A Shewhart‐type Control Scheme to Monitor Weibull Data without Subgrouping

Chen, Jung-Tai

doi:10.1002/qre.1542

Cited by 12 publications

(5 citation statements)

References 29 publications

(47 reference statements)

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“…Pascual and Zhang 29 presented a control chart to monitor the shape parameter based on the amplitude of random samples from the minimum value distribution. Chein 30 used a Shewhart control scheme based on two control charts to simultaneously monitor the shape and scale parameters of Weibull data without subgrouping. Already Dickinson 31 makes use of a CUSUM plot to monitor mean lifetime with censored data from a Weibull distribution.…”

Section: Introductionmentioning

confidence: 99%

About Shewhart control charts to monitor the Weibull mean based on a Gamma distribution

Vasconcelos

Quinino

et al. 2022

Quality & Reliability Eng

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A control chart for the mean of a process whose quality characteristic follows a Weibull distribution is evaluated. In this sense, a transformation that follows an exponential distribution is used involving the parameters of scale and form of a Weibull distribution. Such a transformation allows to obtain analytically the control limits to monitor the mean using the Gamma distribution. Compared with recent results in the literature, lower average run lengths after a change (ARL1) values are measured without the need to use intensive Monte Carlo simulation to obtain the control limits as well as to calculate the ARL1 values. A numerical example is presented in detail to illustrate the efficiency and effectiveness of the developed control chart.

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Section: Introductionmentioning

confidence: 99%

About Shewhart control charts to monitor the Weibull mean based on a Gamma distribution

Vasconcelos

Quinino

et al. 2022

Quality & Reliability Eng

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“…Because of their reliance on pre‐determined time periods, counting processes miss the opportunity for an outbreak decision that each event offers. Therefore, an alternative in the form of time between events (TBE) has emerged (see Kittlitz, Benneyan, Jones and Champ, Alemi and Neuhauser, Liu et al, Zimmermann et al, Sharma et al, Khoo and Xie, Xie et al, Dogu, Chen, Demirhan and Hamurkaroglu, Qu et al, Zhao and Gilbert, Shafae et al, Yang et al, Kumar and Chakraborti, and Cheng et al). A recent paper by Sparks et al demonstrated that event outbreaks were detected earlier using TBE as compared to counting processes.…”

Section: Introductionmentioning

confidence: 99%

Monitoring events with application to syndromic surveillance using social media data

Sparks

Joshi

Paris

et al. 2020

Engineering Reports

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Availability of time series data in different domains has resulted in approaches for outbreak detection. A popular alternative to detect outbreaks is to use daily counts of events. However, time between events (TBE) has proven to be a useful alternative, especially in the case of sudden, unexpected events. Past work that uses TBE for monitoring events assumes that the in-control number of events is up to 10 per day. In this article, we derive robust monitoring plans that are scalable when the in-control counts are higher than 10 per day but less than 100 per counting period (eg, day). TBE values are generally nonhomogeneous across days and within days. This makes the volume of data to train the technology a challenge, and this challenge increases the volume of data needed to design the charts. This article discusses these challenges and suggests solutions for data that are known to be Weibull-distributed. We present our results in two parts.The first is a simulated dataset that controls parameters of the plan such as the daily counts of events. We then show how the monitoring plans can be applied to the detection of syndromes (ie, disease outbreaks) using social media data.

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“…Recently, Guo and Wang proposed control charts for monitoring the Weibull shape parameter when the sample is type II censored. Chen suggested a Shewhart‐type scheme for monitoring both shape and scale parameters of Weibull data without subgrouping. Azam et al developed an

\overset{X}{true}

chart for Burr‐type XII (BTXII) distribution under repetitive sampling.…”

Section: Introductionmentioning

confidence: 99%

Shewhart control schemes with supplementary 2‐of‐(h + 1) side‐sensitive runs‐rules under the Burr‐type XII distribution

Malela‐Majika

Malandala

Graham

2018

Quality & Reliability Eng

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Control schemes that require strict distributional assumptions are called parametric control schemes. When the distributional assumptions fail to hold, nonparametric control schemes and other schemes based on more flexible probability distributions are needed. The traditional Shewhart control scheme has been improved upon using various techniques, one being the addition of non–side‐sensitive (NSS) and side‐sensitive runs‐rules. Many authors showed that side‐sensitive runs‐rules schemes are significantly superior to NSS runs‐rules schemes. In this paper, we propose side‐sensitive Shewhart‐type trueX¯ schemes supplemented with 2‐of‐(h + 1) standard and improved runs‐rules (where h is a nonzero positive integer) under the violation of the normality assumption for monitoring the process mean. The zero‐state and steady‐state performances of the proposed schemes are investigated using a Markov chain approach. It is observed that the proposed schemes outperform the existing schemes in many situations and possess very interesting zero‐state and steady‐state properties under normal and non‐normal distributions. An illustrative example is provided to facilitate the design and implementation of the proposed schemes.

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A Shewhart‐type Control Scheme to Monitor Weibull Data without Subgrouping

Cited by 12 publications

References 29 publications

About Shewhart control charts to monitor the Weibull mean based on a Gamma distribution

About Shewhart control charts to monitor the Weibull mean based on a Gamma distribution

Monitoring events with application to syndromic surveillance using social media data

Shewhart control schemes with supplementary 2‐of‐(h + 1) side‐sensitive runs‐rules under the Burr‐type XII distribution

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