Search

Distribution-free Shewhart-type control charts are proposed for future sample percentiles based on a reference sample. These charts have a key advantage that their in-control run length distribution do not depend on the underlying continuous process distribution. Tables are given to help implement the charts for given sample sizes and false alarm rates. Expressions for the exact run length distribution and the average run length (ARL) are obtained using expectation by conditioning. Properties of the charts are studied, via evaluations of the run length distribution and the ARL. These computations show that in certain cases the proposed charts have attractive ARL properties over standard parametric charts such as the CUSUM and the EWMA. Calculations are illustrated with several short examples. Also included is a numerical example, using data from Montgomery (1997), where an application of the precedence chart produced slightly different results.

An overview of the literature on some nonparametric or distribution-free quality control procedures is presented for univariate data. A nonparametric control chart is defined along with some general motivations and formulations. Various advantages of these charts are highlighted while some disadvantages of the more traditional, distribution-based. control charts are pointed out. Specific observations are made in the course of the review of articles and constructive criticism is offered. so that opportunities for further research can be identified. Connections to some areas of active research are made. such as sequential analysis, that are of relevance to process control. It is hoped that this article would lead to a wider acceptance of distribution-free control charts among the practitioners and would serve as an impetus to future research and development in this area.

Precedence tests are simple yet useful nonparametric tests based on two specified order statistics from two independent random samples or, equivalently, on the count of the number of observations from one of the samples preceding some order statistic of the other sample. The probability that an order statistic from the second sample exceeds an order statistic from the first sample is termed the precedence probability. When the distributions are the same, this probability can be calculated exactly, without any specific knowledge of the underlying common continuous distribution. This fact can be utilized to set up nonparametric prediction intervals in a number of situations. In this paper, prediction intervals are considered for the number of second sample observations that exceed a particular order statistic of the first sample. To aid the user, tables are provided for small sample sizes, where exact calculations are most necessary. The same tables can be used to implement a precedence test for small sample sizes.

Precedence tests are considered in the context of four classes of one-sided Lehmann-type alternatives: $G=F^k (k>1); G=1- (1-F)^k (k1)$, where F and G are two continuous cumulative distribution functions. If an optimal precedence test (one with the maximal power) is determined for one of these four classes, the optimal tests for the other classes of alternatives can be derived. Application of this is given using the results of Lin and Sukhatme (1992) who derived the best precedence test for testing the null hypothesis that the lifetimes of two types of items on test have the same distribution. The test has maximum power for fixed k in the class of alternatives $G=1-(1-F)^k)$ with $k

Precedence tests are simple yet useful nonparametric tests based on two specified order statistics from independent random samples or, equivalently, on the count of the number of observations from one of the samples preceding some order statistic of the other sample. The probability that an order statistic from the second sample exceeds an order statistic from the first sample is termed the precedence probability. When the distributions are the same, this probability can be calculated exactly, without any specific knowledge of the underlying common continuous distribution. This fact can be utilized to set up nonparametric prediction intervals in a number of situations. In this paper, prediction intervals are considered for the number of second sample observations that exceed a particular order statistic of the first sample. To aid the user, tables are provided for small sample sizes, where exact calculations are most necessary. The same tables can be used to implement a precedence test for small sample sizes. Finally, a combinatorial identity is proved. Keywords: Distribution-free; Extremes; Exceedance and Precedence; Nonparametric; Order statistics.

Precedence tests are simple yet robust nonparametric procedures useful for comparing two or more distributions. In this paper precedence type tests are considered when the data contain some right-censored observations. Generalizing the precedence statistic for uncensored data, the precedence tests for censored data are based on the Kaplan-Meier estimators of the respective distribution functions and the corresponding quantile functions. An overview of the literature is given for the two-sample as well as some multi-sample problems. Some further problems are indicated.

An overview of some nonparametric procedures based on precedence (or exceedance) statistics is given. The procedures include both tests and confidence intervals. In particular, the construction of some simple distribution-free confidence bounds for location difference of two distributions with the same shape is considered and some properties are derived. The asymptotic relative efficiency of an asymptotic form of the corresponding test relative to Wilcoxon's two-sample rank-sum test and the two-sample Student's t-test is given for various cases. Some K -sample problems are discussed where precedence type tests are useful, along with a review of the literature.