Search

The vast majority of control schemes related to the sequential probability ratio test (SPRT) are designed for the purpose of monitoring only the process mean. Nonetheless, most manufacturing processes are vulnerable to external factors that cause the process mean and variability to change simultaneously. It is, therefore, crucial to consider a joint scheme for monitoring both the location and scale parameters of a production process. In this article, we develop a scheme that combines both mean and variance information in a single SPRT, known as the omnibus SPRT (OSPRT) chart. Expressions for the run-length properties of the OSPRT chart are derived by means of the Markov chain approach. We also propose optimal designs for the OSPRT chart based on two different metrics, i.e. by minimising the average time to signal and the average extra quadratic loss. Through a comprehensive analysis, this article reveals that the optimal OSPRT chart outperforms the classical $ \bar{X} $ X ¯ -S, weighted-loss cumulative sum, absolute-value SPRT, and two maximum weighted-moving-average-type charts. The optimal OSPRT chart also has the advantage of collecting a small number of samples on average before producing a decision. Finally, the implementation of the OSPRT chart is presented with a wire bonding industrial dataset. [ABSTRACT FROM AUTHOR]

There have been some advances in multivariate control charts in recent years. This paper presents a new simultaneous scheme for monitoring both the mean and variability of a multivariate normal process in a single chart, which is developed by improving and modifying another recently proposed scheme. We not only propose a new control scheme but also make it adaptive by varying all control chart parameters. Our scheme, for the first time, considers the process variability in two forms: "covariance matrix" and "multivariate coefficient of variation (MCV)". This scheme, again for the first time, considers simultaneous monitoring of the MCV with another process parameter (in our case, the mean vector). In addition, we develop a Markov chain model to compute the average run length and average time to signal values. We conduct extensive numerical analyses to measure the performance of the proposed scheme in two scenarios of process variability. At last, we present a numerical example by using a real dataset from a healthcare process to illustrate how the scheme can be implemented in practice. [ABSTRACT FROM AUTHOR]

Time-between-events (TBE) charts use the time interval T between events to monitor process shifts (or failure rates λ). This paper presents a two-sided TBE cumulative sums (CUSUM) chart called a weighted CUSUM(WCUSUM)chart for detecting either a deterioration (decrease in T) or an improvement (increase in T) in the condition of a process. A new kind of WCUSUM chart that has an additional charting power parameter w is proposed here. A WCUSUM chart’s efficiency can be improved by using the parameter w, based on an estimated value of the mean shift. In addition, a methodology and optimal design are presented for minimising the average loss. Construction of the WCUSUM chart is illustrated by considering a random shift δ in λ (including both increasing and decreasing shifts) in the design. [ABSTRACT FROM AUTHOR]

This paper examines the exponentially weighted moving average (EWMA)chart with estimated process parameters. As the run length distribution is skewed when the process is in-control or slightly out-of-control, the average run length (ARL) provides less meaningful interpretation of a chart’s performance. Therefore, in this paper, the median run length (MRL) and expected MRL (EMRL) are used as alternative performance criteria. Additionally, the methodology for computing the EMRL of the EWMAchart with known process parameters is presented. Since the performance of the EWMAchart is affected by estimation error, a study on the minimum number of Phase-I samples required so that the chart with estimated parameters has a desired performance is conducted. As this study reveals that a large number of Phase-I samples are needed, optimal design procedures for minimising the out-of-control MRL and EMRL of the EWMAchart with estimated process parameters are suggested. By using these proposed procedures, the EWMAchart with estimated parameters will have a closer performance to its known parameters counterpart, even with a reasonable number of Phase-I samples. The construction of the MRL based EWMAchart with estimated parameters is illustrated using real data and compared with the corresponding chart based on ARL. [ABSTRACT FROM PUBLISHER]