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30 The PCB Magazine • March 2015 ally use 95% and are interested in the lower bound as a worst case scenario. Correlation Coefficient (Pearson's): measures the strength of the linear relationship between the data set and the chosen distribu- tion. If the distribution fits the data well, when the points are plotted on a probability plot graph, these points will fall on a straight line (superimposed on, or very close to, the diago- nal line) and the correlation coefficient will ap- proach 1. Carries a maximum value of 1. Distributions: a spatial array of data val- ues, or the space in which the data occupy. An empirical distribution is based on sample data, whereas a theoretical distribution is based on possible values of a random variable. Weibull and Lognormal are the most frequently used distributions. Estimation Methods: least squares or maximum likelihood methods. Equality of Parameters: statistical test to check whether two or more data sets have the same shape, scale, or threshold parameter. Typical tests return a 95% confidence interval and a p-value; the default p-value for statisti- cal significance is 0.05 (α = 0.05), so a p-value below this is statistically significant (there is a statistical difference). Eta (η): determines the spread of the Weibull distribution. A larger Eta value stretches the dis- tribution, while a smaller Eta value squeezes the distribution. For the Weibull distribution it's always the 63.21 percentile of the distribution. Referred to as the "scale" parameter. Hazard Function: a measure of the like- lihood of failure as a function of time, and is unique for each distribution. Infant Mortality (β < 1): failures that occur early during reliability testing and are caused by manufacturing defects such as poor workmanship, out-of-spec processing, substan- dard manufacturing and/or assembly practices, etc. Lower / Upper Bound: Confidence inter- vals are often not symmetric about the estimate, so we specify precision as a distance to the esti- mated lower or upper bound. We generally use the lower bound as a worst case scenario when a large parameter value is considered good. Conversely, if the proportion of nonconform- ing units was being estimated, the upper con- fidence limit would be the worst case scenario. Lognormal: the second most commonly used distribution in reliability to explain the location [Mean (µ)] and scale [Std Dev (σ)] of the data. This distribution has a lower bound (left tail) that is zero (0). The threshold param- eter can be set to any positive value to move the lower bound. MTTF (mean time to failure): a measure of the center of the distribution of failure times, the average or expected failure time that takes into account censored observations. Nonparametric: does not use, or make assumptions about the parameters of a popula- tion. Parameters: unknown population values that are estimated by the values of correspond- ing sample statistics. The lognormal distribu- tion has two parameters, location, and scale, with a third optional nonzero threshold param- eter. Likewise, the Weibull distribution has two parameters: shape and scale, with a third op- tional nonzero threshold parameter. Parametric: a distribution described by one or more parameters. For example, the nor- mal distribution family is identified by its mean (µ) and standard deviation (σ). Percent: percent of population that has failed. Percentile: time of failure (e.g., days, hours, cycles, etc.). Precision: the distance from the estimate to either the lower or upper bound of the cor- responding confidence interval. RELIABILITy TESTING AND STATISTICS continues Feature