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A control chart is proposed which monitors the conformance of a sample to an in-control distribution using the quantile or inverse cumulative distribution function. This method permits detecting changes in the distributional shape which may be undetecte..

A model for the measurements from a multiple stream process is analysed as a special case of a multivariate control chart by principal components analysis. The principal components meet the objective of partitioning the control problem into statistics that are sensitive to two types of assignable causes. Simple test statistics result and performance analyses are provided.

Principal components are useful for multivariate process control. Typically, the principal component variables are often selected to summarize the variation in the process data. We provide an analysis to select the principal component variables to be included in a multivariate control chart that incorporates the unique aspects of the process control problem (rather than using traditional principal component guidelines).

A significant practical disadvantage of multivariate statistical process control is that it is difficult to determine which of the monitored variables is responsible for the out-of-control signal. While there have been several proposed techniques and diagnostics, most of these have disadvantages. Rather than an ad hoc selection, we use three approaches to develop a diagnostic for a chi-square chart and generate the same statistic from each approach. Consequently, intuitive interpretations of the diagnostic are provided and previous proposals are simplified by a focus on a single metric.

In this study, the effect of incorrect order identification on parameter estimation and forecasting for the vector autoregressive moving average model has been conducted via a Monte Carlo simulation. Five parameter sets, labeled A to E, for a bivariate ARMA(1,1) model were specified within the feasible regions of stationarity and invertibility. It was found that the estimated parameter values for the ARMA(2,1) and ARMA(1,2) models had biases approaching zero, while those for the ARMA(2,0), ARMA(1,0) and ARMA(0,1) models exhibited persistent biases. The forecast findings for the underfitted models are contrary to the univariate results of Ledolter and Abraham (1981) and Kunitomo and Yamamoto (1985). However the findings are consistent with Akaike's (1969). This study has shown that an underfitted model is less desirable than an overfitted one in term of forecast error variances.

Simultaneous confidence intervals for the p means of a multivariate normal random variable with known variances may be generated by the projection method of Scheffe and by the use of Bonferroni's inequality. It has been conjectured that the Bonferroni intervals are shorter than the Scheffe intervals, at least for the usual confidence levels. This conjecture is proved for all p≥2 and all confidence levels above 50%. It is shown, incidentally, that for all p≥2 Scheffe's intervals are shorter for sufficiently small confidence levels. The results are also applicable to the Bonferroni and Scheffe intervals generated for multinomial proportions.