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1.3 The concepts of reliability and robust engineering in diesel engine system
1.3.5 The concepts of quality, robustness, and quality loss function
1.13 shows that in order to control the failure rate, either the strength needs to be increased (i.e., move the strength probability curve to the right or reduce its distribution range) or the stress has to be reduced. In the example of peak cylinder pressure, in order to reduce the pressure for better durability, the control factors such as engine compression ratio, intake manifold boost pressure or fuel injection timing need to be modified, and this affects engine performance and emissions. The durability analysis on the stress and strength distributions helps determine the maximum design limit and the nominal design/calibration target of design parameters (e.g., peak cylinder pressure and exhaust manifold gas temperature) that can be used for a durable system design. These limits or nominal targets can ensure the engine will not be overloaded and the structural strength is designed sufficiently strong.
1.3.5 The concepts of quality, robustness, and quality
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’. Such a definition of quality is suitable for diesel engine system design. More details about quality and reliability engineering are provided by Chandrupatla (2009).
The quality of an engine product, as designed and manufactured, refers mainly to its consistency of conformance to the customer’s requirements in performance, durability, and packaging attributes. As illustrated in Fig.
1.14, quality is an intermediate design goal of engine system design, and it assembles and measures all three design attributes. Quality ultimately extends or evolves to reliability in the time-in-service domain. During the course of diesel engine system design, the measurement and assessment of quality in performance, durability, packaging and their synthesis should not be overlooked. The quality target can be used as an objective in design optimization.
The demand for a product is usually affected by attributes and price (Hazelrigg, 1998). The quality and reliability of engine performance, durability and packaging features directly affect the brand image and product demand of diesel engines. It should be noted that sometimes people think a reliability problem is such a serious one that the product cannot function, while a quality problem is often regarded as a less serious one that the product can still function but with nuisance. That is a misunderstanding and wrong perception of the concepts of reliability and quality from an engineering sense. In fact, the severity of a problem can be characterized by a cost function of quality loss. A small loss of quality may cause a small cost to the customer without affecting the basic use of the product, while a large loss of quality at a moment of time in service during the lifetime of the product may cause a catastrophic failure of the function. Both scenarios present a reliability problem of different severities.
Before Dr Genichi Taguchi developed the methodology of continuous quality loss function, in the traditional discrete ‘pass–fail’ quality theory where samples were viewed as either pass or fail, a design within the range of specification was viewed as equally good, while any design outside the specification was viewed as equally bad (Fig. 1.14). However, the quality perception by the customer is not so simple. A product that is barely within the specification is certainly not as good as a product that is perfectly on the target. Therefore, quality loss, or functional performance loss, should be a continuous and gradual event with respect to the functional performance rather than a discrete or step event depicted in the traditional quality theory.
Quality engineering or robust design is a process to obtain the response that is insensitive to noise factors. Robust design requires a quantitative definition of quality. As mentioned earlier, the loss of quality is actually continuous rather than discrete and sudden when the product quality deviates from the
Probability
Design B Design B
Not equally good Specifi cation limits
Design A Design A
Very badNominal target
Nominal target Nominal target
Equally good (for Design B and the Design A within spec limits) Functional performance (Y)
Functional performance Functional performance (Y)
Lower boundSpecifi cation limits Quality loss function: tf: functional tolerance Ccf: cost to functionality if tolerance is exceeded Upper bound LYC YYC YqLYqLYupper ()LY()LY=(=(uppe =(upper =(r –)YY–)YY+(+(C +(C 2=(2=(2 2+(2+(cf =(cf =( f
cf+(cf+(lo+(lo+(we+(we+(r+(r+( ftt2tt2 fttf–)2–)Y–)
Quality loss Quality loss
Specifi cation limits
Equally bad (for Design A outside limits)
Equally bad (for Design A outside limits) Best GoodAcceptable
Bad 1.14 Quality loss function.
nominal target due to various noise factors. The product quality is commonly defi ned by using a quality loss function (Fowlkes and Creveling, 1995). As shown in Fig. 1.14, the two designs (A and B) have different probabilistic distribution curves for a particular functional performance parameter. The specifi cation is defi ned by a nominal target and a tolerance range for acceptable limits from a lower specifi cation limit to an upper limit. The design A has a larger population of samples (i.e., higher probability) around the ‘good’
nominal target but widely spread samples outside the specifi cation range due to a larger standard deviation. On the other hand, the design B has a shifted and narrower probability distribution curve which gives very few samples meeting the ‘good’ nominal design target although all of its samples are within the specifi cation range. This example illustrates that ‘within specifi cation’
and ‘on target’ do not have the same meaning. Therefore, it is important to consider the probability distribution characteristics when evaluating different designs.
Dr Genichi Taguchi promoted the idea of not just getting all the units within the specifi cation limits but getting all the units on target. He developed the methodology of quality loss function to evaluate the fi nancial impact of the tolerance range. Taguchi defi ned the quality loss of an off-target product performance, due to deviation from the nominal target, as the life-cycle monetary losses caused by functional variability and harmful side effects related to customer functional tolerance and the cost to society. He defi ned that the losses represent a summation of rework, repair, warranty cost, customer dissatisfaction, bad reputation, and eventual loss of market share for the manufacturer. He defi ned that the loss of quality as a cost increases quadratically with the deviation from the target, and the quality reaches the best at the nominal target. He used the quality loss function to quantify the quality of a design and determine the tolerances.
Various models have been proposed to estimate the product quality loss by using the mean value and the standard deviation of the response. Figure 1.14 and Table 1.5 show the quality loss function. Table A.1 also summarizes the related formula used in statistics. The two basic sample statistics to quantify variability are Y and sSV2 , which describe the central location and the width of the probability distribution. A histogram is another way to describe the distribution of the frequency of occurrence. From the average quality loss equation shown in Table 1.5,
L YL YL YL YL YL YL YL YL Yqqqqqqqqq(((( ) ) ªCCCCCCCCCCCCCCCCCqqqqqqqqq · [ · [ssSVSV2222222 + ( + ( + ( + ( + ( + (YYYYYYYYYYYYYYYYY – YYYYYtargettarget) ]) ]) ]2222222 1.1 where Cq is a quality loss coeffi cient, it is observed that minimizing the variance sSV2
(i.e., variability) or making the average response Y on the target Ytarget can reduce the quality loss. Such a method developed by Taguchi lays out the theoretical ground of robust design.
Quality includes not only the conformance of geometric tolerances,
but also the conformance of functional requirements. For example, a television’s quality can be measured by its appearance and the sharpness of the image. For diesel engine system design, engine product quality refers to the conformance to the requirements of a combination of performance, durability, and packaging. The quality loss function developed by Taguchi is most useful to quantify the deviation of quality in the area of packaging design and manufacturing tolerance. In general, it is diffi cult to apply the quality loss function directly to diesel engine system design because it is diffi cult to quantify the monetary cost during the system design for the deviation of a design attribute. An easier way to utilize the concepts of quality and quality loss in system design is to use an attribute parameter in engineering units instead of the cost in monetary units. The quality loss of an engine attribute can be simplifi ed as a continuous function of another dependent parameter. For instance, as shown in Fig. 1.15, if we want to quantify the quality loss of EGR rate or coolant heat rejection, the quality loss function can be constructed as a weighted function of engine outlet coolant temperature and NOx emissions, which are dependent upon EGR rate and heat rejection. The coolant temperature is an indicator of durability and increases with coolant heat rejection. NOx emissions are affected by EGR rate, which in turn directly affects the coolant heat rejection. The lower the EGR rate or heat rejection, the higher the NOx emissions. Another example of quality loss is the effect of air–fuel ratio. A deviation to higher air–fuel ratio than the nominal target causes excessively high peak cylinder pressure, while a deviation to lower air–fuel ratio results in high soot or high exhaust manifold gas temperature. Essentially, the quality loss function in engine system design can be simplifi ed as any continuous composite function that may be used as the objective function in system optimization in order to determine the nominal design target and allowable tolerances.
Another key measure of robustness in Taguchi’s robust design for quality improvement is the signal-to-noise ratio (or the S/N ratio). Good quality requires the performance be on target with low variability. Taguchi focused
Table 1.5 Formulae of Taguchi’s quality loss in robust design Parameter name Parameter
symbol Formula Taguchi’s quality
loss Lq(Y) Lq(Y) = Cq · (Y – Ytarget)2 Taguchi’s mean
square deviation CMSD
CMSD ni n
n
i i
n
= 1 (( ii –– ) = 1 ((((YYYYYYiiiii ––––
=1
2
S S=1
S S
S Y Y S
S(Y –Y S
S((YY ––YY S S((YYYYYYii ––YYYYYY S S(YYYYii –YYYY ) = S
S ) = 1 S
S 2 1 S
S ) =) =22 S S ta ) =) =2 S
S ta S
S Y Y S
S YY YYta S
S Y Y rg S
S rg S
S et S
S et S
S S YYYYYY) + ( –) +) + ( –) +) +) +) + ( –222222222222 ( –( –( –( –( –( –YYYYYY YYYYtatarget)))222222222222 Taguchi’s
average quality loss
L Yq L Yq L Y( ) L Y( )
L Y L YL YL YL YL YL YL YL YL Yqqqqqqq( )( )( )( )==CCCCCqqqqqqq··CCCCCMSDDDDDD====CCCCCCCCCCCCCCCCCCCCCCCCCCCqqqqqq····[[[[[[[[ss22222222++++++++( –( –( –( –( –( –YYYYYYYYYYYYYYYYYYYYYYYYYYY YYYYYtatarget) ]) ]) ]22222222 ªCCCCCCCCCCCCCCCCCqqqqqqqq· [· [· [· [· [· [· [· [sss222222222SSSSSSSSVV + ( –+ (+ (+ (+ (+ (+ ( –YYYYYYYYYYYYYYYYY–––––––––––––––––YYYYtatatargrgetet) ]))))))))))))))))))222222222
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).