Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability http://pio.sagepub.com/
Accelerated degradation tests for reliability estimation of a new product: A case study for washing machines Filippo De Carlo, Orlando Borgia and Mario Tucci Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability published online 9 September 2013 DOI: 10.1177/1748006X13500650 The online version of this article can be found at: http://pio.sagepub.com/content/early/2013/09/05/1748006X13500650
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Accelerated degradation tests for reliability estimation of a new product: A case study for washing machines
Proc IMechE Part O: J Risk and Reliability 0(0) 1–12 Ó IMechE 2013 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/1748006X13500650 pio.sagepub.com
Filippo De Carlo, Orlando Borgia and Mario Tucci
Abstract Accelerated degradation test is a valuable technique able to provide information on the duration of highly reliable products. It is widely used in electronics, where component life often cannot be estimated in an acceptable time with the classic reliability estimation techniques. In the mechanical engineering sector, however, accelerated degradation tests are not so common. The purpose of this study is to evaluate the applicability of accelerated degradation test methodology to a new mechanical subassembly of a washing machine. In particular, we tried to identify which was the most appropriate degradation parameter, choosing among three possible alternatives. The methodology was applied to the new oscillating group of a washing machine, with oversized dimensions and innovative materials. The first selection of elements that could be monitored initially provided three parameters: the drum deformation, the bearing temperature and the vibrations of the rotation shaft. The research allowed the identification of the deformation as the most appropriate parameter for the reliability estimation of the oscillating unit. The originality of this study lies in the fact that accelerated degradation tests of washing machines is not discussed in earlier studies. In addition, the application of such methodology to select the best from three different parameters is not studied earlier. In this study, another peculiarity of accelerated degradation test has been emphasized: it is possible to quickly enrich the know-how on a new product, allowing an indepth knowledge of new elements, in far more rapid speed than using the traditional approach.
Keywords Accelerated degradation test, reliability, washing machines
Date received: 15 May 2013; accepted: 15 July 2013
Introduction The increasing struggle in the global market is forcing companies to reduce the time-to-market (TTM) of new products. So, every company aiming at customer satisfaction tries to offer a functional product, safe and reliable, in the shortest possible time. New products must be introduced into the market quickly with innovative characteristics and at a competitive cost,1 without compromising their efficiency and reliability.2 Moreover, reliability knowledge is crucial for transforming maintenance from a bare cost into a competitive advantage3,4 and for managing availability issues.5,6 By means of the sole monitoring of the time-to-failure, it is increasingly tough to assess the duration of reliable products through the traditional lifetime testing techniques. Actually, in such cases, the conventional analysis cannot, in fairly short times, either identify the product weaknesses (due to design or production) or confirm the predictions regarding the useful life.7 In
order to get more information in a little time, researchers have merged conventional reliability testing with accelerated life tests (ALTs) and accelerated degradation test (ADT). ALT8 is a test in which the intensity of the applied stress exceeds the normal use. This approach can reduce the time needed to observe the effect of the stress on the item. Through these tests, the fault process is quickened and the time before the breakdown becomes smaller. During ALT execution, researchers look for traditional failures, called ‘‘hard failures’’ permanently affecting the functionality of the product. Anyway, if the number Department of Industrial Engineering, University of Florence, Florence, Italy Corresponding author: Filippo De Carlo, Department of Industrial Engineering, University of Florence, Viale Giovan Battista Morgani, 40-50134 Firenze, Italy. Email: [email protected]
2 of hard failures is low at the end of an ALT, it is difficult or impossible to analyze life data and to make meaningful inferences on the product reliability. In such cases, it could be useful to arrange an ADT, which focuses on not-happened failures, the so-called soft failures.9 These are the damages caused by the degradation process that will eventually lead to failure and malfunction. Both ALT and ADT aim at the determination of the reliability functions.10 More generally, starting from the overstress test data, they try to deduce the reliability functions under normal conditions of use. This article aims at filling some of the gaps in the literature by extending ADT to the field of household appliances. The methodology was applied to the new oscillating group of the washing machine, with oversized dimensions and innovative materials. In particular, we tried to identify which is the most appropriate degradation parameter, choosing among three possible alternatives, in order to estimate reliability parameters, focusing especially on the warranty period. The use of such methodology for the oscillating group of washing machines is original and brought interesting results, both in terms of reliability performance acquaintance and of a deeper expertise of the new product. The latter was more quickly achieved in comparison to what would be needed with a conventional approach. The remaining part of this article is structured as follows: ‘‘State of the art’’ section exposes the state of the art, while in the ‘‘Methods’’ section, an overview of ADTs is presented. Then, the ‘‘Case study’’ section is presented while, in the ‘‘Results’’ section, the outcomes of the experimentation are highlighted. Afterward, a the results are discussed, followed by a final section of conclusions and remarks.
State of the art The international literature shows an important development of ADTs in recent years.11,12 It should also be noted that there is not any evidence of ADTs applied to washing machines, which are one of the most common household appliances. Even applications of ALTs in this area are uncommon.13 In recent years, ADTs have been applied to engineering fields14 to evaluate and assess product reliability. Earlier, in the 1980s, ADTs were used in other scientific sectors, for example, in biology. For instance, we can find early applications to estimate the speed of a biological degradation.15 Later on, ADTs were applied to the industrial engineering field, especially in electronics14,16 and electricity.17 Degradation analysis methods are nowadays widely applied to light-emitting diodes (LEDs).18 These equipments are relatively young and can be operated for a long time, even tens of thousands of hours consecutively. Hence, they require some special tests to verify their reliability without the need of waiting for years: several authors report the examples of tests on these devices.19 In mechanical engineering, ADTs have not
Proc IMechE Part O: J Risk and Reliability 0(0) been applied as widely as in electrical engineering, even if the problem of aging and wear of machines have been studied for many years.20 In a recent article,21 the author shows, through the use of data degradation, the reliability assessment of a train wheel using a simple linear model of the performance decay. The influence of more than one performance on the failure mechanism is the basis of another recent study,22 in which a multivariate analysis model is proposed: the observation and analysis of the statistical results are made for a variable at a time. In carrying out such degradation tests on LEDs, a dependency among the several system performance is supposed. This has led to a better reliability estimation, compared to estimates in which each performance is independent from the others.
Methods The objective of ADTs is to evaluate the degradation of a system subjected to high stress, in order to make some inferences about the performance in normal conditions of use. Degradation data may provide more reliability information than traditional fault data analysis. Degradation analysis is accomplished with statistical tools, to provide useful hypotheses about the statistical distribution of the product life.23 For each degradation parameter chosen, it should be possible to define a threshold beyond which the failure occurs. At the moment in which the degradation passes the threshold, we assume that a virtual failure, or a soft-failure, occurs. Such point is expected to be the time to failure of the unit. This is defined, in fact, as the time in which performance degrades below the specified level or in which degradation reaches the threshold. The monitored degradation can correspond to a physical parameter of the product, such as the corrosion of a metal plate. In other cases, degradation may be a product performance, such as the brightness of a LED. Nelson24 first observed that the performance of many products get worse as their lifetime increases. This decline, generally slow, can be accelerated by a stress higher than the one for which the system was designed. In his article, he showed how the strength to break an electrical connection depends on both time and temperature. The acceleration of stress can have various forms,25–27 as shown in Figure 1. In constant stress ADTs, samples are tested under a uniform overstress for the entire duration of the experiment. A special case of such technique was applied in our research. Let us now assume that the ADT is executed on n identical units and that, during the test, each of them is controlled periodically to measure the critical feature yij , where i indicates the unit and j is the time at which the inspection is performed. The degradation of the feature yij is hence given by equation (1) yij = g tij ; b1i ; b2i ; . . . ; bpi + eij ð1Þ
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3 Table 1. Extrapolation models for the time to failure. Model
Linear Exponential Power law Logarithmic
l=a t+b l = b eat l = b ta l = a lnðtÞ + b
l represents the nominal life, t is the time and a and b are parameters of the model.
Figure 1. Stress acceleration in ADTs. Depending on the type of stress acceleration, we can define three different test degradation types comparing them to the user-level stress: (a) constant overstress (dotted line), (b) step stress (step line) and (c) progressive stress (continuous line).
where g(tij ; b1i ; b2i ; . . . ; bpi ) is the function of degradation of unit i at time tij b1i ; b2i ; . . . ; bpi are the unknown parameters of the model, and eij is the term that indicates the error. The units tested can undergo degradation in many ways and cross the threshold according to numerous patterns. In general, however, as time goes by, the degradation rises together with the probability that the critical feature value would exceed the threshold.28 If we call G the threshold value and T the time in which the fault occurs, the probability that a failure occurs before a certain time t is defined in equation (2) FðtÞ = PðT4tÞ = P½yðtÞ5G = P g tij ; b1i ; b2i ; . . . ; bpi 5G
Considering the previous equation, we note that the likelihood of a fault depends on the degradation parameter value, which, in turn, is a function of the stress level. ADTs are usually performed by applying very high levels of stress, aiming at further accelerating failure mechanisms and at generating a greater number of damaging events. This makes it possible to reduce the uncertainty of the test results. To perform ADTs, it is advantageous to define in advance the threshold value that may result from experience, design process or experimental measurements. In any case, once the tests are made, it is possible to fine-tune it. When performing an ADT, degradation is measured as time goes by. With a time-based regression,29 you can extrapolate the degradation trend until it crosses the threshold, providing the expected product time to failure. Such a regression may be based on a linear, exponential, power law or logarithmic base model (see Table 1). Once chosen the most suitable regression type, you can calculate a and b. If we then call si a generic stress level (with 1 \ i \ j, s1 is the lower overstress while sj is
the higher), we can find the intersection of the degradation trend with the threshold, getting a mean time to failure (MTTF) l(si ). Repeating the test on other similar items, always applying the same stress level, we obtain a collection of estimated lives for the stress level si . This, together with the other estimated sets of lives corresponding to the different overstresses l(s1 ), . . . , l(sj ), can be used in a data analysis procedure to get the useful life in normal use conditions. The result of an ADT analysis can be summarized in a graphical way showing the failure probability density function (PDF) for each level si and the deduced reliability functions for the design stress level.
Case study In this research, we were facing the problem of evaluating, in short times, the reliability performance of a new component of a washing machine during the warranty period, namely the first 2 years. The distinguishing feature of the new model was an higher load capability in the same space. This was obtained with a higher slenderness of the mechanical parts given by innovative composite materials. Former reliability studies were showing that the critical mechanical components were inside the oscillating group, consisting essentially of the drum and the basket. Such a system had historically required the higher technical service compared to other subassemblies of the washing machines. Since the new model was an evolution of the previous ones, it seemed natural that the oscillating group would still have been the main responsible for the appliance reliability. It was then decided to assess whether the ADT approach could be effective in evaluating the reliability of the oscillating unit, compared to traditional approaches. In order to evaluate the mechanical reliability of the system, it was decided to overstress it by a higher imbalance of the load in the drum. With this stress, the deformation of the drum would be amplified and it would get closer to the tub. At the same time, the bearings became hotter and the rotation shaft vibrated more. The company experts therefore suggested us three different parameters, which could be linked to the overall system mechanical degradation: the drum deformation, the bearing temperature and the vibrations of the rotation shaft. Threshold values were
4 available only for the first two, coming from a finite element method (FEM) analysis made by the design department. Since there was not any clear reason to discard any one of them, we decided to test them all. Planning the ADT in order to assess the reliability during the warranty period, we decided to test the washing machines for 500 cycles of 30 min each, corresponding to about 2 years of washes. To optimize the duration of the tests, the cycle was reduced to the only spinning step, where the biasing mechanism is more present. All the phases with no influence on the searched failure were therefore cut off. The duration of each washing cycle was so reduced from 1.5 h to 30 min. The wash program selected was the most widely chosen by consumers: 60 °C cotton wash.30 We chose a constant stress model where the degradation was measured by alternating overstress cycles with normal load ones. In fact, with the overstress applied during the measurement, we would have measured the elastic over-deformations and not only the deformation caused by the degradation process, while our focus was on measuring the permanent deformation of the oscillating unit. The sample consisted of 24 washing machines, divided into eight groups, subjected to three stress levels, all above the maximum imbalance of the drum permitted in normal use (400 g). The three levels of stress applied in the three runs were 650, 800 and 950 g. In order to perform the ADT, we chose the following measure points: three points for the deformation of the drum, assessed via the drum–tub distance (outer circumference, median and internal), two points for the temperatures (inner and outer bearing) and three points for the vibrations, one on each of the three axes (placed on the outer circumference of the shaft). The threshold values, as previously said, were available only for the drum–tub distance and the bearing temperature. They were deduced from a FEM analysis, while no threshold value was available for vibrations. The test was set to be time censoring, that is, it should stop either for a fault or upon reaching 500 cycles.
Proc IMechE Part O: J Risk and Reliability 0(0) In order not to measure the over-deformation caused by overstress, every 50 cycles, a measurement cycle was performed with the aim of measuring deformations and vibrations. It was carried out with a normal unbalance of 400 g, the maximum allowed by the washing machine controller. Such an approach permitted us to analyze the machine behavior in normal use conditions, however, after undergoing a process of ‘‘aging’’ due to the application of higher loads. On the contrary, temperature was monitored in real time. Four distance sensors were used to measure the drum–tub distance: three staggered and placed on the upper part of the tank and one positioned in the rear. The bearing temperature was continuously monitored, by averaging the values of two thermocouples. Vibrations were measured via three accelerometers, each of which indicated the value of the acceleration along its translation axis.
Results In this section, the main ADT results are shown. As a major premise, we must say that all the experimental data were altered in order not to reveal industrial secrets. Nevertheless, all the contents are still valid if seen from a methodological point of view.
Drum deformation The drum, during the rotation, undergoes a reversible deformation: from the initial cylindrical shape, it tends to flatten, for the centrifugal forces of the motion (see Figure 2). This phenomenon is emphasized as the unbalance increases. For this reason, the section of the drum becomes nearly an ellipse. The distortion amount changes along the side wall of the tub. Therefore, the drum–tub distance varies slightly depending on the axial section in which it is assessed. For this reason, it was decided to measure this distance in three different points.
Figure 2. Deformation of the drum of the washing machine. As the centrifugal force increases, the major axis grows and the minor axis decreases, favoring a reduction of the minimum distance between tub and drum and an increase of the maximum. The bold arrows on the left picture show the direction of deformations.
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Figure 3. Evolution of the degradation parameters for the drum–tub distance for one of the eight washing machines tested. The data shown come from a sensor positioned in the front part of the tub. The abscissa axes show the cycles. As is clearly visible, the maximal distance, the minimal distance and the MSE reveal an increasing trend. MSE: mean square error.
The calculation of the mean square error (MSE) is given in equation (3) vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ u N uP u 2 ti = 1 ðxi xÞ ð3Þ MSE = N The numerator is the sum of all the squared differences between the distance data—measured within a
5 centrifuge—and a reference value. The denominator is the number of available data. The reference distance chosen for the numerator was the average of the first 100 distance values during the first use of the washing machine. They were measured during the first operating cycle of the washing machine, when no deformation had yet begun. In Figure 3, drum deformation–related degradation patterns are shown for one of the measuring points of one of the eight washing machines tested. The measuring point shown is positioned in the front part and registered the highest values, compared to the values of the other channels. This is in agreement with the fact that in front of the oscillating group, the stresses are higher. Observing the data in the previous image, we note that when the deformation rises because of the stress, there is the simultaneous increase of the minimum and the maximum distance and of the MSE. The MSE was chosen as the deformation parameter, because it represents an overall measure of the deformation of the whole drum and not only the point of maximum or minimum of deformation. Considering all the test measurements, it was clear that, on average, the MSE trend was rising in conjunction with the number of cycles performed, which is consistent with the physical degradation phenomenon. In Figure 4, the degradation points for the tested washing machines are shown. Grouping the MSE trends of all the 24 washing machines tested
Figure 4. Drum–tub degradation. The graph shows the relationship between the mean square error and the time: on the abscissa, there are the cycles, and on the ordinate, the degradation parameter values (data have been protected for industrial privacy). The big horizontal line is the threshold of the MSE. The other lines show the parameter trends of each machine.
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Figure 5. MSE of the drum–tub distance. In the diagram, the trends of the MSE for the three stress levels of 650, 800 and 950 g, respectively, are shown for all the washing machines tested. MSE: mean square error.
by the three overstress levels, we got the tendencies, as shown in Figure 5.
Bearing temperature The temperature acquisition system permitted us to monitor and register values during all the cycles performed by the washing machines, and not only every 50 cycles, as in the previous case. The shape of the temperature during an usage cycle appears to be oscillatory. The degradation parameter chosen for the temperature was therefore the maximum value of a whole usage cycle. This is corresponding to the bearing temperature recorded during the centrifuge. The graph of the trends of the average values, for all the machine tested, is shown in Figure 6. Even in this case, we can note the consistency between the maximum temperature and the physical degradation phenomenon: the maximum value is proportional to the number of cycles. The higher the gradient of the straight line, the more accelerated is the mechanism of degradation.
Vibrations The vibrations of the oscillating unit are forced, since they are caused by the unbalanced load. The vibrational study considered the overall acceleration of the oscillating group, the acceleration along each one of the three axes and the rotation speed. All of these parameters have shown an oscillatory behavior, with maximum amplitudes during the centrifugal phase. The degradation parameter chosen for acceleration is the maximum effective value for each second (the effective value of an oscillating physical value is the magnitude that it would have in a continuous regime, for the same amount of time and for the same time). The expression of the effective value is the root mean square, as shown in equation (4) vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ u N uP 2 u xi t ð4Þ RMS = i = 1 N The measured accelerations vary according to the axis. Axis 2 is the oscillating group rotation axis, Axis 3
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Figure 6. Maximum temperature of the bearing. In the picture, the trends of the highest bearing temperature for the three stress levels of 650, 800 and 950 g, respectively, are shown.
Figure 7. Acceleration of the drum–tub. In the picture, the effective value of the acceleration of one of the machines tested during a wash cycle is shown. The three accelerations grow in steps up to the maximum value, which occurs precisely in the centrifuge.
is the vertical one while Axis 1 is normal to the previous two. The trend of the acceleration of each axis during a washing cycle is shown in Figure 7. The maximum effective value of Axis 3 acceleration was analyzed, and the resulting trends are shown in Figure 8. As can be seen from the displayed data, a correlation between the acceleration and the aging of the washing machine is not so clear. In addition, when the overstress increases, you do not note a clear corresponding growth in the effective value of the acceleration. Finally, many
measurements have not been completed due to technical problems. For all these reasons, the acceleration parameter was not further analyzed in this study.
Result analysis and discussion Aggregating the data of each stress level, it was possible to make a linear regression of the trends of the degradation parameter average values over time. In order to compare the geometrical deformation with the
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Figure 8. Vertical acceleration. In the picture, the average trend of the maximum vertical acceleration during every cycle is shown. As it can be noted from the picture, the trend does not reveal a clear relation to the overload.
temperature, it was decided to normalize the values of each test with the same overstress. Normalization was made dividing the outcomes by the initial value, leading to the results shown in Figure 9. Observing the resulting trends, it is clearly visible that in both cases, there is a correspondence between higher overloads and greater deformation. We can observe that the slopes are higher in the graph of the geometrical deformation. In the next sections, further consideration about the test outcomes will be presented.
Drum–tub distance The threshold value for the drum–tub MSE was confirmed during the testing activity. In fact, during a test, a ‘‘hard’’ failure in a washing machine oscillating group occurred. In such an occasion, just before the fault, the value of the mean square root of the drum–tub distance was only 8% below the threshold. It is very interesting to note the remarkable correspondence between the theoretical value, based on FEM analysis and the experimental one.
All MSE test values were inserted in the ALT software to perform the data analysis and to extract reliability information. First, soft failures were plotted on a Weibull probability chart in order to get the reliability curves for each stress level. Then, the three Weibull failure PDFs were used to infer the PDF in normal conditions. In Figure 10, the Weibull probability chart is shown. In this way, with the aid of commercial ADT software (ReliaSoft ALTA7), it was possible to identify a Weibull distribution with characteristic life a and shape factor b = 0.91 for the normal use (400 g of unbalance). This parameter indicates a typical decreasing failure rate (DFR) system, in which a better running-in phase should be accomplished. Once the probabilistic functions for normal load conditions are known, all reliability estimates could be made, starting from the reliability evaluation during the warranty period.
Bearing temperature The second parameter analyzed was the maximum temperature of the bearing. As already said, some
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Figure 9. Trend of normalized degradation parameters. The diagram shows the trends of the MSE of the drum–tub distance and the maximum temperature of the bearing. The values are normalized to their initial value, in order to compare them on the same scale. MSE: mean square error.
Figure 10. Weibull probability chart. In the picture, the Weibull probability chart of soft failures is shown, in the three different conditions of accelerated stress. The linear regression is possible when in the abscissa, the logarithm of the (soft) time to failure is plotted, and in vertical axis, the following function is applied: ln[ln 1/(1 2F(t))], where F(t) is the experimental unreliability function.
relationship between the overload and the aging phenomenon of the oscillating group was manifest. In fact, degradation caused by the imbalance implicated an increase in the temperature of the bearing. The ALT analysis produced the results visible in Figure 11.
ALT approach lets us infer the reliability functions in normal load conditions: the failure PDF determined was a Weibull function with a well-determined characteristic life and a shape factor b = 1:80. This denotes an increasing failure rate (IFR) over time due to aging.
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Figure 11. Failure probability density functions (PDFs). In the diagram, the experimental PDFs for each stress level are shown. The points are the soft failures obtained from the intersection of the average temperature trends with the threshold level (derived from finite element method (FEM) analysis).
As for the drum–tub deformation, we could calculate the reliability values after 500 and 1250 cycles. These values were lower than those previously obtained. A strong reduction of the MTTF was also observed in temperature-based evaluations, when compared to the results gained from the drum–tub distance. A possible explanation of such differences may reside in the fact that the threshold value for the temperature, obtained with FEM analysis, was very low, around 60°. This limit level could be not correct and a proof of this was that during the tests, it was reached and passed a few times but no damage occurred. A threshold adjustment could not be done because no historical reliability information were available for the new equipment.
Conclusion The purpose of this study was to evaluate the applicability of ADTs to a new mechanical subassembly of a washing machine, in order to verify the possibility of quickly obtaining reliability information on a new and innovative model. We had three possible alternative degradation parameters and we had tried to identify which was the most appropriate. The three parameters were the drum deformation, the bearing temperature and the vibrations of the rotation shaft. The last one was the first to be discarded because we could not
observe a sharp correlation between the vibrations and the aging of the washing machine. Furthermore, an intensification of the overstress did not result in a welldefined consequent growth of the acceleration effective value. The bearing temperature could have been a good ADT parameter but the threshold defined was probably too low. A threshold adjustment could not be made because no historical reliability information was available. Accordingly, the research allowed the identification of the MSE of the drum–tub distance as the most appropriate deformation parameter for the reliability estimation of the oscillating unit. The goodness of the threshold derived from a FEM model was confirmed by a hard failure in which it was possible to find a MSE very close to the upper limit value. Finally, it should be emphasized that the execution of the measuring cycles under conditions of maximal user load permitted us to analyze the new models of washing machines after a period of overstress. The washing machines appeared artificially aged, and this made it possible to identify in advance their weak points before putting them on the market. The company, as a consequence of the analysis, considered the idea of redesigning some of the new components which resulted weaker than expected and some others which showed some weaknesses during ALT execution.
De Carlo et al. The main advantages of the procedure proposed here are the possibility to compare the different predictions and, where appropriate, to choose the most conservative. On the contrary, the main drawback is the need to increase the effort required in the design phase and during the implementation of the sensors on the hardware. In conclusion, ADT is confirmed to be an excellent technique for evaluating reliability performance of new systems, even in an area in which its application is not so frequent. Future research will try to improve thermal characterization of the composite material of the drum in order to improve the FEM model. In such a way, it would be possible to walk two parallel paths for the accelerated determination of the oscillating group reliability, and this would give greater confidence to the inferences of the technique. Since this new ADT approach seems to be promising, the authors are willing to apply it to some other areas in which they are working, such as the quick determination of reliability of Formula 1Ò engines and the reliability assessment of assembly line robots. Declaration of conflicting interests The authors declare that there is no conflict of interest. Funding This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors. References 1. Meeker WQ and Shi Y. Planning accelerated destructive degradation test with competing risks. In: Shi Y (ed.) Contributions to accelerated destructive degradation test planning. Ames, IA: Iowa State University, 2010, pp.36–56. 2. Pawar KS, Menon U and Riedel JCKH. Time to market. Integrated Manuf Syst 1994; 5(1): 14–22. 3. De Carlo F, Borgia O, Tucci M, et al. A rule based expert system for maintenance as a competitive advantage. In: Proceedings of the annual reliability and maintainability symposium, Fort Worth, TX, 26–29 January 2009, pp.448–453. New York: IEEE. 4. Borgia O, De Carlo F, Peccianti M, et al. The use of dynamic object oriented Bayesian networks in reliability assessment: a case study. In: Cigolini RD, Desmuhk AV, Fedele L, et al. (eds) Recent advances in maintenance and infrastructure management. London: Springer-Verlag, 2009, pp.153–170. 5. Racioppi G, Monaci G, Michelassi C, et al. Availability assessment for a gas plant. Petrol Tech Q 2008; 13(Suppl. 2): 33–37. 6. De Carlo F, Borgia O and Tucci M. Risk-based inspections enhanced with Bayesian networks. Proc IMechE, Part O: J Risk and Reliability 2011; 225(3): 375–386. 7. Liao C-M and Tseng S-T. Optimal design for step-stress accelerated degradation tests. IEEE T Reliab 2006; 55(1): 59–66.
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