Moving range EWMA control charts for monitoring the Weibull shape parameter

A control chart based on double exponentially weighted moving average and Benjamini‐Hochberg multiple testing procedure is proposed that controls the false discovery rate (FDR). The proposed control chart is based on probabilities (or P values) to accept or reject the null hypothesis of the underlying process is in control. To make a decision, instead of using only the current probability, previous “m” probabilities are considered. The performance of the control chart is evaluated in terms of average run length (ARL) using Monte Carlo simulations. Procedure for estimation of parameters used in the control chart is also discussed. The proposed control chart is compared with previous control charts and found to be more efficient in controlling the false discovery rate.

Section: Introductionmentioning

confidence: 99%

An efficient double exponentially weighted moving average Benjamini‐Hochberg control chart to control false discovery rate

Nawaz¹,

Azam

Aslam

2019

“…Moreover, a host of researchers have considered the problems related to monitoring the shape parameter of Weibull and related models in the recent times. Akhundjanov et al considered some moving range EWMA control schemes for monitoring the Weibull shape parameter. Chan et al addressed monitoring the Weibull shape parameter with type II censored data.…”

Section: Introductionmentioning

confidence: 99%

Design and comparison of some Shewhart‐type schemes for simultaneous monitoring of Weibull parameters

Gong

Mukherjee

2018

Weibull distribution is one of the most important probability models used in modeling time between events, system reliability, and particle sizes, among others. Therefore, efficiently and consequently monitoring certain changes in Weibull process is considered as an important research topic. Various statistical process monitoring schemes have been developed for monitoring different process parameters, including some for Weibull parameters. Most of these schemes are, however, designed to monitor and control a single process parameter, although there are two important model parameters for Weibull distribution. Recently, several researchers studied various schemes for jointly monitoring the mean and variance of a normally distributed process using a single plotting statistic. Nevertheless, there is still dearth of researches in joint monitoring of non‐normal process parameters. In this context, we develop some control schemes for simultaneously monitoring the scale and shape parameters of processes that follow the Weibull distribution. Implementation procedures are developed, and performance properties of various proposed schemes are investigated. We also offer an illustrative example along with a summary and recommendations.

“…With transforming the Weibull data to the SEV distribution, the one‐sided and two‐sided control charts based on the sample range of a random sample from the SEV distribution with complete and type 2 censored data are developed by Pascual and Zhang and Pascual and Li, respectively. Akhundjanov and Pascual presented the EWMA control charts based on moving range statistics for single observations. Chan et al developed the one‐sided and two‐sided control charts based on an unbiased estimator of σ = 1/ β under a fixed scale parameter for type 2 censored data.…”

Section: Introductionmentioning

confidence: 99%

An exponentially weighted moving average chart based on likelihood‐ratio test for monitoring Weibull mean and variance with subgroups

Wang

Cheng

2017

Monitoring changes in the Weibull mean and variance simultaneously is of interest in quality control. The mean and variance of a Weibull process are determined by its shape and scale parameters. Most studies are focused on monitoring the Weibull scale parameter with fixed shape parameter or the Weibull shape parameter with fixed scale parameter. In this paper, we propose an exponentially weighted moving average chart based on the likelihood‐ratio test and an inverse error function called ELR chart to monitor changes in the Weibull mean and variance simultaneously. The simulation approach is used to derive the average run length. We compare our proposed chart with other existing control charts for 3 cases, including scale parameter changes with fixed shape parameter, shape parameter changes with fixed scale parameter, and both parameters changes. The results show that the ELR chart outperforms the other control charts in terms of average run length in most cases. Two numerical examples are used to illustrate the applications of the proposed control chart.