Identifying the period of a step change in high‐yield processes

Abstract

Quality control charts have proven to be very effective in detecting out-of-control states. When a signal is detected a search begins to identify and eliminate the source(s) of the signal. A critical issue that keeps the mind of the process engineer busy at this point is determining the time when the process first changed. Knowing when the process first changed can assist process engineers to focus efforts effectively on eliminating the source(s) of the signal. The time when a change in the process takes place is referred to as the change point. This paper provides an estimator for a period of time in which a step change in the process non-conformity proportion in highyield processes occurs. In such processes, the number of items until the occurrence of the first non-conforming item can be modeled by a geometric distribution. The performance of the proposed model is investigated through several numerical examples. The results indicate that the proposed estimator provides a reasonable estimate for the period when the step change occurred at the process non-conformity level.

A Review and perspective on surveillance of Bernoulli processes

“…For a high quality process with Bernoulli data, this is a difficult problem. See Noorossana et al for a change point method for the CCC chart. The performance of many of the standard methods has not been adequately compared based on the steady‐state ANOS metric with the random‐shift model. We strongly recommend that the Bernoulli CUSUM chart be included in all comparisons. Besides the work of Ryan et al , no research has been carried out on the extensions of the Bernoulli methods to multinomial data with more than two outcomes. More work is needed on the robustness of the various methods with respect to violations of the assumption of independence of the Bernoulli observations and the assumption of a constant in‐control value of p . The risk‐adjusted approach of Steiner et al allows the in‐control Bernoulli probability to vary from item‐to‐item.…”

Change Point Estimation in the Mean of Multivariate Linear Profiles with No Change Type Assumption via Dynamic Linear Model

“…Change types are divided into step (single step and multiple steps), drift, monotonic (isotonic and antitonic), and sporadic changes. Step change point estimation using maximum likelihood approach has been considered by Samuel et al ., Pignatiello and Samuel, and Noorossana et al . In order to estimate drift change point, Perry and Pignatiello and Perry et al .…”

Bayesian change point estimation in Poisson-based control charts

“…ML estimators have also been extended for step change scenarios in correlated Poisson observations (Niaki and Khedmati 2012;2013a;Sharafi et al 2013). Similar methods were extended to other attributes including binary data (Perry et al 2007b;Noorossana et al 2009;Amiri et al 2011;Hou et al 2013;Niaki and Khedmati 2013b).…”