Reliability is defined as the probability that a component part, equipment, or system will satisfactorily perform its intended function under given circumstances (such as environmental conditions, operating time, frequency and thoroughness of maintenance for a specified period of time). Predicting reliability with some degree of confidence is dependent on correctly defining a number of parameters. For example, choosing the type of distribution that matches the data is of primary importance for accurate results. Individual component failure rates must be based on a large enough population to reflect current normal usages. There are also empirical considerations, such as the slope of the failure rate, calculating the activation energy, and determining environmental factors (such as temperature, humidity and vibration). Finally, there are electrical stressors in electronic assemblies such as voltage and current.

Reliability engineering can appear somewhat abstract in that it involves statistics; yet it is engineering in its most practical form. At the EMPF, we are often asked to help our valued partners determine that the proper design performs its intended mission. Product reliability is seen as a testament to the robustness of the design as well as the integrity of the quality and manufacturing commitments of an organization.

The Bathtub Curve
The lifetime of a population of units can be divided into three distinct periods. Figure 6-1 shows the reliability “bathtub curve” which describes the cradle to grave instantaneous failure rates vs. time. The initial steep slope from the start to where the curve begins to flatten, is the early life period or infant mortality period. This period is characterized by a decreasing failure rate that occurs during the early life of a population of units. The weaker units fail leaving a population that is more robust. The next period, the flat portion of the graph, is called the useful life period. Failures occur randomly, but at a nearly constant rate. The third period begins at the point where the slope begins to increase and extends to the end of the graph. This is the wearout period when units become old and begin to fail at an increasing rate.

Early Life Period
Some of the design techniques the EMPF utilizes to ensure reliability include: burn-in (to stress devices under constant operating conditions); power cycling (to stress devices under the surges of turn-on and turn-off); temperature cycling (to mechanically and electrically stress devices over the temperature extremes); vibration; testing at the thermal destruct limits; and highly accelerated stress and life testing. In order to mitigate these risks in a product line, the manufacturer may choose to consume some of the early useful life of an assembly by stress screening. This technique allows the resulting population to begin its operating life somewhere closer to the flat portion of the bathtub curve instead of at the initial peak. The amount of screening needed for acceptable quality is a function of the process grade as well as history.

Useful Life Period
As the product matures, the weaker units die off, the failure rate becomes nearly constant, and modules have entered what is considered the normal life period. This period is characterized by a relatively constant failure rate. It is difficult to predict which failure mode will be manifested, but the rate of failure is predictable. The length of this period is also referred to as the system life of a product or component. It is during this period of time that the lowest failure rate occurs. The useful life period is the most common time frame for making reliability predictions. The failure rates calculated from MIL-HDBK-217 and Telcordia-332 apply only to this period.

Wearout Period
As components begin to fatigue or wearout, failures occur at increasing rates. Wearout in electronics assemblies is usually caused by the breakdown of electrical components that are subject to physical wear and electrical and thermal stress. It is this area of the graph that the mean time between failures (MTBFs) or failures in time rates (FIT - number of failure per billion device-hours) calculated in the useful life period no longer apply. A product with a MTBF of 10 years can still exhibit wearout in two years. No parts count method can predict the time to wearout of components. Electronics in general are often designed so that the useful life extends past the design life. This way wearout should never occur during the
useful life of a module. For example, most electronics are obsolete within 20 years; MTBFs could extend 35 years or longer.

Weibull Analysis
The Weibull distribution is a very flexible life distribution model that can be used to characterize failure distributions in all three phases of the bathtub curve. The basic Weibull distribution has two parameters, a shape parameter, often termed beta (b), and a scale parameter, often termed eta (h). The scale parameter, h, determines when, in time, a given portion of the population will fail, i.e. 63.2%. The shape parameter, b, is the key feature of the Weibull distribution that enables it to be applied to any phase of the bathtub curve. A b<1 models a failure rate that decreases with time, as in the infant mortality period. A b=1 models a constant failure rate, as in the normal life period. And a b>1 models an increasing failure rate, as during wear-out. There are several ways to view this distribution, including probability plots, survival plots and failure rate versus time plots. The bathtub curve is a failure rate vs. time plot. The Weibull distribution is given by Equation 6-1:


The results of various bs on the Weibull analysis can be seen in Figure 6-2. Notice how, if all curves are combined, the resultant graph is similar to a bathtub curve.

The EMPF not only uses Wiebull analysis routinely but also teaches the process as a part of our electronics manufacturing training. This distribution, for example, allows modeling to be done with a minimal amount of error. At the EMPF we engage our students with practical applications on how to utilize the various forms of reliability modeling. For more information on engineering and other training classes, please contact Ken Friedman at 610.362.1200, extension 279 or via email at kfriedman@aciusa.org.