Geometric charts with bootstrap-based control limits using the Bayes estimator

Abstract

Geometric charts are effective in monitoring the fraction nonconforming in high-quality processes. The incontrol fraction nonconforming is unknown in most actual processes; therefore, it should be estimated using the Phase I sample. However, if the Phase I sample size is small the practitioner may not achieve the desired in-control performance because estimation errors can occur when the parameters are estimated. Therefore, in this paper, we adjust the control limits of geometric charts with the bootstrap algorithm to improve the in-control performance of charts with smaller sample sizes. The simulation results show that the adjustment with the bootstrap algorithm improves the in-control performance of geometric charts by controlling the probability that the in-control average run length has a value greater than the desired one. The out-of-control performance of geometric charts with adjusted limits is also discussed.

Percentile bootstrap control chart for monitoring process variability under non-normal processes

“…In recent years, the bootstrap control charts are considered best using Bayes estimator in high quality processes for monitoring the fraction nonconforming (cf., [28]). The performance of different types of robust estimators is also addressed by Moheghi et al [29], Dizicheh et al…”

Weighted-Likelihood-Ratio-Based EWMA Schemes for Monitoring Geometric Distributions

“…Zhang et al [10] addressed several theoretic issues related to the design of geometric schemes. Based on geometric distribution, Hong and Lee [11] investigated the performance of Bayes estimator and maximum likelihood estimation for the geometric scheme, and Kim and Lee [12] used the Bayes estimator to design a geometric scheme with bootstrap-based control limits. Moreover, Mohammadian et al [13] utilized riskadjusted schemes to monitor health-care systems.…”