This paper concerns the design and analysis of the standard deviation control chart with estimated limits. We consider an extensive range of statistics to estimate the in-control standard deviation (Phase I) and design the control chart for real-time process monitoring (Phase II) by determining the factors for the control limits. The Phase II performance of the design schemes is assessed when the Phase I data are uncontaminated and normally distributed as well as when the Phase I data are contaminated. We propose a robust estimation method based on the mean absolute deviation from the median supplemented with a simple screening method. It turns out that this approach is efficient under normality and performs substantially better than the traditional estimators and several robust proposals when contaminations are present.

When in-control parameters are unknown, they have to be estimated using a reference sample. Due to the use of different reference samples in phase I, the control chart performance in phase II will vary across practitioners. This variation is especially large for small sample sizes. To prevent low in-control average run lengths, new corrections for Shewhart control charts are proposed that guarantee a minimum in-control performance with a specified probability. However, a minimum in-control performance guarantee generally lowers the out-of-control performance. To balance the tradeoff between in-control and out-of-control performance, the minimum performance threshold and specified probability can be adjusted as desired. The corrections are given in a closed form so that the bootstrap method, which has recently been suggested, is no longer required. The performance of our proposed correction is illustrated by simulating some practical situations. Furthermore, a comparison is made with tolerance intervals and self-starting control charts.

This article studies estimation methods for the location parameter. We consider several robust location estimators as well as several estimation methods based on a phase I analysis, i.e., the use of a control chart to study a historical dataset retrospectively to identify disturbances. In addition, we propose a new type of phase I analysis. The estimation methods are evaluated in terms of their mean-squared errors and their effect on the X control charts used for real-time process monitoring (phase II). It turns out that the phase I control chart based on the trimmed trimean far outperforms the existing estimation methods. This method has therefore proven to be very suitable for determining X phase II control chart limits.

Lean Six Sigma (LSS) is an originally industry-based methodology for cost reduction and quality improvement. In more recent years, LSS was introduced in health care as well. This article describes the experiences of the University Medical Center Groningen, the second largest hospital in the Netherlands, with LSS. It was introduced in 2007 to create the financial possibility to develop innovations. In this article, we describe how LSS was introduced, and how it developed in the following years. We zoom in at the traumatology department, where all main processes have been analyzed and improved. An evaluation after 5 years shows that LSS helped indeed reducing cost and improving quality. Moreover, it aided the transition of the organization from purely problem oriented to more process oriented, which in turn is helpful in eliminating waste and finding solutions for difficult problems. A major benefit of the program is that own employees are trained to become project leaders for improvement. Several people from the primary process were thus stimulated and equipped to become role models for continuous improvement

When designing control charts the in‐control parameters are unknown, so the control limits have to be estimated using a Phase I reference sample. To evaluate the in‐control performance of control charts in the monitoring phase (Phase II), two performance indicators are most commonly used: the average run length (ARL) or the false alarm rate (FAR). However, these quantities will vary across practitioners due to the use of different reference samples in Phase I. This variation is small only for very large amounts of Phase I data, even when the actual distribution of the data is known. In practice, we do not know the distribution of the data, and it has to be estimated, along with its parameters. This means that we have to deal with model error when parametric models are used and stochastic error because we have to estimate the parameters. With these issues in mind, choices have to be made in order to control the performance of control charts. In this paper, we discuss some results with respect to the in‐control guaranteed conditional performance of control charts with estimated parameters for parametric and nonparametric methods. We focus on Shewhart, exponentially weighted moving average (EWMA), and cumulative sum (CUSUM) control charts for monitoring the mean when parameters are estimated.

Problem: Health care today is facing serious problems: quality of care does not meet patients' needs and costs are exploding. Inefficient utilization of expensive operating rooms is one of the major problems in many hospitals worldwide. A benchmark study of 13 hospitals in the Netherlands and Belgium showed that, for a variety of reasons, surgery consistently started too late. Approach: For a short and a somewhat longer period, two selected hospitals from the benchmark study agreed to record the start times of the first operation each day for each of their operating rooms. In addition to start times, the improvement team also recorded potential influence factors (covariates, or X's). Statistical techniques used during the project were statistical graphics, Pareto charts, histograms, box plots, time-series plots, Box–Cox transformations, and ANOVA to determine possible influential factors. Results: It is shown that anesthesia technique and specialty are influence factors. However, the poor planning and scheduling process turned out to be the most important factor in the delay of start times. After introducing a new planning process, the hospitals involved were able to gain substantial cost savings, increased efficiency, and substantial reductions of the delay in start times for surgery.