The division typically produces one to a few publications on new statistical methods each year. A list of publications on some research from the past few years is shown below below. Following the publication list, an example of current work on the development of novel statistical methods, useful both at NIST and elsewhere, is presented in more detail.

## Summary

Since the formation of the Statistical Engineering Division in 1947, division staff, through their interdisciplinary research with NIST scientists and engineers, occasionally encounter problems that cannot be addressed using existing, or textbook, statistical methods. On such occasions, appropriate division staff conduct original research in mathematical and/or computational statistics, leading to new and more broadly applicable statistical methods. The division's unique contributions to the general methods of statistics tend to concentrate in areas where the measurement science activities at NIST present new challenges in planning and analyzing high precision data on high-accuracy measurement systems. So, many of the divisions original contributions fall into the following areas:

- Bayesian methods for metrology,
- statistical calibration and measurement assurance,
- experiment designs,
- components-of-variance estimation,
- methods for the design and analysis of interlaboratory comparisons, and
- measurement process control. The division also conducts limited research in some areas enabled by modern computing systems:
- computer intensive methods (bootstrap, permutation procedures, general distribution-free methods) and
- image analysis methods.

## Description

## Major Accomplishments

The following are research publications written by SED staff and collaborators.

- Zhang, N. F. (2000). "Statistical Control Charts for Monitoring the Mean of a Stationary Process", to appear in the Journal of Statistical Computation and Simulation.

- Vangel, M. G. and Rukhin, A. L. (1999). "Maximum-Likelihood Analysis for Heteroscedastic One-Way Random Effects ANOVA in Interlaboratory Studies," Biometrics, 55, 302-313.

- Vangel, M. G. (1998). "ANOVA Estimates of Variance Components for Quasi-Balanced Mixed Models," Journal of Statistical Planning and Inference, 70, 139-148.

- Rukhin, A. L. and Vangel, M. G. (1998). "Estimation of a Common Mean and Weighted Means Statistics, Journal of the American Statistical Association, 93, 303-309.

- Zhang, N. F. (1998). "Estimating Process Capability Indices for Autocorrelated Data", Journal of Applied Statistics, 25(4), 559-574.

- Zhang, N. F. (1998). "A Statistical Control Chart for Stationary Process Data," Technometrics, 40(1), 24-38.

- Zhang, N. F. (1997), "Detection capability of residual control chart for stationary process data," Journal of Applied Statistics, 24(4), 475-492.

- Wang, C. M. and Lam, C. T. (1997). "A mixed-effects model for the analysis of circular measurements," Technometrics, 39 (2), 119-126.

- Brown, E. B., Iyer, H. K. and Wang, C. M. (1997). "Tolerance intervals for assessing individual bioequivalence," Statistics in Medicine, 16, 803-820.

- Liu, H.K. (1997), "High-dimensional empirical linear prediction", Advanced Mathematical Tools in Metrology III, 79-90.

- Filliben, J. J. and Li, K. C. (1997), "A systematic approach to the analysis of complex interaction patterns in two-level factorial design," Technometrics, 39 (3), 286-297.

- Wang, C. M. and Iyer, H. K. (1996). "Sampling plans for obtaining tolerance intervals in a balanced one-way random-effects model," Communications in Statistics - Theory and Methods, 25 (2), 313-324.

- Wang, C. M. and Lam, C. T. (1996). "Confidence limits for proportion of conformance," Journal of Quality Technology, 28 (4), 439-445.

- Liao, C. T., Vecchia, D. F., and Iyer, H. K. (1996), "Construction of orthogonal two-level designs of user-specified resolution where N is not 2**k," Technometrics, 38, 342-353.

- Vangel, M. G. (1996). "Confidence Intervals for a Normal Coefficient of Variation", The American Statistician, 15, 21-26.

- Eberhardt, K. R. and Mee, R. W. (1996), "A comparison of uncertainty criteria for calibration," Technometrics, 38 (3), 221-229.

- Kacker, R., N. F. Zhang and C. Hagwood (1996) "Real-time Control of a Measurement Process," Metrologia, 33, 433-445.

- Coakley, K. J. (1996), "A Bootstrap Method for Nonlinear Filtering of EM-ML Reconstructions of PET Images," International Journal of Imaging Science and Technology, Vol. 7, 54-61.

- Ahlbrandt, R. A., Vecchia, D. F., and Iyer, H. K. (1995), "Optimum design of serial measurement trees," Journal of Statistical Planning and Inference, 48, 379-390.

- Zhang, N. F. and J. P. Pollard (1994) " Analysis of Autocorrelations in Dynamic Processes," Technometrics, 36, 354-368.

- Wang, C. M. and Iyer, H. K. (1994). "Tolerance intervals for the distribution of true values in the presence of measurement errors," Technometrics, 36, 162-170.

- Wang, C. M. (1994). "On estimating approximate degrees of freedom of chi-squared approximations," Communications in Statistics - Simulation and Computation, B23(3), 769-788.

- Vangel, M. G. (1994). "One-Sided Nonparametric Tolerance Limits." Communications in Statistics: Simulation and Computation, 23, 1137.

- Hsu, J. C., Hwang, J. T. G., Liu, H. K. and Rugreg, S. T. (1994). "Confidence intervals associated with tests for bioequivalence," Biometrika, 81 103-114.

- Galambos, J. and Hagwood, C. (1994). "An unreliable Server Characterization on the Exponential Distribution," Journal of Applied Probability 31, 274-279.

- Eberhardt, Keith R. and Mee, R. W. (1994). "Constant-Width Calibration Intervals for Linear Regression," Journal of Quality Technology, Vol 26, 21-29.

- Wang, C. M. (1992). "Prediction intervals for a balanced one-way random-effects model," Communications in Statistics - Simulation and Computation, B21(3), 671-687.

- Wang, C. M. (1992). "Approximate confidence intervals on linear combinations of expected mean squares," Journal of Statistical Computation and Simulation, 43, 229-241.

- Vangel, M. G. (1992). "New Methods for One-Sided Tolerance Limits for a One-Way Balanced Random-Effects ANOVA Model," Technometrics, 34, 176-185.

- Hwang, J. T. and Liu, H. K. (1992). "Existence and nonexistence theorems of finite diameter sequential confidence regions for errors-in-variables models," Statistics and Probability Letters 13, 45-55.

- Galambos, J. and Hagwood, C. (1992). "The Characterization of Distribution Function by the Second Moments of the Residual Life," Commun. Statist.-Theory and Methods 21, 1463-1468.

- Hagwood, C. (1992). "The Calibration Problem as an Ill-Posed Inverse Problem," Journal of Statistical Planning and Inference 31, 179-185.

- Wang, C. M. (1991). "Approximate confidence intervals on positive linear combinations of expected mean squares," Communications in Statistics - Simulation and Computation, B20(1), 81-96.

- Vecchia, D. F. and Iyer, H. K. (1991). "Exact moments of the quartic assignment statistic with an application to multiple regression," Communications in Statistics-Theory and Methods, 20, 3253-3269.

- Mee, R. W., Eberhardt, Keith R., Reeve, C. P. (1991). "Calibration and Simultaneous Tolerance Intervals for Regression," Technometrics, Vol. 33, No. 2, pp. 211-220.

- Schiller, S. and Eberhardt, Keith R. (1991). "Combining Data from Independent Chemical Analysis Methods," Spectrochimica Acta.

- Coakley, K. J. (1991), "A Cross-Validation Procedure for Stopping the EM Algorithm and Deconvolution of Neutron Depth Profiling Spectra," IEEE Transactions on Nuclear Science, Vol. 38, 9-16.

- Zhang, N. F., G. A. Stenback and D. M. Wardrop (1990) "Interval Estimation of Process Capability Index," Communications In Statistics - Theory and Methods, 19(12), 4455-4470.

- Zhang, N. F., (1990) "Group Delay, Partial Group delay and Index-lag relationship for Multidimensional Processes," Commun. In Statistics-Theory and Methods, 19(9), 3137-3145.

- Wang, C. M. (1990). "On the lower bound of confidence coefficients for a confidence interval on variance components," Biometrics, 46, 187-192.

- Wang, C. M. (1990). "On ranges of confidence coefficients for confidence intervals on variance components," Communications in Statistics - Simulation and Computation, B19(4), 1165-1178.

- Iyer, H. K. and Vecchia, D. F. (1990). "Minimum cost inspection intervals for a two-state process," Journal of Quality Technology, 22, 210-222.

- Hwang, J. T. and Liu, H. K. (1990). "Sequential confidence regions in inverse regression problems," Annals of Statist. 18 1389-1399.

- Vecchia, D. F., Iyer, H. K. and Chapman, P. L. (1989). "Calibration with randomly changing standard curves," Technometrics, 31, 83-90.

- Vecchia, D. F. and Iyer, H. K. (1989). "Exact distribution-free tests for equality of several linear models," Communications in Statistics-Theory and Methods, 18, 2467-2488.

- Iyer, H. K. and Vecchia, D. F. (1989). "Exact moments of the symmetric cubic assignment statistic," Communications in Statistics-Theory and Methods, 18, 4309-4320.

- Hagwood, C. (1989). "A Renewal Theorem in Multidimensional Time," Australian Journal of Statistics, 31, 130-137.

- Mee, R. W., Eberhardt, Keith R. and Reeve, C. P. (1989). Computing Factors for Exact Two-Sided Tolerance Limits for a Normal Distribution," Communications in Statistics-Simulation and Computation,18.

- Eberhardt, Keith R., Reeve, C. P. and Spiegelman, C. H. (1989). "A Minimax Approach to Combining Means, With Practical Examples," Chemometrics and Intelligent Laboratory Systems.

- Croarkin, Mary C. (1989). "An Extended Error Model for Comparison Calibration", Metrologia 26, 107-113.

- Liggett, W. S. (1989), "Estimation of an Asymmetrical Density from Several Small Samples," Biometrika, 76, 13-21.

- Wang, C. M. (1988). "One-sided confidence intervals for the positive linear combination of two variances," Communications in Statistics - Simulation and Computation, B17(1), 283-292.

- Wang, C. M. (1988), "Beta-expectation tolerance limits for balanced one-way random-effects model," in Probability and Statistics: Essays in Honour of Franklin A. Graybill, J. N. Srivastava Ed., p. 285, Amsterdam: North Holland.

- Yao, Y.C., Vecchia, D. F., and Iyer, H. K. (1988). "Linear calibration when the coefficient of variation is constant," Essays in Honor of F. A. Graybill, (Monograph), (J. N. Srivastava, Ed.), North-Holland, 297-309.

- Mulrow, J. M., Vecchia, D. F., Buonaccorsi, J. P. and Iyer, H. K. (1988). "Problems with interval estimation when data are adjusted via calibration," Journal of Quality Technology, 20, 233-247.

- Liggett, W. S. (1988), "Estimation of the Error Probability Density from Replicate Measurements on Several Items," Biometrika, 75, 557-567.

## Organizations

## Former Staff

Various staff of the Statistical Engineering Division, including faculty appointees from the the University of Maryland, U. of Maryland Baltimore County, Colorado State University.

## Customers/Contributors/

Collaborators

Visiting Guest Researchers and Fellows from academia.