The concept of quality has gained increasing importance over the last decades. Regarding the production process of a company, the quality control implementation allows companies to offer a higher quality product, which has positive influence on customer satisfaction. This paper aims to reflect the importance of statistical methods for quality control. Based on the two broad areas of statistical inference, parameter estimation and hypothesis testing, we demonstrate the usefulness of such methods in problem solving when the proportion of defective items is considered.

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A control chart is a very common tool used to monitor the quality of business processes. An estimator of the process variability is generally considered to obtain the control limits of a trueX¯ chart when parameters of the process are unknown. Assuming Monte Carlo simulations, this paper first compares the efficiency of the various estimators of the process variability. Two empirical measures used to analyze the performance of control charts are defined. Results derived from various empirical studies reveal the existence of a linear relationship between the performance of the various estimators of the process variability and the performance of trueX¯ charts. The various Monte Carlo simulations are conducted under the assumption that the process is in both situations of in‐control and out‐of‐control. Copyright © 2015 John Wiley & Sons, Ltd.

The problem of missing data is a common feature in any study, and a single imputation method is often applied to deal with this problem. The first contribution of this paper is to analyse the empirical performance of some traditional single imputation methods when they are applied to the estimation of the Gini index, a popular measure of inequality used in many studies. Various methods for constructing confidence intervals for the Gini index are also empirically evaluated. We consider several empirical measures to analyse the performance of estimators and confidence intervals, allowing us to quantify the magnitude of the non-response bias problem. We find extremely large biases under certain non-response mechanisms, and this problem gets noticeably worse as the proportion of missing data increases. For a large correlation coefficient between the target and auxiliary variables, the regression imputation method may notably mitigate this bias problem, yielding appropriate mean square errors. We also find that confidence intervals have poor coverage rates when the probability of data being missing is not uniform, and that the regression imputation method substantially improves the handling of this problem as the correlation coefficient increases.

The concept of quality has gained increasing importance over the last decades. Regarding the production process of a company, the quality control implementation allows companies to offer a higher quality product, which has positive influence on customer satisfaction. This paper aims to reflect the importance of statistical methods for quality control. Based on the two broad areas of statistical inference, parameter estimation and hypothesis testing, we demonstrate the usefulness of such methods in problem solving when the proportion of defective items is considered.