Solder Joint Reliability, or SJR, is the ability of solder joints to remain in conformance to their visual/mechanical and electrical specifications over a given period of time, under a specified set of operating conditions. SJR is often expressed as a probability value at a given confidence level, and is therefore discussed in the context of a given population of devices. Simply put, SJR is a measure of the likelihood that a solder joint will not fail throughout its intended operating life, subject to the various thermo-mechanical stresses that it encounters in the course of its operation.
Solder joint reliability has two aspects - 1) component-level solder joint reliability; and 2) board-level solder joint reliability. Component-level SJR deals basically with the reliability of solder joints within the package structure itself prior to board mounting, and is primarily assessed by performing reliability tests on unmounted parts. Board-level SJR deals with the reliability of the solder joints of a package after it has been mounted on a board or substrate, encompassing both the solder-to-package and solder-to-board interfaces.
Board-level SJR is more representative of the reliability of a package operating in the field, but requires a more complex system of assessment (since board-level reliability testing is more difficult to implement).  As a prudent approach, most companies perform both component- and board-level SJR testing before releasing a product with previously uncharacterized solder joint systems.
The importance of solder joint reliability became more emphasized in recent years as a result of two factors: 1) the shift of the semiconductor industry to lead-free solders; and 2) the emergence of fine-pitched surface-mount packages that employ hundreds of solder joints for electrical connection.
The shift to lead-free solder is in response to the industry's initiative to make its operations more environment-friendly by eliminating the use of materials that cause damage to the environment, which in this case is the lead-containing Pb/Sn solder used for lead finish.
Electronics manufacturers are willing to make the transition to Pb-free solders, but are concerned with the reliability implications of such a transition.  Thus, companies are ensuring that all the necessary modeling and reliability tests are conducted on their products before these are released with new solder joint material.  Industry-standard reliability tests are performed to generate reliability data proving that the new Pb-free solders meet the solder joint reliability requirements of the industry prior to their release.
There are three major mechanisms of solder joint failure, although these often interplay with each other simultaneously.  These are: 1) tensile rupture or fracture due to mechanical overloading; 2) creep failure, or damage caused by a long-lasting permanent load or stress; and 3) fatigue, or damage caused by cyclical loads or stresses.  Thus, solder joint reliability studies must take these mechanisms into consideration.
As mentioned earlier, one way to analyze solder joint reliability is to perform solder joint modeling, or analysis of solder joint strengths and weaknesses using computer models. This is usually done through finite element analysis. Solder joint modeling must be performed at different levels to take into consideration all aspects of solder joint reliability.  Experts perform solder joint modeling at board level, component level, joint level, and microstructure level.  The use of modeling at the design stage of a solder joint system to make it inherently reliable by design is known as 'Design-for-Reliability', or DFR.
Aside from modeling, solder joint reliability is also assessed through reliability testing.  Reliability testing consists of subjecting representative samples bearing the solder joint of interest to industry-standard reliability tests so that: 1) factors that cause or accelerate the various solder joint failure mechanisms will be uncovered and understood; and 2) actual reliability data may be generated for further analysis.
Fatigue, or failure due to loading with cyclical stresses, is a major concern in solder joint reliability.  Temperature cycling, or TC,  which accelerates fatigue failures, is therefore an important ingredient of any component-level or board-level solder joint reliability program.  Since bulk of real-life solder joint failures are caused by the mismatch between the coefficients of thermal expansion between the component and the substrate, board level thermal cycling in air has become an industry standard for assessing solder joint reliability.
Conventional temperature cycling, however, is considered by many as a conservative test, since the device package and the board or substrate on which it is mounted reach almost the same peak temperatures under this test (isothermal system). In real-world applications, however, the temperature experienced by the package may be significantly higher than that of the board because of the heat contributed by the operating device's junction temperature. To simulate this aspect,  many companies employ power cycling for SJR testing. Power cycling is a reliability test that subjects the device to alternating 'power on' and 'power off' conditions, while keeping the ambient temperature in control.
Aside from temperature cycling, other reliability tests performed by companies to assess component-level SJR include pressure cooker testing (PCT), mechanical shock testing, vibration testing, and high-temperature storage testing.   Board-level SJR tests, aside from board-level temperature cycling, include board-level high-temp operating life testing (HTOL) and temp-humidity-bias testing (THB), as well as innovative tests such as the board drop test and the board bend test.
Just like SJR, the solder joint quality of units being shipped to customers is also a challenge to manage. Since visual inspection is not highly effective in weeding out devices with potential solder joint issues, new technologies have emerged to help companies increase the solder joint quality of devices and assemblies being shipped to customers, an example of which is automated x-ray inspection systems (AXI).  Electrical testing at different temperatures or mechanical loading conditions to check for increased interconnection resistances is also employed.
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