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Control charts are the most popular tool to detect the occurrence of an assignable cause in a production process. Traditional control charts are based on the approximation with the normal distribution. In many practical situation, however, assuming normality is not adequate. Under these situations, the use of traditional control chart may lead to erroneous decisions. For handling non-normal process distributions one may use non-parametric control charts, however these methods are rather inefficient. Another approach is to use a generalized distribution. In this work the univariate g -and- h distribution is used to approximate non-normal process distributions.

Economic reliability group acceptance sampling plans are developed assuming that the lifetime of a submitted product follows the inverse-Rayleigh or log-logistic distribution. For various acceptance numbers, sample size and producer's risks, plans with minimum experimental time are obtained that are smaller than for conventional plans. The results are illustrated by tables and examples.

This paper considers the problem of estimating the mean μ Y of a finite population of the study variable Y using information on an auxiliary variable X . Motivated by Singh and Ruiz Espejo two classes of estimators (product-to-product and ratio-to-ratio) are proposed and their properties under large sample approximation are derived. Double sampling versions of the suggested classes of estimators are also presented. Numerical studies are used to demonstrate the performance of the suggested estimators compared with other estimators.

One-sided cumulative sum control charts are constructed for controlling the parameters of a random variable with zero-truncated binomial distribution. It is observed that the Average Run Length (ARL) of the resulting control charts change considerably for a slight shift in the parameters of the distribution under study.

Moments of order statistics and an ordered sample are used to define a test statistic for the null hypothesis that the considered random variable has half logistic distribution. The percentiles of the test statistic are evaluated and the power of the test is computed. The developed statistic is used to construct confidence intervals for the scale parameter of the population. The results are illustrated by an example.

This article investigates the quality loss index QLI proposed by Samajdwar et al. for normal variables. The probability distribution of QLI and its components are obtained. The first component represents a quality loss index for the process variability, while the second component represents a quality loss index for the shift in the process mean. Moreover, a method is derived allowing to estimate the nonconformance probability in either side of the target value for normal variables. Finally, an additive property of the quality loss index is established, which enables to define an composite quality loss index and use it within a continual process improvement strategy. The composite quality loss index indicates the process performance and identifies the parameter(s) which show a potential for improvement.

In this paper, new quality control charts for the mean are considered using robust extreme ranked set sampling ( RERSS ) method. The new charts are compared with the classical control charts using simple random sampling ( SRS ) and ranked set sampling methods ( RSS ). It is found that the RERSS charts perform better than all other charts based on SRS and RSS methods in terms of their average run length ( ARL ).