Mean and variance of an alternating geometric process: An application in warranty cost analysis

Arnold, Richard; Chukova, Stefanka; Hayakawa, Yu; Marshall, Sarah

doi:10.1002/qre.2964

Cited by 5 publications

(5 citation statements)

References 28 publications

(65 reference statements)

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“…Arnold et al (2020b) applied an alternating GP for modelling a system's lifetime and repair time and obtained results on the mean and variance functions of corresponding counting processes. Arnold et al (2022) proposed two new approaches for computing the mean and variance functions of two counting processes related to the alternating GP and applied them in warranty cost analysis. Wang et al (2022) proposed a single-component repairable system model with a repairman assuming that the successive working time interval of the component and the successive repair time interval after the repair is described by the extended GP.…”

Section: Related Literaturementioning

confidence: 99%

A rate randomized geometric process with applications

Asadi,

2024

Naval Research Logistics

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The geometric process has been widely studied in various disciplines and applied in reliability, maintenance and warranty cost analysis, among others. In its applications in maintenance policy optimisation, the geometric process assumes constant repair effectiveness by its process rate. Nevertheless, in practice, maintenance effectiveness may differ from time to time and can therefore be better depicted by a random variable. Motivated by this argument, this paper proposes a new variant of the geometric process, which is referred to as the rate randomized geometric process (RRGP). The probabilistic properties of the RRGP are then investigated. The maximum likelihood method is utilised to estimate the parameters of the RRGP. Numerical examples are given to show its applicability in both maintenance policy optimization and fitting real‐world failure datasets.

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Section: Related Literaturementioning

confidence: 99%

A rate randomized geometric process with applications

Asadi,

2024

Naval Research Logistics

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“…The alternating geometric process (alternating GP) is proposed by [24]. It combines the ideas of the GP and the alternating renewal process [21].…”

Section: Alternating Geometric Process (Alternating Gp)mentioning

confidence: 99%

“…It combines the ideas of the GP and the alternating renewal process [21]. The following definition of the alternating GP is given by [24].…”

Section: Alternating Geometric Process (Alternating Gp)mentioning

confidence: 99%

Some Extended Geometric Processes and Their Estimation Methods

Yin

2022

2022 4th International Conference on System Reliability and Safety Engineering (SRSE)

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Modelling the failure process of a system is one of the most important problems in the reliability and maintenance research community. The geometric process (GP) is widely used for modelling the failure process because it can describe the phenomenon that the working times after repairs become shorter and shorter. This article reviews the geometric process and its extensions based on existing research. It also reviews relevant methods for estimating parameters, model performances, and widely used distributions for times to first failures. Future challenges for the GP-like processes will be discussed.

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“…From the managerial perspective, the warranty return rate and warranty cost are essential for companies to maintain their brand reputation and control the cost budget. [27][28][29] Therefore, this paper aims to integrate the ALT and warranty return rate considerations to design a modified RASP (MRASP). The operating characteristic (OC) function of the MRASP is derived from the accelerated time-to-failure data rather than normal-use time-to-failure data.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, they did not consider the warranty return rate and warranty cost for designing the plan. From the managerial perspective, the warranty return rate and warranty cost are essential for companies to maintain their brand reputation and control the cost budget 27–29 …”

Section: Introductionmentioning

confidence: 99%

A modified reliability acceptance sampling plan with warranty return rate consideration under Weibull‐distributed accelerated lifetime data

Wang,

Shu

2024

Quality & Reliability Eng

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Warranty is a standard and essential policy for today's products. The period and cost of warranty are majorly affected by the reliability of products. Therefore, validation and verification of product reliability are required to control warranty costs and sustain the brand reputation. In this paper, we propose a modified reliability acceptance sampling plan (MRASP) for product reliability validation. The operating characteristic function of the MRASP is derived by considering the accelerated time‐to‐failure data with Type‐II censoring, which follows a Weibull distribution. To minimize the number of failures required for the accelerated life test and consider the sampling risk constraints, we constructed an optimization model to determine the optimal plan design of the proposed MRASP. Following the optimal plan design, practitioners can set the number of failures required in the accelerated life test to estimate the lifetime capability of the submitted lot and decide the lot disposition using the acceptance benchmark. In addition, the lifetime capability estimation can be used to infer the warranty return rate and warranty cost of the lot, which is valuable for practitioners to formulate the warranty budget. Finally, we illustrate a real‐world case to demonstrate the practicality and applicability of the proposed method.

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Mean and variance of an alternating geometric process: An application in warranty cost analysis

Cited by 5 publications

References 28 publications

A rate randomized geometric process with applications

A rate randomized geometric process with applications

Some Extended Geometric Processes and Their Estimation Methods

A modified reliability acceptance sampling plan with warranty return rate consideration under Weibull‐distributed accelerated lifetime data

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