Statistical Failure Rate Research Articles

Blue Waters system and component reliability

SummaryThe Blue Waters system, installed in 2012 at NCSA, has the largest component count of any system Cray has built. Blue Waters includes a mix of dual‐socket CPU (XE) and single‐socket CPU, single GPU (XK) nodes. The primary storage is provided by Cray's Sonexion/ClusterStor Luster storage system delivering 35 PB (raw) storage at 1 TB/s. The statistical failure rates over time for each component including CPU, DIMM, GPU, disk drive, power supply, blower, etc and their impact on higher level failure rates for individual nodes and the systems as a whole are presented in detail, with a particular emphasis on identifying any increases in rate that might indicate the right‐side of the expected bathtub curve has been reached. Strategies employed by NCSA and Cray for minimizing the impact of component failure, such as the preemptive removal of suspect disk drives, are also presented.

High-Tolerance Thin-Film Solder Joints for Electrical Interconnection in Harsh Environments

This paper presents a pioneering use of thin-film solder joint in the electrical interconnection of high-temperature thin-film sensors, which aims to improve the low tolerance of traditional soldered balls in extreme environments. The structure of the thin-film solder joint, composed of silver foil, solder joint paste, and metal wire, has a negligible mass compared to traditional soldered balls. As a result, the inertia force on the solder joint/substrate interface during vibration and force impact is greatly reduced, improving the reliability of the solder joint under thermal-mechanical coupling impacts. The thin-film solder joint has been verified using both metal (AgPd paste) and ceramic (TiB2/SiCNO paste) solders, and can withstand extreme environments such as thermal shock and high "g" loading. The designed thin-film solder joint can withstand impact energy of up to 3 J at 1000 °C without failure, which is 6 times higher than that of traditional soldered balls (with a statistical failure rate of up to 67% under 0.5 J impact). The thin-film solder joint was successfully used for electrical interconnection of high-temperature thin-film strain gauges, demonstrating excellent reliability under thermal-mechanical coupling impacts at 1000 °C. Our high-tolerance thin-film solder joints show promising potential for use in electrical interconnection in harsh environments.

Robust stabilization of power systems subject to a series of lightning strokes modeled by Markov jumps: Attracting ellipsoids approach

Power systems are subject to stochastic faults and process random noise. The faults (due to e.g. lightning strokes) can be temporary or permanent. When a lightning stroke hits a transmission line, the circuit breakers open to clear the fault and reclose. The resulting parameters changes are modelled as a discrete-time Markov jumps in this paper using the practical statistical failure rates. System parameters are also subject to random noise e.g. line reactance’s depend on the conductors spacing which in turn depends on stochastic wind speeds. This paper presents a novel power system excitation control robust against such stochastic uncertainties. The design is based on a derived sufficient condition in the framework of linear matrix inequalities (LMI), and the attracting ellipsoid approach. The effectiveness of the proposed control is tested on a multi-machine power system.

Burn-in-Testing (BIT) Challenge: to BIT or not to BIT?

Abstract Burn-in testing (BIT) is a costly undertaking. Predictive modeling enables shading useful light on what and how should be tested, if at all. Three analytical (“mathematical”) predictive models recently suggested by the author are addressed in this mini-review: 1) A model based on the analysis of the infant mortality portion (IMP) of the bathtub curve (BTC) suggests that the non-random time derivative of the expected “statistical” failure rate (SFR) at the beginning of the IMP could be viewed as a suitable criterion (“figure of merit”) to answer the basic question of the BIT undertaking: “to BIT or not to BIT?” 2) A model based on the analysis of the random failure rate (RFR) of the mass-produced components that the manufactured product of interest is comprised of suggests that the above derivative is, in effect, the RFR variance of these components. 3) A model based on the use of the kinetic multi-parametric Boltzmann-Arrhenius-Zhurkov (BAZ) constitutive equation is employed to establish the BIT's adequate duration and level, if this kind of failure-oriented-accelerated-testing (FOAT) is found to be necessary. The theoretical findings are illustrated by calculated data. It is concluded that predictive modeling should always precede the actual BIT, that analytical modeling should always complement computer simulations and that future work should address the experimental validation and possible extension of the obtained results and recommendations.

To Burn-In, or Not to Burn-In: That’s the Question

In this paper it is shown that the bathtub-curve (BTC) based time-derivative of the failure rate at the initial moment of time can be considered as a suitable criterion of whether burn-in testing (BIT) should or does not have to be conducted. It is also shown that the above criterion is, in effect, the variance of the random statistical failure rate (SFR) of the mass-produced components that the product manufacturer received from numerous vendors, whose commitments to reliability were unknown, and their random SFR might vary therefore in a very wide range, from zero to infinity. A formula for the non-random SFR of a product comprised of mass-produced components with random SFRs was derived, and a solution for the case of the normally distributed random SFR was obtained.

Corrosion resistance of brazed aluminum in ethanol/water mixtures at high temperatures

This study investigated the corrosion of aluminum in various ethanol/water mixtures. It has been shown that a critical corrosion temperature exists at which a sudden exothermic corrosion occurs. This critical corrosion temperature is dependent on presence of water and increases with increasing water concentration. This corrosion is independent of the atmosphere. Furthermore, it was demonstrated that denaturants in ethanol with a carbonyl group will further increase the critical corrosion temperature. This increase is due to a reaction of water and carbonyl to carbonyl-hydrate which reacts with the aluminum oxide surface forming a passivation layer. The critical corrosion temperature has been defined by the reaction of aluminum with ethanol. Thereby, the same energy is always released, independent of the water concentration. However, the presence of water influences the activation energy of this reaction. The observed corrosion of aluminum depends on the exposed surface area. Consequently, with increasing surface area, a higher statistical failure rate is observed. This is most likely due to defects in the passivation layer of aluminum.

Analytical bathtub curve with application to electron device reliability

To better understand the physics of degradation of mass-produced electron devices (ED) one has to be able to distinguish between the impact of the favorable statistics-related process resulting in lower failure rates with time and the unfavorable degradation (aging) process leading to higher failure rates. In this analysis it is shown how the degradation-related failure rate can be determined from the analytically approximated experimental bathtub curve and the predicted statistical failure rate (SFR) data. The case, when the SFR is distributed normally, is used as a suitable illustration. The suggested methodology can be employed in the design and analysis of the next ED generations. It can be used also beyond the ED field, when there is a need to assess, in various applied science problems, the roles of the two irreversible processes in question.

Statistics-related and reliability-physics-related failure processes in electronics devices and products

The well known and widely used experimental reliability "passport" of a mass manufactured electronic or a photonic product — the bathtub curve — reflects the combined contribution of the statistics-related and reliability-physics (physics-of-failure)-related processes. When time progresses, the first process results in a decreasing failure rate, while the second process associated with the material aging and degradation leads to an increased failure rate. An attempt has been made in this analysis to assess the level of the reliability physics-related aging process from the available bathtub curve (diagram). It is assumed that the products of interest underwent the burn-in testing and therefore the obtained bathtub curve does not contain the infant mortality portion. It has been also assumed that the two random processes in question are statistically independent, and that the failure rate of the physical process can be obtained by deducting the theoretically assessed statistical failure rate from the bathtub curve ordinates. In the carried out numerical example, the Raleigh distribution for the statistical failure rate was used, for the sake of a relatively simple illustration. The developed methodology can be used in reliability physics evaluations, when there is a need to better understand the roles of the statistics-related and reliability-physics-related irreversible random processes in reliability evaluations. The future work should include investigations on how powerful and flexible methods and approaches of the statistical mechanics can be effectively employed, in addition to reliability physics techniques, to model the operational reliability of electronic and photonic products.

Electronic Part Failure Rates in Space Environments

Much conjecture exists regarding the special effects of space environments as reliability stressors on common electronic parts. To understand the unique risks associated with these additional factors, it is useful to envision their presence as superimposed sources of activation energy. This, in turn, demands a general mathematical model for part failure rate synthesis which relates statistical risk with energy level. Such a mathematical model has been developed and is worthy of close examination from the view-point of additional space environment risks. Thus, an energy level concept affords mathematical equations from which the statistical risks in ``unproven'' operational environments can be inferred from an extrapolation of a wealth of conventional operational experience. This paper contends that advances in the art of space material test and evaluation must have their roots in a comprehensive understanding of terrestrial tests and statistical failure rate criteria. Any useful comprehension must be based upon a rank order of part stressors where ground environment factors are essential prerequisites. Once examined from an energy viewpoint, failure tendencies and their underlying material mechanisms can be usefully depicted mathematically using energy as a helpful common denominator. It remains then to deliberate upon the appropriate material test evidences to establish tables of part usage risk for space environments with the same level of completeness as has been established for terrestrial operating conditions.