Risk-embedded Bayesian acceptance sampling plans via conditional value-at-risk with Type II censoring

Hsieh, Chung-Chi; Lu, Yu-Ting

doi:10.1016/j.cie.2013.04.012

Cited by 22 publications

(9 citation statements)

References 48 publications

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“…where TCðn; r; l; T 0 Þ is the total cost which consists of four components and the equality constraint as shown in ( 8) ensures that the producer's and consumer's risks are maintained at the levels already agreed-upon. The four cost components that constitutes the aggregate cost function are formulated using evidence from the literature (Kwon, 1996a;Hsieh and Lu, 2013). The following are the cost components that constitute the aggregate cost: hai the acceptance cost, hbi the rejection cost, hci the time-consumption cost and hdi the inspection cost.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Evidence from the literature suggests that the rejection cost is the cost due to units that are not put on test (Kwon, 1996a;Hsieh and Lu, 2013). Therefore if we consider c r as the cost units for items that are not tested, then, the rejection cost can be expressed as…”

Section: Problem Formulationmentioning

confidence: 99%

“…Using a Bayesian approach, Kwon (1996aKwon ( , 1996b pioneered the development of RASPs under Type-II censoring scheme for products under warranty and included warranty cost as acceptance cost while designing the plan. Eventually, Huang et al (2008), Tsai et al (2008) and Hsieh and Lu (2013) adopted the idea of inclusion of warranty cost as acceptance cost for designing RASPs for warrantied products using Type-II censoring scheme. Since most of the products under warranty are highly reliable, using Type-II censoring scheme to design the sampling plans for such products can be very time consuming.…”

Section: Introductionmentioning

confidence: 99%

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Optimum reliability acceptance sampling plan using Type-I generalized hybrid censoring scheme for products under warranty

Chakrabarty

Chowdhury

Roy

2020

IJQRM

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PurposeThe purpose of this paper is to design an optimal reliability acceptance sampling plan (RASP) using the Type-I generalized hybrid censoring scheme (GHCS) for non-repairable products sold under the general rebate warranty. A cost function approach is proposed for products having Weibull distributed lifetimes incorporating relevant costs.Design/methodology/approachFor Weibull distributed product lifetimes, acceptance criterion introduced by Lieberman and Resnikoff (1955) is derived for Type-I GHCS. A cost function is formulated using expected warranty cost and other relevant cost components incorporating the acceptance criterion. The cost function is optimized following a constrained optimization approach to arrive at the optimum RASP. The constraint ensures that the producer's and the consumer's risks are maintained at agreed-upon levels.FindingsOptimal solution using the above approach is obtained for Type-I GHCS. As a special case of Type-I GHCS, the proposed approach is also used to arrive at the optimal design for Type-I hybrid censoring scheme as shown in Chakrabarty et al. (2019). Observations regarding the change in optimal design and computational times between the two censoring schemes are noted. An extensive simulation study is performed to validate the model for finite sample sizes and the results obtained are found to be in strong agreement. In order to analyze the sensitivity of the optimal solution due to misspecification of parameter values and cost components, a well-designed sensitivity analysis is carried out using a real-life failure data set from Lawless (2003). Interesting observations are made regarding the change in optimal cost due to change in parameter values, the impact of warranty cost in optimal design and change in optimal design due to change in lot sizes.Originality/valueThe research presents an approach for designing optimal RASPs using Type-I generalized hybrid censoring. The study formulates optimum life test sampling plans by minimizing the average aggregate costs involved, which makes it valuable in dealing with real-life problems pertaining to product quality management.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimum reliability acceptance sampling plan using Type-I generalized hybrid censoring scheme for products under warranty

Chakrabarty

Chowdhury

Roy

2020

IJQRM

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“…The proposed models can be solved using packages available for SVM problems. The risk aversion of a decision maker is incorporated by Hsieh and Lu () in decisions concerning Bayesian acceptance sampling plans . A censoring scheme is considered where n items are placed in a test until r of them fail.…”

Section: Other Applicationsmentioning

confidence: 99%

Conditional value‐at‐risk beyond finance: a survey

Filippi

Guastaroba

Speranza

2019

Int Trans Operational Res

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A large number of problems involve making decisions in an uncertain environment and, hence, with unknown outcomes. Optimization models aimed at controlling the trade‐off between risk and return in finance have been widely studied since the seminal work by Markowitz in 1952. In financial applications, shortfall or quantile risk measures are receiving ever‐increasing attention. Conditional value‐at‐risk (CVaR) is arguably the most popular of such measures. In the last decades, optimization models aimed at controlling risk have been applied to several application domains different from financial optimization. This survey provides an overview of the main contributions where CVaR is incorporated into an optimization approach and applied to a context different from financial engineering. The literature is classified following an application‐oriented perspective. The applications cover classical areas studied in operational research—such as supply chain management, scheduling, and networks—and less classical areas such as energy and medicine. For each area, concise paper excerpts are provided that convey the main ideas of the problems studied, and analyze how the CVaR has been used to cope with different sources of uncertainty. Finally, some open research directions are outlined.

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“…For a consumer durable product, warranty cost is an indispensable cost. Several papers acknowledged the importance of warranty cost while designing LTSPs under usage stress (Kwon, 1996; Huang et al ., 2008; Tsai et al ., 2008; Hsieh and Lu, 2013; Tsai et al ., 2015; Chakrabarty et al ., 2020a, b, etc.). But to the best of our knowledge, no paper so far has included warranty cost while designing LTSPs under accelerated life test setting.…”

Section: Introductionmentioning

confidence: 99%

On the economic design of optimal sampling plan under accelerated life test setting

Chakrabarty

Roy

Chowdhury

2022

IJQRM

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PurposeIn order to reduce avoidably lengthy duration required to test highly reliable products under usage stress, accelerated life test sampling plans (ALTSPs) are employed. This paper aims to build a decision model for obtaining optimal sampling plan under accelerated life test setting using Type-I hybrid censoring scheme for products covered under warranty.Design/methodology/approachThe primary decision model proposed in this paper determines ALTSP by minimizing the relevant costs involved. To arrive at the decision model, the Fisher information matrix for Type-I hybrid censoring scheme under accelerated life test setting is derived. The optimal solution is attained by utilizing appropriate techniques following a nonlinear constrained optimization approach. As a special case, ALTSP for Type-I censoring is obtained using the same approach. ALTSP under Type-I hybrid censoring using the variance minimization approach is also derived.FindingsOn comparing the optimal results obtained using the above mentioned approaches, it is found that the cost minimization approach does better in reducing the total cost incurred. Results also show that the proposed ALTSP model under cost function setting has considerably lower expected testing time. Interesting findings from the sensitivity analysis conducted using a newly introduced failure dataset pertaining to locomotive controls are highlighted.Originality/valueThe research introduces a model to design optimum ALTSP for Type-I hybrid censoring scheme. The practical viability of the model makes it valuable for real-life situations. The practical application of the proposed model is exemplified using a real-life case.

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Risk-embedded Bayesian acceptance sampling plans via conditional value-at-risk with Type II censoring

Cited by 22 publications

References 48 publications

Optimum reliability acceptance sampling plan using Type-I generalized hybrid censoring scheme for products under warranty

Optimum reliability acceptance sampling plan using Type-I generalized hybrid censoring scheme for products under warranty

Conditional value‐at‐risk beyond finance: a survey

On the economic design of optimal sampling plan under accelerated life test setting

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