Probabilistic Design for Reliability

A pinch of probability is worth a pound of perhaps.

—James G. Thurber, American writer and cartoonist

Background/Incentive

Here are some of the major problems envisioned and questions asked in connection with today’s practices concerning reliability evaluations and assurances of electronic and photonic devices, products, and systems:

• • Electronic and photonic products that underwent highly accelerated life testing (HALT) [1-3] (see also Chapter 10), passed the existing qualifying tests (QT) and survived burn-in testing (BIT) often exhibit premature field failures. Are today’s methodologies and practices adequate? [4]. Do industries need new approaches to qualify their products, and if they do, what should be done differently? Could or should the existing practices be improved to an extent that if the product passed the QT, there is a way to assure that it will satisfactorily perform in the field?
• • In many applications, such as aerospace, military, long-haul communications, and medical (see, for example, [5]) high reliability of electronics and photonic materials and products is particularly imperative. Could the operational (field) reliability of such products be assured, if it is not predicted, that is, not quantified?
• • And if such a quantification is found to be necessary (in many situations it is the case), could it be done on the deterministic, that is, on a nonprobabilistic basis, or are probabilistic risk analyses a must [6-8]?
• • Should electronic product manufacturers keep shooting for an unpredictable and, perhaps, unachievable, very long, such as 20 years or so, product lifetime or, considering that every 5 years a new generation of devices appear on the market and that 20-year predictions are rather shaky, should electronic products manufacturers settle for a shorter, but well-substantiated, predictable, and assured lifetime, with a high (actually, adequate) probability of nonfailure?
• • How should such a lifetime be related to the acceptable (specified) probability of nonfailure for a particular product and application? It is clear that if a high probability of failure is acceptable, the projected lifetime will be long, and vice versa, the lifetime of a product will be short, if the accepted/ specified probability of its failure is low.

• • Considering that the principle of superposition does not work in reliability engineering, how to establish the list of the crucial accelerated tests, the adequate physically meaningful stressors and their combinations and levels, and how to bridge the gap between what one “sees” during the accelerated tests [preferably of failure-oriented-accelerated-testing (FOAT) type, geared to a physically meaningful predictive model] and what will they supposedly (most likely) “get” in the field conditions?
• • The best engineering product is the best compromise between the requirements for its reliability, cost-effectiveness, and (short-as-possible) time-to- market; it goes without saying that, in order to make any kind of optimization possible, the reliability of such product should also be quantified, but how could such an optimization be done?
• • The bathtub curve (BTC), the experimental “reliability passport” of mass- fabricated electronic products, reflects the inputs of two critical irreversible processes: the statistics-of-failure process, statistical failure rate (SFR), that results in a reduced failure rate with time (this trend is particularly strongly pronounced at the initial, infant mortality, portion of the BTC) and physics- of-failure (aging, degradation) process that leads to an increased failure rate with time (this trend is explicitly exhibited by the BTC wear-out portion). Could these two critical processed be separated [9]? The need for that is due to the obvious incentive to minimize, in one way or another, the role and the rate of aging, and this incentive is especially significant for products like lasers, solder joint interconnections, and others, which are characterized by long wear-out portions and when it is economically infeasible to restrict the product’s lifetime to the steady-state situation when the two irreversible processes in question compensate each other.
• • The last, but, as they say, not the least questions asked have to do with burn- in testing (BIT) [10-13]. BIT is an accepted practice in electronic and photonic manufacturing for detecting and eliminating early failures (“freaks”) in newly fabricated products prior to shipping the “healthy” ones that survived BIT to the customer(s). BIT is a costly undertaking: early failures are avoided and the infant mortality portion of the BTC is supposedly eliminated at the expense of the reduced yield. But what is even worse is that the elevated BIT stressors might not only eliminate “freaks,” but could cause permanent damage to the main population of the “healthy” products. It is not even clear if BIT is needed at all, the first question is “to BIT or not to BIT?” When highly accelerated life testing (HALT) is relied upon to do the BIT job, it is not even easy to determine whether there exists a decreasing failure rate with time at all. Even if the BIT-related question cannot be given an exhaustive answer, could it at least shed some useful “quantitative light” on the BIT process so that the best strategy possible could be developed?
• • In many of today’s reliability problems, human factor plays an important role: quite often equipment/instrumentation reliability (both hard- and software) and human performance contribute jointly to the outcome of a particular mission or an extraordinary situation. How could the interaction and integration of a human and a system be considered [14]?

In this chapter, these problems are addressed and the related questions are, at least partially, answered using the probabilistic-design-for-reliability (PDfR) concept [15-20].

PDfR and its “ten commandments”

The PDfR concept is an effective means for improving the state of the art in the electronics and photonics reliability field by quantifying, on the probabilistic basis, the operational reliability of a material, a product, or a system. This concept enables predicting the never-zero probability of failure under the given loading conditions and after the given time in operation, and to use this information as a suitable and physically meaningful criterion of the product’s expected performance. The following 10 major (governing) principles (“commandments”) reflect the rationale behind the PDfR concept:

• 1. When reliability of a product is imperative, and this is typically the case, ability to predict it is a must; reliability cannot be assured if it is not quantified [20].
• 2. Nothing is perfect, and the difference between a highly reliable and an insufficiently reliable product or a system is “merely” the difference in the levels of their never-zero probabilities of failure, and therefore such a quantification, to be consistent and trustworthy, should be done on the probabilistic basis [21,22]; in effect, reliability is part of applied probability and probabilistic risk management (PRM) bodies of knowledge, and includes the item’s (system’s) dependability, durability, maintainability, reparability, availability, and testability; that is, probabilities of the corresponding events or characteristics. Each of these characteristics is measured as a certain probability and could be of a greater or lesser importance depending on the particular function and operation conditions of the item or the system, and consequences of failure; applied probability and probabilistic risk management approaches and techniques put the art of Reliability Engineering on a “reliable” ground.
• 3. Reliability evaluations cannot be delayed until the product is made; they should start at the design stage, but, if possible, should be taken care of at all the significant stages of the product’s life: at the design stage, when reliability is conceived; at the accelerated testing stage, using electrical, optical, environmental, and mechanical instrumentation; at the production/manufacturing stage, when reliability is implemented; and, if necessary and appropriate, also in the field; then there will be a reason to believe that a “genetically healthy” product is created and its “health” could be maintained by using various prognostics-and-health monitoring (PHM) methods, as well as redundancy, troubleshooting, and other more or less well-established means that could be considered to maintain adequate reliability level, especially if the “genetic health” of the product is not as high as it could and should be [22].
• 4. Product’s reliability cannot be low, but need not be higher than necessary either: it has to be adequate for the given product and application, considering its lifetime, environmental conditions, and consequences of failure; overengineered and overrobust products that “never fail” are most likely more expensive than they could and should be; certainly, the required and, if possible, even specified probability of failure (or safety factor) should be well substantiated, thoroughly quantified and should be different for an electronic or a photonic device or a module installed in a space shuttle, a nuclear warhead, in a passenger aircraft, or in a household product. For example, three classes of electronic products could be suggested:

Class I: The product has to be made as reliable as possible; failure should not be permitted (some military or space objects);

Class II: The product has to be made as reliable as possible, but only up to a certain level of demand; failure is a catastrophe (civil engineering structures, bridges, ships, aircraft, cars);

Class III: The reliability does not have to be very high. Failures are permitted, but should be restricted (consumer products, commercial electronics, and agricultural equipment).

• 5. The best product is, as is well known, the best compromise between the requirements for its reliability, cost-effectiveness and time-to-market; it goes without saying that such a compromise cannot be achieved if reliability is not quantified.
• 6. One cannot design a product with quantified, assured and optimized reliability by limiting the effort to the widely used today “black box”—the HALT; understanding the underlying physics of failure is crucial, and therefore highly cost-effective and highly focused FOAT should be considered and conducted as HALT’S possible and natural extension (see Chapter 10).
• 7. FOAT, a “white/transparent box,” aimed at understanding the physics of failure, should be geared to a limited number of predetermined simple, easy-to-use, and physically meaningful predictive reliability models, such as the physically meaningful, powerful, and flexible Boltzmann- Arrhenius-Zhurkov (BAZ) model, and is considered as the experimental basis of the PDfR effort (see Chapter 10).
• 8. The physically meaningful, easy-to-use, and flexible multiparametric BAZ equation can be used as a suitable model for the assessment of the remaining “useful” life (RUL) of an electronic product (see Chapter 10). It has been recently demonstrated [23] that this equation is so flexible that that it could also be used in nonelectronic, nonmaterials physics and even in astrobiology.
• 9. Predictive modeling, not limited to FOAT models, and particularly analytical models, confirmed whenever appropriate and possible, by finite element analysis (FEA), is a powerful means to carry out, if necessary, sensitivity analyses (SA) w'ith an objective to quantify and often nearly eliminate failures by making the probability of failure sufficiently low'; this principle is referred to in some other areas of engineering (airspace, maritime, civil, military) as “principle of practical confidence.”
• 10. Consideration of the role of the human factor is highly desirable and could be naturally and easily incorporated, if there is a need for that, into a PDfR analysis [14]: not only “nothing,” but also “nobody” is perfect, and the human role in assessing the likelihood of the adequate performance of a product is getting increasing attention of both system engineers and human psychologists.