On the Polynomial Measurement Error Model

This paper discusses point estimation of the coefficients of polynomial measurement error (errors-in-variables) models. This includes functional and structural models. The connection between these models and total least squares (TLS) is also examined. A compendium of existing as well as new results is presented

Interval Estimation in Structural Errors-in-Variables Model with Partial Replication

Confidence sets are constructed for the coefficients in a structural errors-invariables model with partial replication. These confidence sets are different from the traditional asymptotic confidence sets which have zero confidence levels, where the confidence level of a confidence set is defined to be the infimum coverage probability over the parameter space. The proposed confidence sets have positive confidence levels. Furthermore, it is shown that they have coverage probabilities converging to the nominal levels uniformly in all parameters as the sample size goes to infinity. An optimality property of the proposed confidence set for the slope in the model is also demonstrated.

On the Exponentially Weighted Moving Variance

MacGregor and Harris (J Quality Technol 25 (1993) 106–118) proposed the exponentially weighted mean squared deviation (EWMS) and the exponentially weighted moving variance (EWMV) charts as ways of monitoring process variability. These two charts are particularly useful for individual observations where no estimate of variability is available from replicates. However, the control charts derived by using the approximate distributions of the EWMS and EWMV statistics are difficult to interpret in terms of the average run length (ARL). Furthermore, both control charting schemes are biased procedures. In this article, we propose two new control charts by applying a normal approximation to the distributions of the logarithms of the weighted sum of chi squared random variables, which are respectively functions of the EWMS and EWMV statistics. These new control charts are easy to interpret in terms of the ARL. On the basis of the simulation studies, we demonstrate that the proposed charts are superior to the EWMS and EWMV charts and they both are nearly unbiased for the commonly used smoothing constants. We also compare the performance of the proposed charts with that of the change point (CP) CUSUM chart of Acosta‐Mejia (1995). The design of the proposed control charts is discussed. An example is also given to illustrate the applicability of the proposed control charts