November 1, 2015 Version 0.5.2 Date 2015-10-31 Title Statistical Process Control -Collection of Some Useful Functions Author Sven Knoth Maintainer Sven Knoth Depends R (>= 1.8.0) Description Evaluation of control charts by means of the zero-state, steady-state ARL (Average Run Length) and RL quantiles. Setting up control charts for given in-control ARL. The control charts un...

RU4LEtWH&!4sl-A'ERG RU4LEtWH&!4sl Fig. 1. Fig. 1. Entropy per cell as function of average run length. Entropy per cell as function of average run length. distributed: for tl 2 0 for tl < 0 where t, is the (continuous) run length. The average run length is f, = 6. (20) Now, suppose the continuous run length tl is quantized to obtain the discrete run length t : t = [t1] + 1 (21) where [tl] = larg...

The aim of this study is to develop an automatic control loop monitoring system. The first step includes the detection of changes and of oscillations in the control error and in the control signal. To determine the parameters of the statistical change detection test (a CUSUM test), the average run length (ARL) function is exploited. To detect oscillations, a modified version of Hägglund’s appro...

In this paper, we address the problem of online change detection of Markov-modulated time series models. For simplicity, we look at Auto-regressive time-series models the parameters of which are modulated by a nite-state homogeneous Markov chain. We propose a Cumulative Sum based statistical test to detect abrupt changes is such processes. Computation of average run length functions, in particu...

The Markov-Bernoulli geometric distribution is obtained when a generalization, as a Markov process, of the independent Bernoulli sequence of random variables is introduced by considering the success probability changes with respect to the Markov chain. The resulting model is called the MarkovBernoulli model and it has a wide variety of application fields. In this study, some characterizations a...

At the start of a production run, the parameters of the distribution of a quality characteristic are frequently unknown. If the quality characteristic should by monitored on-line by means of a control chart and the production run length is too short, then it is impossible to get a sufficient Phase I number of samples allowing for the correct estimation of parameters and the evaluation of the ch...

BACKGROUND There is considerable recent interest in the monitoring of individual surgeon or hospital surgical outcomes. If one aggregates data over time and assesses performance with a funnel plot, then the detection of any process deterioration or improvement could be delayed. The variable life adjusted display (VLAD) is widely used for monitoring on a case-by-case basis, but we show that use ...

The control chart is a very popular tool of statistical process control. It is used to determine the existence of special cause variation to remove it so that the process may be brought in statistical control. Shewhart-type control charts are sensitive for large disturbances in the process, whereas cumulative sum (CUSUM)–type and exponentially weighted moving average (EWMA)–type control charts ...

In order to provide a balanced protection against range of shift sizes in high-quality processes, new one-sided adaptive truncated exponentially weighted moving average (ATEWMA) control chart with known and estimated parameters is developed for monitoring time-between-events (TBE) data. A dedicated Markov chain model established evaluating the run length properties operating conditions. Further...