements over the life cycle under specific application conditions.
According to Chandrupatla (2009), ‘reliability is the probability that a system or component can perform its intended function for a specified interval under stated conditions’. According to O’Connor (2002), ‘reliability is the probability that an item will perform a required function without failure under stated conditions for a stated period of time’. As summarized by Rausand and Hoyland (2004), until the 1960s reliability was defined as ‘the probability that an item will perform a required function under stated conditions for a stated period of time’. They pointed out that a more preferred and more general definition of reliability given by ISO 8402 standard was that ‘reliability is the ability of an item to perform a required function, under given environmental and operational conditions and for a stated period of time.’ A required function here may be a single function or a combination of functions that is necessary to provide a specified service. A hardware system may pass the initial quality specification test on the factory’s manufacturing assembly line, but it may not perform reliably over a specified period of time in customer usage. Rausand and Hoyland (2004) defined that ‘according to common usage, quality denotes the conformity of the product to its specification as manufactured, while reliability denotes its ability to continue to comply with its specification over its useful life. Reliability is therefore an extension of quality into the time domain’.
In diesel engine system design, reliability is the ability of how reliable to maintain the quality of performance, durability, and packaging over time after the engine is put into service. Reliability is not a design attribute.
Instead, it is a characteristic of the product quality extended into the time domain. By definition, reliability contains two key factors: a probabilistic impact by noises and time. Those factors are illustrated in the ‘bathtub’
curve of reliability in Fig. 1.16. When a product is produced as marginally acceptable with respect to its specifications, a little additional external noise can cause a failure in service in the early life of the product. The decreasing failure rate in Fig. 1.16 suggests infant mortality, which means defective items fail early and the failure rate decreases over time as they fall out of the population. The constant failure rate characterizes the bottom of the ‘bathtub’ curve. It is caused by random failure events associated with external or internal environment noise factors or customer usage noise factors. Eventually, the cumulative effects of deterioration noise factors (e.g., wear out) and environment/usage noise factors cause the end-of-life failure, which is characterized by an increasing failure rate as time goes on.
The goal of design for reliability is to make the useful product life longer.
The goal of robust design is to make the design insensitive to all the noise factors during the product life.
In general, reliability can be classified into three categories: hardware,
software, and human. The scope of diesel engine system design is primarily concerned with hardware reliability of engine components and system.
Reliability can be deduced from a probability distribution function of the time to failure (Rausand and Hoyland, 2004). Reliability is usually expressed by the following means:
1. Failure rate and mean time to failure (Fig. 1.13, for example, 1% of failure in total population by 250,000 miles; or 100,000 miles of passenger car operation with no engine tune-ups; or one million miles of commercial truck operation before the overhaul).
2. Number of failures over a period of time (e.g., RN/1000 or the number of repairs per thousand units).
3. Probability of the event that the time to failure is longer than the specified useful life (for example, if the specified useful life is three years and the time to failure is four years, the reliability is 100%).
4. R = 1 – Pfailure, where Pfailure is the probability of failure or the failure rate. The failure rate at a given mileage can be measured from the warranty information of the engines in service.
To further illustrate the noise and time factors in reliability, Fig. 1.13 shows an example of structural reliability in the random probability distribution diagram of the stress–strength interference model. It should be noted that the
Early-life failure, infant mortality due to piece-to- piece noise factors
Failures during normal design life, random failures due to environment or customer
usage noise factors
End-of-life failure, wear-out due to deterioration
noise factors
Limit of useful life
Failure rate
Running-in period of new machine
Time in service
Wear-out failure period Normal running period
1.16 Reliability ‘bathtub’ curve.
probability distribution curves of stress and strength shown in the top part of Fig. 1.13 are constructed by considering noise factors, and they may or may not include a time factor (recall that one of the noise factors discussed earlier is changes over time). In the time-in-service domain, the stress or load in usage varies with time in an uncontrolled manner. The strength of the component also varies with time because the component deteriorates in material properties over time due to failure mechanisms like creep and corrosion. This time-dependent characteristic is shown in the bottom part of Fig. 1.13. The reliability expressed by the time-to-failure is then the time until the stress exceeds the strength. It should be noted that, since there is a high level of uncertainty involved, it is very difficult to predict reliability with statistical methods or precise mathematical calculations.
The role of reliability in engine system design
Reliability is affected by all the phases of a product life cycle (engineering design, manufacturing, operation, and maintenance). Reliability engineering is a process to ensure reliability is controlled in the design stage. Reliability engineering efforts control the risks by addressing the causes of failures in order to prevent or minimize their occurrence. Although reliability can be improved by controlling production variability and human variation in manufacturing and quality control or by implementing preventive maintenance strategies, design plays a vital role to determine the reliability. The concept of design for reliability was elaborated by Kececioglu (2003) and Kumar et al. (2006). More in-depth discussions on reliability in engine system design are provided in Chapter 2. The fundamentals on reliability can be found in Ireson et al. (1996), Bignonnet and Thomas (2001), Kuehnel et al.
(2005), Dodson and Schwab (2006), Klyatis and Klyatis (2006), Rahman et al. (2007), Zhou and Li (2009), and Klyatis (2010).
1.3.7 System design – from ‘design for target’ to ‘design for variability’ and ‘design for reliability’
Overview of system design methodologies
As discussed earlier, variability and reliability are nondeterministic in nature.
Without considering the statistical probability distribution of the attribute the design for a point target would be either an over-design or under-design. A reliable and robust design of a diesel engine system requires the following design methodologies:
∑ design for target (i.e., design for a specific point target, either nominal or limit)
∑ design for variability (i.e., design for both mean value and tolerance
range of the nominal target to achieve a robust and sensitive design)
∑ design for reliability (i.e., design for time-dependent variability or design-for-time-degradation).
Among the above three methods, design for target is the foundation and the basic technique in system design. It is a deterministic design approach.
Many analytical techniques can be applied effectively in this category for a precise design. The rest of the book gives a thorough introduction to this basic technique to strengthen the foundation. Design for variability is a more advanced technique and is nondeterministic. It expands the point design in design for target to a more complex one-dimensional design by adding the probability distribution of the attribute parameter. The probability distribution involves uncertainty and the design loses its precise nature. Inadequate sampling in measurement or test data may make the probability distribution inaccurate. Design for reliability is more complicated because it further expands the one-dimensional design to a two-dimensional design by adding the random factor of time-in-service into the model. Design for reliability is the least precise in nature due to more uncertainties involved. Owing to the difficulty of predicting reliability accurately, the time-dependent probability distribution of the attribute parameter may not be accurate. However, once modeled successfully (with the support of a large amount of lab/field/service data), design for reliability will give the best quality of engine system design.
Figure 1.17 illustrates the evolution of these design methodologies. Figure 1.17 shows that the ultimate design goal of diesel engine system design is good reliability in service life.
Design for target
Design for target is the traditional deterministic design approach where a point target is given. It can be further classified into two subsets: design for nominal and design for limit. The target can be either a nominal value (design for nominal) or limit value (design for limit) used in design and calibration.
For example, the engine is designed to have the structural strength to sustain a maximum limit of peak cylinder pressure at 200 bar. In order to ensure the pressure does not exceed the limit of 200 bar under any operating condition with all the noise factors, the engine rated power needs to be calibrated at a peak cylinder pressure of only 180 bar as a nominal target under standard lab conditions. The difference of 20 bar serves as a design margin to cover any deviations from the standard nominal (Fig. 1.18). Design for target is a very useful and still prevalent approach in engine system and component designs for both steady-state and transient topics. In the mathematical formulation of design for target, the number of equations matches the number of unknowns so that a deterministic solution can be found. Two examples of design for target are provided below:
1.17 Engine system design optimization – design for target, variability, and reliability.
Functional response
TargetProgress
Probability Probability
Optimum
Design parameter Design for target– deterministic optimization Optimum meanInitial mean x1x2x3 Design parameter Optimum meanOptimum specification limits Design for variability–probabilistic optimization (without time-based effect) Functional response
Functional response At time T
Constraint Optimum mean Design parameters vary wit time due to wear, fatigue, etc. Design for reliability – reliability-based optimizatio (with time-based effect) Probability
Progress Tim service
1. At a given engine speed and power, assuming the air–fuel ratio and EGR rate are known requirements, find turbine area and EGR valve opening.
2. For a transient emissions cycle with prescribed engine speed and load varying as a function of time, assuming the transient history of the air–fuel ratio and EGR rate are known, find the transient history of the turbine area and EGR valve opening as a function of time.
Design for target is the fundamental design technique in diesel engine system design and a stepping stone toward the more advanced nondeterministic designs. The shortcoming of design for target is that without the information of the probability distributions of the attribute parameters or reliable previous experience, it is difficult to select an appropriate target value in order to achieve a design that is neither over-designed nor under-designed. Design for variability needs to be used to address this issue.
Design for variability
Design for variability addresses the effects of both control factors and noise factors in order to control both the mean value and the variation range of the attribute parameters by changing the control factors. Design for variability includes two subsets: robust design and sensitive design, one for noise input factors and the other for control input factors. The goal of design for variability is to achieve a reliable design that is insensitive to noise factors but sensitive
3 Nominal
design target Nominal calibration
target
Calibration
limit Design limit (failure limit)
2 1
New lab engine, the worst cylinder
Piece-to-piece noise, internal noise (e.g., in-vehicle), external noise (e.g., weather)
Piece-to-piece noise, change-over-time noise (wear), customer usage noise, internal noise (e.g.,
sensor), external noise (e.g., weather)
Probability
4
Functional or attribute value (e.g., peak cylinder pressure) 3-sigma tolerance
of design limit
1.18 Engine system design constraints or limits.
to control factors. The reliable design means that the probabilistic distribution of the system response has a reasonable mean value and deviation range so that a predetermined percentage of population satisfies the requirements of performance, durability, or packaging without failures. The response can be any parameter of performance, durability, or packaging.
Robustness means that the system/component response is insensitive to, or not adversely affected by, the variation of the input noise factors within a range of circumstances, even though the sources of variability have not been eliminated. Robustness can be measured by the signal-to-noise (S/N) ratio. It is the effect of noise factors that robust design wants to control, via changes in the control factors. Robust design is the process to achieve the defined robustness. Sensitivity analysis, mean value design (for setting the nominal target), and tolerance design (for setting the specification range) are three important tasks in robust design.
Robust design should not be confused with sensitive design. The engine needs to be a sensitive system which responds quickly to the control input factors, for example, to achieve good transient performance. Note that the system needs to be sensitive to the control factors rather than the noise factors.
When noise factors present, it is desirable for the engine system to be insensitive to the noises in order to ensure a stable operation under uncertainties.
There are numerous examples of robust design in engine applications. For example, the fuel system of the diesel engine must provide a consistent supply of liquid fuel regardless of external or internal noise factors. Inconsistent fuel delivery may cause engine stumbles when cruising, accelerating and decelerating, rough or rolling engine idle, and other drivability issues. Higher temperatures in the engine may lead to fuel vaporization which may cause insufficient fuel delivery to the injectors. A robust fuel delivery design needs to isolate or minimize the impact of these unfavorable external temperatures.
Statistical probability distributions of random parameters are required in design for variability. Several types of distribution can be used to model the input factors, such as normal, uniform and Beta distributions (Table A.2).
The combination of the probability distributions of different input factors generates a probability distribution of the output response. Appropriate mean and standard deviations of the control factors can be searched or optimized simultaneously in order to achieve the desirable distribution of the response.
The design solution produced by such a design-for-variability approach is usually a more cost-effective and more robust design than that obtained by using the deterministic design approach.
As shown in Fig. 1.19, when multiple design constraints exist, as is usually the case with engine design, the deterministic approach cannot completely handle design-for-limit if the limit value of only one constraint is used because that single point does not serve as the limiting case for all the design constraints. For example, if a design-for-limit case requires an
analysis at peak cylinder pressure of 200 bar, this case would give a lower exhaust manifold temperature than a case of 180 bar cylinder pressure due to higher air–fuel ratio. Therefore, this case cannot be used to assess the durability of the exhaust manifold. The probabilistic approach of design for variability does not have this limitation because it produces the statistical distributions of all the design constraints simultaneously so that all the design constraints can be easily identified, as illustrated in Fig. 1.19. A multi-objective optimization can then be conducted to try to seek a solution that satisfies all the constraints. Monte Carlo simulation is an effective tool used in design for variability and this topic is detailed in Chapter 3.
Some research work related to design for variability and robust design was reported in the literature in the areas of emissions, cooling, and vehicle fuel economy. Yan et al. (1993) and Dave and Hampson (2003) used the DoE method and Monte Carlo simulation to analyze the robust design of emissions and engine BSFC. Rahman and Sun (2003) analyzed engine cooling system design to control coolant temperatures. Catania et al. (2007) presented a robust optimization for vehicle fuel economy analysis.
Design for reliability
Design for reliability is design for variability extended into the time-in-service domain. One example is turbocharger matching to account for the variation
Probability Probability Probability
Probability Probability Probability
Peak cylinder pressure
Coolant heat rejection Turbocharger speed Compressor outlet air temperature Exhaust manifold gas
temperature Exhaust manifold pressure 3
3
3
3
3
3 2
2
2
2
2
2 1
1
1
1 4
4
4
4
4
4 1
1
1.19 Coordination between different engine system design targets and constraints.
in exhaust restriction caused by soot loading changes in the DPF. Exhaust restriction (the pressure drop across the aftertreatment system) significantly affects turbocharger matching and engine system design. When the exhaust restriction becomes higher, the turbine expansion ratio and the engine air flow rate usually reduce. This results in a decrease in peak cylinder pressure but an increase in exhaust manifold gas temperature. The nominal design point of turbocharger matching is dependent on exhaust restriction. Unlike the muffler-only exhaust system that has a deterministic back pressure at the rated power condition, modern diesel engines equipped with a DPF have a randomly fluctuating back pressure over time, increasing during the soot accumulation phase or decreasing after DPF regeneration. Matching the turbocharger for a clean DPF or a fully loaded DPF yields very different results. If the probabilistic distribution of the exhaust restriction during the vehicle lifetime can be found, the turbocharger can be matched better to balance the system efficiency and durability.
Like design for target, design for variability/reliability is often carried out with optimization techniques. In reliability-based design optimization (RBDO), in order to reduce computing time, it is useful to first conduct a deterministic optimization to pre-screen, and then apply the probabilistic variations of the uncertainties to the pre-screened sub-optimal solutions for further optimization. The RBDO usually consists of the following steps:
1. Deterministic design-of-experiments (DoEs) variable pre-screening to identify key factors.
2. Deterministic DoE response surface fit to build emulator models.
3. Non-time-dependent nondeterministic variability analysis with key factors.
4. Time-dependent nondeterministic reliability optimization with key factors.
5. Confirmation runs.
These optimization topics are elaborated in Chapter 3.