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Research Papers

Comparison of Prognostic Health Management Algorithms for Assessment of Electronic Interconnect Reliability Under Vibration OPEN ACCESS

[+] Author and Article Information
Pradeep Lall

Auburn University,
NSF-CAVE3 Electronics Research Center,
Auburn, AL 36849

Ryan Lowe

Air Force Research Laboratory,
Eglin, FL 32542

Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received January 1, 2014; final manuscript received July 31, 2014; published online September 19, 2014. Assoc. Editor: Y. C. Lee.

J. Electron. Packag 136(4), 041013 (Sep 19, 2014) (8 pages) Paper No: EP-14-1004; doi: 10.1115/1.4028163 History: Received January 01, 2014; Revised July 31, 2014

This paper compares three prognostic algorithms applied to the same data recorded during the failure of a solder joint in ball grid array component attached to a printed circuit board. The objective is to expand on the relative strengths and weaknesses of each proposed algorithm. Emphasis will be placed on highlighting differences in underlying assumptions required for each algorithm, details of remaining useful life calculations, and methods of uncertainty quantification. Metrics tailored specifically for prognostic health monitoring (PHM) are presented to characterize the performance of predictions. The relative merits of PHM algorithms based on a Kalman filter, extended Kalman filter, and a particle filter all demonstrated on the same data set will be discussed. The paper concludes by discussing which algorithm performs best given the information available about the system being monitored.

Previously a measurement technique known as resistance spectroscopy (RS) [1-4] has been demonstrated to effectively provide advanced warning of failure in electronics as they are subjected to a variety of harsh environments such as drop/shock [5], vibration [6], and simultaneous vibration and temperature [7]. The techniques ability to quantify damage prior to failure in a solder joint allows insight into the health of components attached to a circuit board to be monitored and mitigating action to be planned in the event of an impending failure. While crucial to PHM for electronics, the data measured by the RS technique are inherently noisy due to the dynamic environment that electronics systems operate in. Prognostic algorithms process the noisy data and forecast the expected time of failure of the device under test. It is convenient to assign a name to an algorithm based on a distinguishing feature of the algorithm. For prognostic algorithms based on recursive filters, typically the algorithm is named by the tracking part of the algorithm. But it is important to note that tracking is only half of the PHM algorithm, model based forecasting techniques use smoothed estimates of noisy data from the tracking algorithm to predict failures.

The first method described is based on a Kalman filter [8-10], which is a widely used tracking algorithm. The Kalman filter assumes a system of ordinary differential equations can be used to model the system being tracked and that noise in both the model and measurement system is Gaussian in nature. In this paper, the tracking is applied to damage of electronics. The extended Kalman filter [11] allows nonlinear differential equations to be used to describe the system being tracked. Lastly, the particle filter [12-15] is a generalization of both the Kalman and extended Kalman filters and is completely general. Any manner of nonlinear equation can be implemented in the particle filter with any arbitrary contribution of non-Gaussian noise. The particle filter is considered state of the art in nonlinear filtering, but is also the most complicated. In Secs. 4–6, PHM algorithms based on each of the filters will be described and their results quantified. The paper will conclude by comparing the merits of the three algorithms and providing guidance for choosing the best algorithm based on the available information.

A set of test boards with multiple package architectures were used for experimental measurements. The test board includes package architectures such as plastic ball-grid arrays, chip-array ball-grid arrays, tape-array ball-grid arrays, and flex-substrate ball-grid arrays. The experimental matrix has ball counts in the range of 64–676 input–output, pitch sizes are in the range of 0.5 mm–1 mm, and package sizes are in the range of 6 mm–27 mm. The package parameters of this board are shown in Table 1. Representative sample of the test board is shown in Fig. 1.

The test assemblies were subjected to vibration testing on a LDS Model V722 vibration table. A step stress profile was used to gradually ramp up the stress level to induce damage (Fig. 2). The individual random stress profiles used in the step stress are shown in Fig. 3. Section 2.1 will discuss how the transient response of a package during random vibration testing was monitored for a leading indicators of failure.

Relating Damage to Resistance.

The daisy chained resistance of a package was used as a leading indicator of failure. The observed history of the resistance of the package during vibration testing is shown in Fig. 4. At approximately 5.8 h the package experiences its first intermittent open event. In the following plots large resistance values have been truncated for clarity. The resistance of an open event of 300 Ω or more makes it difficult to discuss milli-ohm changes on a plot. Additional details quantifying the applicability of the measurement system for capturing intermittent events in advance of the traditional definition of failure can be found in Refs. [3-6]. The failure criteria for resistance change outlined in industry standards JESD22-B103 (JEDEC 2006) and IPCSM785 (IPC 1992) for the number, duration, and severity of intermittent events is used as the definition of failure. It should be noted that the smaller step increases of 0.05 Ω during the first 90 min of the test are experimental noise which can be reproduced by motion of the system connections during shock and vibration. Resistance data 2 h after the initiation of the test till failure has been studied for the construction of a feature vector for identification of impending failure. A subset of the resistance data has been used since field data will often involve electronic assemblies with accrued damage and not involve pristine assemblies. Figure 5 shows a zoomed view of the input data highlighting the experimental noise between two hours and failure. The experimental noise is due in part to the challenges with overcoming the variance in contact resistance in the presence of transient dynamic motion in shock or steady-state vibration. Step changes in the resistance data can be seen at 2.8 and 4.9 h, respectively. However, the distinctive increase of about 25 mΩ during the vibration test is easily discernible even in the presence of experimental noise. The change in resistance is attributed to change in geometry, since the resistivity of the solder interconnect is expected to stay constant. Since the material properties and geometry of a solder ball are nonlinear, a finite element method was used to map the change in resistance of an interconnect to the state of plastic strain that the interconnect was feeling [3-6]. Ultimately a failure threshold of 3.125 Ω was established.

The RS technique provides the experimental foundation for the work presented in this document. Essentially the technique is a very narrow band pass filter, but is implemented in an unexpected manner compared to traditional noise filters. The ability of the filter to reject noise at frequencies not related to the signal makes the technique very robust. Application of the RS method is described in extensive detail in Refs. [3-6]. The RS method for prognostics has been applied to a variety of interconnect alloys ([3-6]: SAC305, SnPb, and HiPb), interconnect geometries (copper columns [3-6], HiPb columns/microcoils [16]), and Molex computer connectors [17]. In this paper, the system being studied is SAC305 ball grid array interconnects.

For the Kalman filter based algorithm the resistance of the solder joint, measured using spectroscopy, was assumed to most closely be described by a quadratic model. Based on this assumption the system of equations relating the resistance, R, to its derivatives, R· and R·· is shown in Eq. (1). This equation also allows the prorogation of the system forward by time step Ts. The index K represents the state of the system at the current time step, while K − 1 represents the state of the system at the previous time step.Display Formula

(1){RR·R··}K=[1Ts0.5Ts201Ts001]{RR·R··}K-1=Rk-1+R·k-1Ts+0.5R··k-1Ts2R·k-1+R··k-1TsR··k-1

The second derivative of a quadratic system is a constant, which is represented by the relationship R··K=R··K-1. There are two free parameters in the Kalman filter which affect the importance given to measured data and the system model. The first free parameter, the measurement noise term, is set by estimating the amount of noise in the experimental setup before testing starts. The second parameter, the process noise term, is related to the belief that the system model is accurate. Based on observations and experience the parameters were, respectively, set to 5 × 10−5 Ω and 1 × 10−9 Ω.

To forecast remaining useful life in the electronics being monitored it is necessary to use the Kalman filter to estimate the state of the system, and then using the model defined in Eq. (1) forecast when the system will propagate to the failure threshold, Rf. Using the failure threshold as the final state of the system allows calculation of the remaining useful life as below:Display Formula

(2)Rf=Rk+R·ktRUL+0.5R··ktRUL2

The uncertainty of each prediction was quantified using the posterior error covariance estimated by the Kalman filter. As an engineering approximation the uncertainty is calculated using a straight line approximation. Then, the uncertainty from the linear approximation is superimposed on the failure prediction obtained from Eq. (2). This is a trade off in accuracy, for the benefit of algorithm simplicity. Assuming that the feature vector and its first derivative are normal random variables (Gaussian), then a straight line approximation of the time to failure can beDisplay Formula

(3)tRUL=Rf-RKR·K

where tRUL is the time to failure, Rf is the failure threshold, RK is the estimated state of the system (resistance), and R·K is the estimate of the first derivative. The numerator will have a variance equal to the variance of the position estimate, which is directly available in the posterior error covariance matrix as P(1,1). The denominator will have a variance equal to the variance of the first derivative estimate, directly available as P(2,2). IfDisplay Formula

(4)σF2=P(1,1)
Display Formula
(5)σR2=P(2,2)

then it is demonstrated in Ref. [10] that the non-Gaussian distribution resulting from the ratio of two normal distributions with variances of σF2 and σR2 can be integrated to find the equivalent 68.4% probability range around the mean.Display Formula

(6)σRUL=1.86σFσR

The mean of the distribution from the straight line approximation is disregarded since better methods are available to solve for the predicted RUL. The uncertainty estimate around the RUL prediction includes a number of simplifying assumptions about the nature of the system and should only be taken as a rough estimate.

The Kalman filter based PHM algorithm is a combination of a tracking filter defined by Eq. (1), a prediction of remaining useful life in Eq. (2), and an uncertainty prediction from Eq. (6). The next set of figures show three prediction snapshots from the Kalman filter based PHM algorithm. In each figure the top section shows the information that was available at the time the prediction was made. The lower section shows a superposition of the prediction on top of the full data set (Figs. 6–8). Only because we are simulating our ability to predict failure based on previously recorded data can we show the lower plot as a reference to the reader. In practice the lower plot is not available. Three snapshots are shown, but remaining useful life was predicted after each new data point was processed. In practice the recursive nature of the Kalman filter based algorithm would be beneficial due to its ease of implementation and low computational overhead. At no point would the full time history of recorded data need to be stored.

Using PHM metrics (Figs. 9–11) which are specifically designed to quantify accuracy and precision of predictions [18] a quantitative description of results can be determined. The alpha lambda plot is a summary of all of the predictions and the associated uncertainty. The beta metric is a measure of precision, and relative accuracy is an accuracy metric that is more sensitive to errors closer to the actual failure. In the plots the pink shaded region is a goal region for the predictions and represents ±20% of the actual remaining useful life. Using results from the beta metric and relative accuracy metric a single number can be used to quantify the overall performance of the predictions. A cost function, defined in Refs. [11,14], is a weighted average of the beta metric and relative accuracy metric for each prediction step. In this implementation the cost function was evaluated as 0.843. A perfect score on the cost metric is zero, and the worst possible score is one.

For the extended Kalman filter based algorithm the resistance of the solder joint, measured using RS, was assumed to most closely be described by an exponential model. Based on this assumption the system of equations relating the resistance, R, to its derivatives, R· and R·· is shown in the following equations. The model parameter b is also estimated inside the filter which is known as online parameter estimation or model adaption.Display Formula

(7)R=ebt
Display Formula
(8)R·=bebt
Display Formula
(9)R··=b2ebt
Display Formula
(10)R·K=R·K-1+R··K-1Ts
Display Formula
(11)RK=RK-1+R·K-1Ts

Exponential term “b” can be adapted to more efficiently represent the underlying process that is damaging the electronics. When using nonlinear equations there is no longer convenient closed form methods for propagating system states into the future to determine remaining useful life as there was with Eq. (2) for the Kalman filter algorithm. Repeated applications of Euler integration is implemented using Eqs. (10) and (11) until the resistance of the package under test is predicted to break the failure threshold. The length of the time step used for the prediction was set at 0.01 h, where the error due to linearization is expected to be about 1% per step. Unfortunately choosing noise terms with the extended Kalman filter requires more experience with the data set. In this implementation artificial noise was added to the filter to improve performance. This approach is commonly used when designing filters for practical applications to achieve smoother state estimates [10]. The process noise and measurement noise was both set as 1 × 10−3 Ω for the extended Kalman filter implementation. The “b” term is initialized as a value of 0.9.

The extended Kalman filter based PHM algorithm is a combination of a tracking filter with a system model defined by Eqs. (7)–(9). Remaining useful life predictions are calculated with the repeated application of Eqs. (10) and (11). Prediction uncertainty is quantified in the same manner as the Kalman filter using Eq. (6). Prediction snapshots are shown in Figs. 12–14; 15–17 and can be compared to Figs. 6–8; 9–11. Three snapshots are shown, but remaining useful life was predicted after each new data point was processed. In practice the recursive nature of the extended Kalman filter based algorithm would be beneficial due to its ease of implementation and low computational overhead. The model adaption capability of this implementation is expected to make the algorithm robust to changing loads and stresses. The ability to implement system models with nonlinear equations makes incorporating physically realistic models into the algorithm easier. PHM metrics for the extended Kalman filter implementation demonstrate that the implementation converges quicker, and is both more accurate and precise than the regular Kalman filter algorithm. The cost function summarizing the total performance of the algorithm is significantly better with a value of 0.520.

The same system dynamics are assumed for the particle filter based PHM algorithm as is used in the extended Kalman filter. Online parameter estimation is also performed in the particle filter, but using different methods than the extended Kalman filter. In the particle filter, an initial distribution is assumed for the “b” parameter and allowed to randomly walk during tracking [12]. The random walk method of model adaption is the simplest approach known to the authors. The reader is directed to [19] for a detailed discussion of different approaches for adapting model terms in the particle filtering framework (Figs. 18–20).

Euler integration is also used to propagate system states forward in time in the particle filter, but there is the addition of noise terms that slightly alter predictions using small levels of random noise. For example the resistance of the package is propagated forward in time using a relationship similar to Eq. (10), with the addition of a noise term. The noise is assumed to be Gaussian in nature and is centered around zero. The standard deviation of the added noise is denoted as w1. The additive noise is roughly analogous to the process noise in the Kalman family of filters [20].Display Formula

(12)RK=RK-1+R·K-1Ts+N(0,w1)

As described in Ref. [14] the particle filter estimates the state of a system using a series of discrete particles that approximate a probability distribution. The significance of each weight associated with an individual particle is updated after each measurement. In this implementation a Gaussian kernel is utilized for the weight update step.Display Formula

(13)f(x)=1w22πexp(-(RKi-zk)22w22)

The Gaussian kernel shown in Eq. (12) has a mean value centered at the most recent noisy measurement of the system. The estimated position of particle i at time step K is denoted as RKi. The standard deviation of the kernel is denoted as noise term w2.The standard deviation of the Gaussian kernel is analogous to the measurement noise term in the Kalman family of filters. When the estimated state of the system and the measured state of the system are relatively close to each other the Gaussian kernel is a larger value. When the state estimate and measurement differ significantly, the Gaussian kernel is a smaller value. In this implementation the process noise like term was set as 2 × 10−2 and the noise term similar to measurement noise was set as 3 × 10−4. The particle population was set as 30 particles. The particle filter based PHM algorithm is a combination of a tracking filter with a system model defined by Eqs. (7)–(9). Remaining useful life predictions are calculated with the repeated application of Eq. (12) for each separate particle representing the state of the system. In effect the prediction step becomes similar to a Monte Carlo simulation. Prediction uncertainty is quantified based on the predicted distribution generated during the RUL calculation. Unlike with the Kalman filters the resulting RUL prediction distribution is almost always non-Gaussian in nature. Prediction snapshots are shown in Figs. 18–20 and can be compared to Figs. 12–14 and Figs. 6–8. Three snapshots are shown, but remaining useful life was predicted after each new data point was processed. In practice the recursive nature of the particle filter based algorithm would be beneficial, but unlike the Kalman family of filters implementation is more difficult and in some cases computation overhead could be a burden depending on the situation.

The model adaption capability of this implementation is expected to make the algorithm robust to changing loads and stresses, but due to the inherent randomness in the algorithm results may vary. The ability to implement system models with any manner of nonlinearity makes the filter a powerful choice for representing physical phenomena. PHM metrics for the particle filter implementation demonstrate that the implementation converges quicker, and is both more accurate and precise than the regular Kalman filter algorithm (Figs. 21–24). The cost function summarizing the total performance of the algorithm is the best reported in this paper with a value of 0.263 (Fig. 25).

The performance of three PHM algorithms based on the Kalman filter, extended Kalman filter, and particle filter have been demonstrated on the same data set. Differences in the quadratic model used in the Kalman filter, and the exponential model used in the extended Kalman filter and particle filter have been highlighted. Differences in the remaining useful life prediction portion of the algorithms have also been discussed. The Kalman family of filters uses a rough approximation to quantify prediction uncertainty, while the particle filter has a robust method for representing uncertainty as a generic probability distribution. The repeatability of the particle filter with the implementation in this paper was shown to have some variability, but also was capable of the best performance. The extended Kalman filters use of nonlinear models and model adaption gives it better performance than the simpler regular Kalman filter. The tradeoff between computation burden and performance is summarized in Table 2. In summary no filter implementation is better than another, but rather the best choice of filter depends on the specifics of your application domain. The availability of run to failure data and high resolution failure models is an important criterion for selecting the best implementation. A large number of filtering and PHM algorithms exist, some with names that may be ambiguous as to the details of the algorithm, and two practitioners implementation are not necessarily identical. Without a set of baseline validation data sets like those used in machine learning or hurricane forecasting it is difficult to quantify the absolute performance between PHM algorithms.

The research presented in this paper have been supported by NSF-FRS-1127913 and members of NSF-CAVE3 Electronics Research Center.

Constable, J., and Lizzul, C., 1995, “An Investigation of Solder Joint Fatigue Using Electrical Resistance Spectroscopy,” IEEE Trans. Comp. Packag. Manuf. Technol., 18(1), pp. 142–152. [CrossRef]
Constable, J., 1994, “Use of Interconnect Resistance as a Reliability Tool,” Electronic Components and Technology Conference, 44th Electronic Components and Technology Conference, Washington, DC, May, 1–4, pp. 450–457. [CrossRef]
Lall, P., Lowe, R., and Goebel, K., 2009, “Resistance Spectroscopy-Based Condition Monitoring for Prognostication of High Reliability Electronics Under Shock-Impact,” 59th Electronic Components and Technology Conference (ECTC 2009), San Diego, CA, May 26–29, pp. 1245–1255. [CrossRef]
Lall, P., Lowe, R., and Suhling, J., 2009, “Prognostication Based on Resistance-Spectroscopy for High Reliability Electronics Under Shock-Impact,” ASME Paper No. IMECE2009-13351. [CrossRef]
Lall, P., Lowe, R., Goebel, K., and Suhling, J., 2009, “Leading-Indicators Based on Impedance Spectroscopy for Prognostication of Electronics Under Shock and Vibration Loads,” ASME InterPACK Conference, San Francisco, CA, Jul. 19–23, pp. 1–12. [CrossRef] [CrossRef]
Lall, P., Lowe, R., Goebel, K., and Suhling, J., 2009, “Prognostication for Impending Failure in Leadfree Electronics Subjected to Shock and Vibration Using Resistance Spectroscopy,” International Symposium on Microelectronics (IMAPS), San Jose, CA, Nov. 1–5, pp. 195–202.
Lall, P., Lowe, R., and Goebel, K., 2012, “Prognostication of Accrued Damage in Board Assemblies Under Thermal and Mechanical Stresses,” IEEE Electronic Components and Technology Conference (ECTC), San Diego, CA, May 29–June 1, pp. 1475–1487. [CrossRef]
Lall, P., Lowe, R., and Goebel, K., 2010, “Prognostics Using Kalman-Filter Models and Metrics for Risk Assessment in BGAs Under Shock and Vibration Loads,” 60th Electronic Components and Technology Conference (ECTC), Las Vegas, NV, June 1–4, pp. 889–901. [CrossRef]
Lall, P., Lowe, R., and Goebel, K., 2010, “Use of Prognostics in Risk-Based Decision Making for BGAs Under Shock and Vibration Loads,” Thermal and Thermomechanical Phenomena in Electronics Systems (ITherm), Las Vegas, NV, June 2–5. [CrossRef]
Swanson, D., 2001, “A General Prognostic Tracking Algorithm for Predictive Maintenance,” IEEE Aerospace Conference, Big Sky, MT, Mar. 10–17, Vol. 6, pp. 2971–2977. [CrossRef]
Lall, P., Lowe, R., and Goebel, K., 2012, “Extended Kalman Filter Models and Resistance Spectroscopy for Prognostication and Health Monitoring of Leadfree Electronics Under Vibration,” IEEE Trans. Reliability, 61(4), pp. 858–871. [CrossRef]
Daigle, M., and Goebel, K., 2009, “Model-Based Prognostics With Fixed-Lag Particle Filters,” Annual Conference of the Prognostics and Health Management Society, San Diego, CA, Sept. 27–Oct. 1, Paper No. 37, available at: [CrossRef]
Goebel, K., Saha, B., Saxena, A., Celaya, J., and Christophersen, J., 2008, “Prognostics in Battery Health Management,” IEEE Instrum. Meas. Mag., 11(4), pp. 33–40. [CrossRef]
Lall, P., Lowe, R., and Goebel, K., 2011, “Particle Filter Models and Phase Sensitive Detection for Prognostication and Health Monitoring of Leadfree Electronics Under Shock and Vibration,” IEEE 61st Electronic Components and Technology Conference (ECTC), Lake Buena Vista, FL, May 31–June 3, pp. 1097–1109. [CrossRef]
Orchard, M., and Vachtsevanos, G., 2009, “A Particle-Filtering Approach for On-Line Fault Diagnosis and Failure Prognosis,” Trans. Inst. Meas. Control, 31(3–4), pp. 221–246. [CrossRef]
Pradeep, L., Kewal, P., Ryan, L., Mark, S., Jim, B., Dave, G., and Randall, M., 2012, “Modeling and Reliability Characterization of Area-Array Electronics Subjected to High-G Mechanical Shock Up to 50,000g,” IEEE 62nd Electronic Components and Technology Conference (ECTC), San Diego, CA, May 29–June 1, pp. 1194–1204. [CrossRef]
Lall, P., Sakalaukus, P., Lowe, R., and Goebel, K., 2012, “Leading Indicators for Prognostic Health Management of Electrical Connectors Subjected to Random Vibration,” 13th IEEEE Thermal and Thermomechanical Phenomena in Electronics Systems (ITherm), San Diego, CA, May 30–June 1, pp. 632–638. [CrossRef]
Saxena, A., Celaya, J., Saha, B., Saha, S., and Goebel, K., 2009, “On Applying the Prognostics Performance Metrics,” Annual Conference of the Prognostics and Health Management Society, San Diego, CA, Sept. 27–Oct. 1, Paper No. 39, available at: http://www.phmsociety.org/node/150
Saha, B., and Goebel, K., 2011, “Model Adaptation for Prognostics in a Particle Filtering Framework,” Int. J. Prog. Health Manage., 2(1), p. 006, available at: http://www.phmsociety.org/node/385
Zarchan, P., and Musoff, H., 2005, Fundamentals of Kalman Filtering: A Practical Approach (Astronautics and Aeronautics), 2nd ed., American Institute of Aeronautics and Astronautics, Reston, VA.
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References

Constable, J., and Lizzul, C., 1995, “An Investigation of Solder Joint Fatigue Using Electrical Resistance Spectroscopy,” IEEE Trans. Comp. Packag. Manuf. Technol., 18(1), pp. 142–152. [CrossRef]
Constable, J., 1994, “Use of Interconnect Resistance as a Reliability Tool,” Electronic Components and Technology Conference, 44th Electronic Components and Technology Conference, Washington, DC, May, 1–4, pp. 450–457. [CrossRef]
Lall, P., Lowe, R., and Goebel, K., 2009, “Resistance Spectroscopy-Based Condition Monitoring for Prognostication of High Reliability Electronics Under Shock-Impact,” 59th Electronic Components and Technology Conference (ECTC 2009), San Diego, CA, May 26–29, pp. 1245–1255. [CrossRef]
Lall, P., Lowe, R., and Suhling, J., 2009, “Prognostication Based on Resistance-Spectroscopy for High Reliability Electronics Under Shock-Impact,” ASME Paper No. IMECE2009-13351. [CrossRef]
Lall, P., Lowe, R., Goebel, K., and Suhling, J., 2009, “Leading-Indicators Based on Impedance Spectroscopy for Prognostication of Electronics Under Shock and Vibration Loads,” ASME InterPACK Conference, San Francisco, CA, Jul. 19–23, pp. 1–12. [CrossRef] [CrossRef]
Lall, P., Lowe, R., Goebel, K., and Suhling, J., 2009, “Prognostication for Impending Failure in Leadfree Electronics Subjected to Shock and Vibration Using Resistance Spectroscopy,” International Symposium on Microelectronics (IMAPS), San Jose, CA, Nov. 1–5, pp. 195–202.
Lall, P., Lowe, R., and Goebel, K., 2012, “Prognostication of Accrued Damage in Board Assemblies Under Thermal and Mechanical Stresses,” IEEE Electronic Components and Technology Conference (ECTC), San Diego, CA, May 29–June 1, pp. 1475–1487. [CrossRef]
Lall, P., Lowe, R., and Goebel, K., 2010, “Prognostics Using Kalman-Filter Models and Metrics for Risk Assessment in BGAs Under Shock and Vibration Loads,” 60th Electronic Components and Technology Conference (ECTC), Las Vegas, NV, June 1–4, pp. 889–901. [CrossRef]
Lall, P., Lowe, R., and Goebel, K., 2010, “Use of Prognostics in Risk-Based Decision Making for BGAs Under Shock and Vibration Loads,” Thermal and Thermomechanical Phenomena in Electronics Systems (ITherm), Las Vegas, NV, June 2–5. [CrossRef]
Swanson, D., 2001, “A General Prognostic Tracking Algorithm for Predictive Maintenance,” IEEE Aerospace Conference, Big Sky, MT, Mar. 10–17, Vol. 6, pp. 2971–2977. [CrossRef]
Lall, P., Lowe, R., and Goebel, K., 2012, “Extended Kalman Filter Models and Resistance Spectroscopy for Prognostication and Health Monitoring of Leadfree Electronics Under Vibration,” IEEE Trans. Reliability, 61(4), pp. 858–871. [CrossRef]
Daigle, M., and Goebel, K., 2009, “Model-Based Prognostics With Fixed-Lag Particle Filters,” Annual Conference of the Prognostics and Health Management Society, San Diego, CA, Sept. 27–Oct. 1, Paper No. 37, available at: [CrossRef]
Goebel, K., Saha, B., Saxena, A., Celaya, J., and Christophersen, J., 2008, “Prognostics in Battery Health Management,” IEEE Instrum. Meas. Mag., 11(4), pp. 33–40. [CrossRef]
Lall, P., Lowe, R., and Goebel, K., 2011, “Particle Filter Models and Phase Sensitive Detection for Prognostication and Health Monitoring of Leadfree Electronics Under Shock and Vibration,” IEEE 61st Electronic Components and Technology Conference (ECTC), Lake Buena Vista, FL, May 31–June 3, pp. 1097–1109. [CrossRef]
Orchard, M., and Vachtsevanos, G., 2009, “A Particle-Filtering Approach for On-Line Fault Diagnosis and Failure Prognosis,” Trans. Inst. Meas. Control, 31(3–4), pp. 221–246. [CrossRef]
Pradeep, L., Kewal, P., Ryan, L., Mark, S., Jim, B., Dave, G., and Randall, M., 2012, “Modeling and Reliability Characterization of Area-Array Electronics Subjected to High-G Mechanical Shock Up to 50,000g,” IEEE 62nd Electronic Components and Technology Conference (ECTC), San Diego, CA, May 29–June 1, pp. 1194–1204. [CrossRef]
Lall, P., Sakalaukus, P., Lowe, R., and Goebel, K., 2012, “Leading Indicators for Prognostic Health Management of Electrical Connectors Subjected to Random Vibration,” 13th IEEEE Thermal and Thermomechanical Phenomena in Electronics Systems (ITherm), San Diego, CA, May 30–June 1, pp. 632–638. [CrossRef]
Saxena, A., Celaya, J., Saha, B., Saha, S., and Goebel, K., 2009, “On Applying the Prognostics Performance Metrics,” Annual Conference of the Prognostics and Health Management Society, San Diego, CA, Sept. 27–Oct. 1, Paper No. 39, available at: http://www.phmsociety.org/node/150
Saha, B., and Goebel, K., 2011, “Model Adaptation for Prognostics in a Particle Filtering Framework,” Int. J. Prog. Health Manage., 2(1), p. 006, available at: http://www.phmsociety.org/node/385
Zarchan, P., and Musoff, H., 2005, Fundamentals of Kalman Filtering: A Practical Approach (Astronautics and Aeronautics), 2nd ed., American Institute of Aeronautics and Astronautics, Reston, VA.

Figures

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Fig. 2

Step stress profile for vibration testing that fatigues interconnects to failure

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Fig. 3

Random vibration profile at varying g levels corresponding to the step stress profile outlined in Fig. 2

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Fig. 4

Raw resistance data. The data used as an input data vector are shown in the brackets.

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Fig. 5

Zoomed view of resistance data between 2 h and failure

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Fig. 6

Prediction snapshot at 3.75 h into the test. At this point there has not been sufficient trend for the Kalman filter based PHM algorithm to converge.

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Fig. 7

Prediction snapshot at 4.25 h into the test. With more data available the Kalman filter based PHM algorithm prediction is better.

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Fig. 8

Prediction snapshot near the end of the test. It is particularly evident that the quadratic model is a poor description of the underlying process at this final stage of the components life.

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Fig. 9

Alpha–Lamb metric for the Kalman filter based PHM algorithm summarizing all predictions and the uncertainty in the predictions

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Fig. 10

Beta metric quantifying precision. In general the predictions were both not accurate or precise which is demonstrated in this result.

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Fig. 11

Relative accuracy metric quantifying the performance of the Kalman filter based PHM algorithm

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Fig. 12

Prediction snapshot at 3.75 h into the test using the extended Kalman filter based PHM algorithm. This result is much better than the regular Kalman filter prediction shown in Fig. 6.

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Fig. 13

Prediction snapshot at 4.25 h into the test using the extended Kalman filter based PHM algorithm

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Fig. 14

Prediction snapshot at 5.5 h into the test using the extended Kalman filter based PHM algorithm

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Fig. 15

Alpha–Lamb metric for the extended Kalman filter based PHM algorithm summarizing all predictions and the uncertainty in the predictions

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Fig. 16

Beta metric quantifying precision for the extended Kalman filter based PHM algorithm

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Fig. 17

Relative accuracy metric quantifying the performance of the extended Kalman filter based PHM algorithm

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Fig. 18

Prediction snapshot at 3.75 h into the test using the particle filter based PHM algorithm. This result is much better than the regular Kalman filter prediction shown in Fig. 12 and the method of uncertainty quantification is an improvement over Fig. 6.

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Fig. 19

Prediction snapshot at 4.25 h into the test using the particle filter based PHM algorithm

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Fig. 20

Prediction snapshot at 5.5 h into the test using the particle filter based PHM algorithm

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Fig. 21

Alpha–Lamb metric for the particle filter based PHM algorithm summarizing all predictions and the uncertainty in the predictions

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Fig. 22

Beta metric quantifying precision for the particle filter based PHM algorithm

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Fig. 23

Relative accuracy metric quantifying the performance of the particle filter based PHM algorithm

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Fig. 24

Failure prediction distributions from the particle filter PHM algorithm. Darker lines represent predictions closer to the end of the test.

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Fig. 25

Due to the variable nature of the particle filter implementation the performance of the algorithm can vary significantly. This histogram shows the results of 30 runs of the algorithm on the same data set.

Tables

Table Grahic Jump Location
Table 1 Package architectures on test boarda
Table Footer NoteaPBGA = plastic ball grid array; NSMD = nonsolder mask defined.
Table Grahic Jump Location
Table 2 Performance and computational cost

Errata

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