Shu-Fei Wu

Interval estimation for a Pareto distribution based on a doubly type II censored sample

For a complete sample, Chen [Chen, Z., 1996. Joint confidence region for the parameters of a Pareto distribution. Metrika 44, 191-197] proposed an interval estimation of the parameter @q and a joint confidence region of two parameters of a Pareto distribution. When the first r lifetimes and the last s lifetimes out of n inspected items are missing, doubly type II censoring has arisen. Since Chens method cannot be extended to the doubly type II censored sample case, I proposed another joint confidence region for the two parameters of a Pareto distribution. The interval estimation of parameter @n is also given for a doubly type II censored sample. Since the complete sample case (r=0) and the right type II censored sample case (r=s=0) are special cases of doubly type II censored samples, the proposed confidence region should also be appropriate for these two special cases, and thus can be compared with Chens method based on the area of the confidence region. From the simulation results, it can be found that the proposed method is better than Chens method in obtaining a smaller confidence area. But the difference in area of the two methods becomes very slight when the sample size becomes larger. In this paper, I also proposed the prediction intervals of the future observation and the ratio of the two future consecutive failure times based on the doubly type II censored sample. Finally, an example is given to illustrate the proposed method.

One stage multiple comparisons with the average for exponential location parameters under heteroscedasticity

Two-stage multiple comparisons with the average for location parameters of two-parameter exponential distributions under heteroscedasticity are proposed by Wu and Wu [Wu, S.F., Wu, C.C., 2005. Two stage multiple comparisons with the average for exponential location parameters under heteroscedasticity. Journal of Statistical Planning and Inference 134, 392-408]. When the additional sample for the second stage may not be available, one-stage procedures including one-sided and two-sided confidence intervals are proposed in this paper. These intervals can be used to identify a subset which includes all no-worse-than-the-average treatments in an experimental design and to identify better-than-the-average, worse-than-the-average and not-much-different-from-the-average products in agriculture, the stock market, pharmaceutical industries. Tables of upper limits of critical values are obtained using the technique given in Lam [Lam, K., 1987. Subset selection of normal populations under heteroscedasticity. In: Proceedings of the Second International Advanced Seminar/Workshop on Inference Procedures Associated with Statistical Ranking and Selection. Sydney, Australia. August 1987. Lam, K., 1988. An improved two-stage selection procedure. Communications in Statistics-Simulation and Computation 17 (3), 995-1006]. An example of comparing four drugs in the treatment of leukemia is given to demonstrate the proposed procedures. The relationship between the one-stage and the two-stage procedures is also elaborated in this paper.

Multiple comparison prodecures with the average for exponential location parameters

In this article, multiple comparison procedures with the average of exponential location parameters when sample sizes are equal are under investigation. A subset selection approach and a simultaneous confidence interval approach with minimum expected length are considered for exponential distributions with common known or unknown scale parameter. These procedures will have broad applications in selecting a subset which includes all better-than-the-average treatments in experimental design and/or in identifying all better-than-the-average, worse-than-the-average and not-much-difference-from-the-average products in agriculture, business, manufacturing and other industries. Some numerical approximation approaches using Bonferroni inequality are proposed in this article. Statistical tables to implement these procedures for the case of equal sample size are provided for use in practice. A simulation result indicates that Bonferroni approximation performs better than the confidence interval with equal-tail probability. Computer software programs for calculating the percentage points and for simulation are available from the authors.

A two-sided sequential screening procedure based on individual misclassification error

In order to reduce the cost and time effort of inspection, a two-sided sequential screening procedure based on the individual misclassification error is proposed. The criteria of average outgoing quality and total inspection cost are used to search for the optimal allocation. The generalized formulas of all the desired probabilities for any number of stages of two-sided sequential screening procedures are derived by the use of multivariate normal distribution and matrix operation. An example allocating four screening variables into two-sided single-stage, double-stage and triple-stage sequential screening procedures is illustrated using the derived generalized formulas to search for the best allocation.

Two-stage multiple comparisons with the average for normal distributions under heteroscedasticity

Abstract In this article we propose a two-stage procedure for multiple comparisons with the average for normal distributions under heteroscedasity. One-sided and two-sided confidence intervals are proposed. These intervals can be used to identify a subset which includes all no-worse-than-the-average treatments in an experimental design and to identify better-than-the-average, worse-than-the-average and not-much-different-from-the-average products in agriculture, stock market, medical research, and auto models. An upper limit of critical values are obatined using Bonferroni inequality. But the approximate values are shown to be too conservative compared with the simulation critical values in Table 7. Therefore, simulation critical values should be used in our multiple comparison procedures. Statistical tables and software programs are provided for use in practice.

Multiple comparisons with the average for normal distributions

SYNOPTIC ABSTRACTIn this article we propose some multiple comparison procedures with the average. Simultaneous confidence intervals are considered for normal distributions with common known or unknown variances. These procedures can be used to identify better-than-the-average, worse-than-the-average and not-much-different-from-the-average products in agriculture, stock market, medical research, and auto models. The percentage points for singular multivariate normal and multivariate t distributions are investigated. Furthermore, the case of normal distributions under heteroscedasticity is also developed. An example is given.

A computational algorithm for the evaluation on the lifetime performance index of products with Rayleigh distribution under progressive type I interval censoring

Abstract It is a very important topic these days to assessing the lifetime performance of products in manufacturing or service industries. Lifetime performance indices C L is used to measure the larger-the-better type quality characteristics to evaluate the process performance for the improvement of quality and productivity. The lifetimes of products are assumed to have Rayleigh distribution. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type I interval censored sample. The asymptotic distribution of this estimator is also developed. We use this estimator to build the new hypothesis testing algorithmic procedure with respect to a lower specification limit. Finally, two practical examples are given to illustrate the use of this testing algorithmic procedure to determine whether the process is capable.

Multiple comparisons of exponential location parameters with a control based on doubly censored sample under heteroscedasticity

ABSTRACT In this article, a one-sample procedure for multiple comparisons of exponential location parameters with a control under heteroscedasticity is proposed. The observations are obtained by doubly censored samples. A one-sided and two-sided confidence intervals are used to perform such multiple comparisons. Statistical tables of critical values and an example of comparing four drugs in treating leukemia are provided.

A hypothesis testing procedure for the evaluation on the lifetime performance index of products with Burr XII distribution under progressive type I interval censoring

ABSTRACT It is a very important topic these days to assessing the lifetime performance of products in manufacturing or service industries. Lifetime performance indices CL is used to measure the larger-the-better type quality characteristics to evaluate the process performance for the improvement of quality and productivity. The lifetimes of products are assumed to have Burr XII distribution. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type I interval censored sample. The asymptotic distribution of this estimator is also developed. We use this estimator to build the new hypothesis testing algorithmic procedure with respect to a lower specification limit. Finally, two practical examples are given to illustrate the use of this testing algorithmic procedure to determine whether the process is capable.

Multiple comparisons with the average for exponential location parameters based on doubly censored sample under heteroscedasticity

ABSTRACT In this paper, a one-stage multiple comparison procedures with the average for exponential location parameters based on the doubly censored sample under heteroscedasticity is proposed. These intervals can be used to identify a subset which includes all no-worse-than-the-average treatments in an experimental design and to identify better-than-the-average, worse-than-the-average and not-much-different-from-the-average products in agriculture, emerging market, pharmaceutical industries. The critical values are tabulated in a table for practical use. A simulation study on the confidence length and coverage probabilities is done. At last, an example of comparing four drugs in the treatment of leukemia is given to demonstrate the proposed procedures.