CUSUM Charts for Monitoring the Characteristic Life of Censored Weibull Lifetimes

Dickinson, Rebecca M.; Roberts, Denisa; Driscoll, Anne R.; Woodall, William H.; Vining, G. Geoffrey

doi:10.1080/00224065.2014.11917976

Cited by 46 publications

(52 citation statements)

References 14 publications

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“…For online monitoring, as the carbon fiber data are based on single observation, the CUSUM chart in Dickinson et al is selected for comparison. The settings are the same with those in the simulation studies, and the EWMA parameter

λ

is fixed at

0.05

.…”

Section: A Real Examplementioning

confidence: 99%

“…(2), the LRT statistic for a single observation can be easily constructed when the observed likelihood is achieved. To realize sequential detection, motivated by Agostinelli and Markatou [1], Qiu et al [22], Zhou et al [34] and recalling the popular exponential weighted sum average (EWMA) scheme in quality control, we consider the weighted sum of log-likelihoods (denoted as wl obs (η, β; y, λ)) by the following expression wl obs (η, β; y, λ) = t j =0 w j ,λ l obs (η, β; y j ) (5) where λ is the EWMA smoothing parameter ranging from (0, 1], l obs (η, β; y j ) is the observed log-likelihood of each observation and w j ,λ = λ(1 − λ) t−j is exactly the weight of the EWMA strategy. When j = 0, the mean of the censored Weibull distribution and the noncensoring rate are selected as the "observation" {y 0 , δ 0 }, respectively.…”

Section: Censored Observation-based Weighted-likelihood Control Chartmentioning

confidence: 99%

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Monitoring censored lifetime data with a weighted-likelihood scheme

Zhang

Tsung

Xiang

2016

Naval Research Logistics

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Lifetime experiments are common in many research areas and industrial applications. Recently, process monitoring for lifetime observations has received increasing attention. However, some existing methods are inadequate as neither their in control (IC) nor out of control (OC) performance is satisfactory. In addition, the challenges associated with designing robust and flexible control schemes have yet to be fully addressed. To overcome these limitations, this article utilizes a newly developed weighted likelihood ratio test, and proposes a novel monitoring strategy that automatically combines the likelihood of past samples with the exponential weighted sum average scheme. The proposed Censored Observation‐based Weighted‐Likelihood (COWL) control chart gives desirable IC and OC performances and is robust under various scenarios. In addition, a self‐starting control chart is introduced to cope with the problem of insufficient reference samples. Our simulation shows a stronger power in detecting changes in the censored lifetime data using our scheme than using other alternatives. A real industrial example based on the breaking strength of carbon fiber also demonstrates the effectiveness of the proposed method. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 631–646, 2017

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λ

is fixed at

0.05

.…”

Section: A Real Examplementioning

confidence: 99%

Section: Censored Observation-based Weighted-likelihood Control Chartmentioning

confidence: 99%

Monitoring censored lifetime data with a weighted-likelihood scheme

Zhang

Tsung

Xiang

2016

Naval Research Logistics

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“…Zhang and Chen develop an exponentially weighted moving average approach for such data. Dickinson et al . propose a CUSUM approach and provide a detailed comparison of the various approaches.…”

Section: Future Directionsmentioning

confidence: 99%

Recent Advances and Future Directions for Quality Engineering

Vining

Külahçı

Pedersen

2015

Quality & Reliability Eng

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The origins of quality engineering are in manufacturing, where quality engineers apply basic statistical methodologies to improve the quality and productivity of products and processes. In the past decade, people have discovered that these methodologies are effective for improving almost any type of system or process, such as financial, health care, and supply chains.This paper begins with a review of key advances and trends within quality engineering over the past decade. The second part uses the first part as a foundation to outline new application areas for the field. It also discusses how quality engineering needs to evolve in order to make significant contributions to these new areas.

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“…Let suppose that at the t-th discrete moment a sample .y i , x i /, i D 1, ..., n, from model (3) is available. Adjustments to ancillaries (8) and (9) and pivotal (12) can be used to design simple control schemes for detecting departures from the value D 0 (or, equivalently, ' D ' 0 ). The design of the proposed charts is based on the approximations of order of O P .n 3=2 / given by (21), (22), and (23).…”

Section: Control Charts For Monitoring the Weibull Regression Model Smentioning

confidence: 99%

Monitoring the Shape Parameter of a Weibull Regression Model in Phase II Processes

Panza

Vargas

2014

Qual. Reliab. Engng. Int.

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In this paper, the interest is focused on monitoring profiles with Weibull distributed-response and common shape parameter in phase II processes. The monitoring of such profiles is completely possible by taking the natural logarithm of the Weibull-distributed response. This is equivalent to characterize the correspondent process by an extreme value linear regression model with common scale parameter D 1 . It was found out that from the monitoring of the common log-scale parameter of the extreme value linear regression model, with the help of a simple scheme, it can be obtained important information about the deterioration of the entire process assuming theˇcoefficients as nuissance parameters that do not have to be known but stable. Control charts are based on the relative log-likelihood ratio statistic defined for the log-scale parameter of the log-transformation of the Weibull-distributed response and its respective signed square root. It was also found out that some existing adjustments are needed in order to improve the accuracy of using the distributional properties of the monitoring statistics for relatively small and moderate sample sizes. Simulation studies suggest that resulting charts have appealing properties and work fairly acceptable when non-large enough samples are available at discrete sampling moments. Detection abilities of the studied corrected control schemes improve when sample size increases.Weibull model is fairly flexible and has been found to provide a good description of many types of lifetime data. It has been widely used to model durability of manufactured items as automobile components or the occurrence of tumors in biological and medical studies. Some applications even involve a set of variables that could be correlated to lifetimes. The most effective way to assess the effect of these explanatory variables on lifetimes is by using an appropriate regression model. The WRM with common shape parameter is the most commonly used parametric model to do so.Control charts for monitoring Weibull processes have been developed in previous years. Most of the existing literature suggests methodologies for monitoring functions of the Weibull parameters assuming that one or more of them are known and stable. One of the disadvantages of monitoring functions of Weibull parameters, the mean for example, is the fact that we do not know which parameter shifted when a possible out-of-control signal occurs. Among other authors, for instance, Zhang and Chen 7 propose onesided exponentially weighed moving average (EWMA) charts and Johnson 8 propose cumulative sum (CUSUM) charts for detecting shifts in the Weibull mean assuming that the shape parameter is known. In more recent research works, Dickinson et al. 9 present charting procedures for monitoring changes in the scale parameter of Type I right-censored Weibull lifetime data for a fixed value of the shape parameter. Shafae et al. 10 compare CUSUM control charts for monitoring the mean of time between events of Weibull-distributed observations. The moni...

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CUSUM Charts for Monitoring the Characteristic Life of Censored Weibull Lifetimes

Cited by 46 publications

References 14 publications

Monitoring censored lifetime data with a weighted-likelihood scheme

Monitoring censored lifetime data with a weighted-likelihood scheme

Recent Advances and Future Directions for Quality Engineering

Monitoring the Shape Parameter of a Weibull Regression Model in Phase II Processes

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