Major difficulties in the study of high-quality processes with traditional process monitoring techniques are a high false alarm rate and a negative lower control limit. The purpose of time-between-events control charts is to overcome existing problems in the high-quality process monitoring setup. Time-between-events charts detect an out-of-control situation without great loss of sensitivity as compared with existing charts. High-quality control charts gained much attention over the last decade because of the technological revolution. This article is dedicated to providing an overview of recent research and presenting it in a unifying framework. To summarize results and draw a precise conclusion from the statistical point of view, cross-tabulations are also given in this article. Copyright © 2016 John Wiley & Sons, Ltd.

An Overview of Control Charts for High‐quality Processes

Gamma charts for time between events are very useful in the high-quality processes, which monitor the time until the rth event. The average time to signal (ATS) is adopted to evaluate the performance of Gamma charts, because it reflects both the number and the sampling interval of samples inspected until an out-of-control signal occurs. An ATS-unbiased design for Gamma charts with known parameters is proposed based on the hypothesis test of the scale parameter. For the phase I monitoring, a new ATS-unbiased design with unknown parameters is developed, and a sequential sampling scheme is adopted to start process monitoring as soon as possible. Some specific guidelines to stop updating the control limits are suggested from the convergence of the width between control limits with different phase I sample sizes. Finally, a real example is illustrated to demonstrate the implementation of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.

Design of Gamma Charts Based on Average Time to Signal

Time-between-events control charts are commonly used to monitor high-quality processes and have several advantages over the ordinary control charts. In this article, we present some new control charts based on the renewal process, where a class of absolutely continuous exponentiated distributions is assumed for the time between events. This class includes the generalized exponential, generalized Rayleigh, and exponentiated Pareto distributions. Although we discuss the design structure for all the mentioned distributions, our main focus will be on the generalized exponential distribution due to its practical relevance and popularity. Since the generalized exponential distribution is a generalization of the traditional exponential distribution, the new control chart is more flexible than the existing exponential time-between-events charts. The control chart performance is evaluated in terms of some useful measures, including the average run length (ARL), the expected quadratic loss, continuous ranked probability, and the relative ARL. The effect of parameter estimation using the maximum likelihood and Bayesian methods on the ARL is also discussed in this article. The study also presents an illustrative example and 4 case studies to highlight the practical relevance of the proposal.

Time‐between‐events control charts for an exponentiated class of distributions of the renewal process

Monitoring of time between events with a double generally weighted moving average control chart

In high-yield processes with a low defect rate, the recommendation is to monitor the times between events (TBE) with variables control charts in order to overcome the weaknesses of conventional attribute control charts. In this paper, we incorporate supplementary runs rules into one of the existing Shewhart-type TBE charts, namely the tr -chart, in order to improve its small to moderate size-shift detection ability. Moreover, because the existing tr -chart based on probability limits is biased, we provide a procedure for designing a tr -chart, with or without runs rules, that is unbiased. The performance of several tr -charts with runs rules is investigated, whereas comparisons with EWMA and CUSUM charts are also given. It is seen that some of the runs rules enhanced tr -charts perform substantially better. A real-data example is provided for illustration and some concluding remarks are given.

Improved Shewhart-Type Charts for Monitoring Times Between Events

Exponential charts based on time-between-events (TBE) data are widely investigated and applied in various fields. The average time to signal (ATS) is used instead of the average run length to evaluate the performance of TBE charts, since the ATS involves both the number and the time of samples inspected until a signal occurs. An ATS-unbiased exponential control chart is proposed when the in-control parameter is known. Considering the need in practice to start monitoring a production process as soon as possible, a sequential sampling scheme is adopted and the in-control parameter is estimated by an unbiased and consistent estimator. Some specific guidelines to stop updating control limits are obtained from the relationship between the phase I sample size and the actual false alarm rate. Finally, two real examples are given to illustrate the implementation and efficiency of the proposed method.

Huan Yu

Papers

Design of exponential control charts based on average time to signal using a sequential sampling scheme

Design of Gamma Charts Based on Average Time to Signal