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March 2015 • The PCB Magazine 31 RELIABILITy TESTING AND STATISTICS continues Feature R by C Notation: signifies what reliabil- ity requirement (R) at time (t) we want to meet with level of confidence (C). A R95C95 means 95% probability of survival, R(t), with 95% con- fidence in achieving that requirement. R(t) is viewed as a lower confidence limit on reliabil- ity, denoted as R L . Reliability: percentage of units that will survive a certain length of time. R-Squared (r 2 ): the coefficient of de- termination that represents the proportion of variation that is explained. Calculated by squaring the correlation coefficient. Maxi- mum value of 1. Threshold: parameter that provides an es- timate of the earliest failure time. Useful Life (β = 1): a constant failure rate (constant % fails in the next unit of time) with random failures (independent of time) due to excessively high loads, environmentally in- duced stresses, etc. Wearout, Early (1 < β < 4): early wearout begins with failures of weaker items and pro- gresses to wearout of stronger parts as β moves from 1 to 4. Failures occur due to low cycle fa- tigue, corrosion, aging, friction, etc. Wearout, Rapid (β > 4): highly reliably products, failures occur due to fatigue, corro- sion, aging, friction, etc. Weibayes: a method that combines the Weibull distribution with Bayesian statistics to analyze reliability data that have no failures. To use this method, there are four criteria that must be met. Weibull: the most commonly used distri- bution in reliability used to explain the shape [Beta (β)] and scale [Eta (η)] of the data. This distribution has a lower bound (left tail) that is zero (0). The threshold parameter can be set to any positive value to move the lower bound. Now that we have an understanding of the basic terms used in reliability, let's take a clos- er look at the bathtub curve and its meaning. Figure 1 shows the bathtub curve with its three stages. The three stages of the bathtub curve are de- scribed in table 1. Of importance is the interpretation of the shape (β) in reference to the scale (η). Steep (large) shapes (β) within the design life are a source of concern as there is risk of the en- tire population failing quickly as the parts age into the steep Weibull shape. On the other hand, if the Weibull scale (η) is well beyond the design life, there is negligible probabil- ity of failure before part retirement. In this case, steep shapes (β) are a source of happi- ness. Most steep shapes (β) have a safe period before the onset of failures, where the prob- figure 1: Bathtub curve with its three stages.