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March 2015 • The PCB Magazine 41 RELIABILITy TESTING AND STATISTICS continues Where: X 2 = Chi-square distribution r = Failures C = Confidence level m = Constant β = Shape parameter R L = Lower confidence limit These calculations are easily done using software [9] . For example, we have a requirement to meet a R95C95 specification: 95% reliability (or probability of survival), with a confidence level of 95%, with a required time R(t) of 300 cycles. Historically, the Weibull shape param- eter for this product type has been 4.29; we'll allow zero failures, and censor the testing at 500 cycles. Using Minitab®, we can calculate the sample size as follows: Reliability Test Plan Distribution: Weibull, shape = 4.29 Reliability Goal = 0.95, Target confidence level = 95% Actual confidence level: 95.98% Failures Allowed: 0 Testing Time: 500 Sample Size: 7 One caveat to consider is that parameter estimates result in sample size estimates, and when parameter estimates are based on a small sample size the confidence intervals can be- come wide, which can significantly under or over estimate the sample size. There are a few general assumptions made about the proposed model when it is used to equate accelerated thermal cycling to field use conditions. Primary assumptions include that the thermal cycling coupon is representative of the PCB in terms of design, PTH quality (drill, desmear, glass exposure, copper plating thick- ness, etc.), out-of-plane dimensional move- ment, and workmanship. It's well established that the quality of the PTH has a significant im- pact on reliability [15, 16, 18] , and that the thermal cycling test conditions, with the failures they induce, represent the field use failure mecha- nisms. The model itself is conservative by na- Table 5: 95% confidence limits for the success-failure testing. Feature