Abstract A new control chart, called the θ chart, for monitoring the mean of a process with bivariate quality characteristics is proposed. It can identify a rotation, shift or alternation between the subgroups of the process mean. The conventional application of X 2 chart to identify a sudden shift of the process mean is also expanded to identify a change of the process mean or a change of the process dispersion. Furthermore, when used together, the θ and X 2 charts could provide further insight into the process.
Abstract Estimates of the location and scale parameters, linear in the order statistics of a Type II censored or complete sample, from a continuous symmetric unimodal distribution satisfying certain conditions are obtained. Their coefficients are explicit functions of the expectations of the order statistics or population quantiles from the known parameter‐free standardized distribution. Linear estimates with simpler coefficients are also obtained. The theorems state the complete sample case, and the singly and doubly censored cases. The more general case, the multiple censoring, is an extension of these cases and is indicated. All the estimates obtained are asymptotically efficient in the strict sense.
Abstract Let X 1,X 2,...,X n be a random sample of size from a distribution with probability density function p(x|θ), where the unknown parameter θ belongs to a non-degenerate interval I. The unknown true value of θ will be denoted by θ0.
