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32 The PCB Magazine • March 2015 ability of failure is negligible. The steeper the shape (β), the smaller the variation in times to failure and the more predictable the results of the product. A vertical shape (β) of infinity implies perfect design, manufacturing, and quality control [8] . For example, let's say we have a product that is required to pass 100 thermal cycles. We run two lots and get the following results: Lot 1 Lot 2 Shape (β) 3.4 3.9 Scale (η) 250 125 Lot 2 has a steeper (larger) shape (β) value and we might interpret this lot as more reli- able, but when we consider the scale (η), value lot 1 has 2x that of lot 2. In other words, lot 1 performance is well beyond the design life (100 cycles) and the probability of failure occurring within the design life is negligible. Here's another worked example: Table 2 has plated through-hole thermal cycling data. The data is censored at 300 cycles and is coded as such with 1 = failure, 0 = right censored. Using software, we can fit a distribution to the data set [9] . The first look at the Weibull plot answers two questions: How good is the fit and what is the beta (β), the slope? (Figure 2) The correlation coefficient is 0.976, and the data points line up well on the diagonal line in- dicating we have a good fit. The origin of the blue diagonal line comes from the shape (β) and scale (η) parameters iteratively derived from the Table 1: The three stages of the bathtub curve. Table 2: pTh thermal cycling data. Feature RELIABILITy TESTING AND STATISTICS continues