Estimating error rates for firearm evidence identification is a fundamental challenge in forensic science. This paper describes the recently developed congruent matching cells (CMC) method for image comparisons, its application to firearm evidence identification, and its usage and initial tests for error rate estimation. The CMC method divides compared topography images into correlation cells. Four identification parameters are defined for quantifying both the topography similarity of the correlated cell pairs and the pattern congruency of the registered cell locations. A declared match requires a significant number of CMCs, i.e., cell pairs that meet all similarity and congruency requirements. Initial testing on breech face impressions of a set of 40 cartridge cases fired with consecutively manufactured pistol slides showed wide separation between the distributions of CMC numbers observed for known matching and known non-matching image pairs. Another test on 95 cartridge cases from a different set of slides manufactured by the same process also yielded widely separated distributions. The test results were used to develop two statistical models for the probability mass function of CMC correlation scores. The models were applied to develop a framework for estimating cumulative false positive and false negative error rates and individual error rates of declared matches and non-matches for this population of breech face impressions. The prospect for applying the models to large populations and realistic case work is also discussed. The CMC method can provide a statistical foundation for estimating error rates in firearm evidence identifications, thus emulating methods used for forensic identification of DNA evidence.

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A statistical analysis for key comparisons with linear trends is proposed. The approach has the advantage that it is consistent with the no-trend cases. The uncertainties for the key comparison reference value, which is time dependent in this case, and the degrees of equivalence are also provided. As an example, the approach is applied to key comparison CCEM-K2.

When repeated measurements are autocorrelated, it is not appropriate to use the traditional approach to calculate the uncertainty of the average of the measurements, which assumes that the measurements are statistically independent. In this paper, we propose a practical approach to calculate the corresponding uncertainty and the confidence interval when the data are from a stationary process. For illustration, the approach is applied to two examples: linewidth measurements made by a scanning electron microscope and weight measurements. The results are also extended to the general case in which both Type A and Type B uncertainty components are presented and to the case of weighted means.

Weighted mean has been used to combine means from several sets of measurements, which are either from different laboratories or based on different measurement methods. It is also often used in key comparisons and other inter-laboratory comparisons. However, the traditional estimator of the variance of the weighted mean underestimates the variance. Two new variance estimators are proposed with smaller biases, smaller mean square errors and much better coverage probabilities for the correspondingly formed intervals. In metrology, the uncertainties based on Type B evaluation which are not based on statistical analysis of data cannot be ignored. In the later part of this paper, the results are extended to the general case with both Type A and Type B uncertainty components being presented.