×

Design of accelerated life test sampling plans with a nonconstant shape parameter. (English) Zbl 1159.91463

Summary: Accelerated life test sampling plans (ALTSPs) provide information quickly on the lifetime distribution of products by testing them at higher-than-usual stress level to induce early failures and reduce the testing efforts. In the traditional design of ALTSPs for Weibull distribution, it is assumed that the shape parameter remains constant over all stress levels. This paper extends the existing design of ALTSPs to Weibull distribution with a nonconstant shape parameter and presents two types of ALTSPs; time-censored and failure-censored. Optimum ALTSPs which satisfy the producer’s and consumer’s risk requirements and minimize the asymptotic variance of the test statistic for deciding the lot acceptability are obtained. The properties of the proposed ALTSPs and the effects of errors in pre-estimate of the design parameters are also investigated.

MSC:

91B82 Statistical methods; economic indices and measures
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bai, D. S.; Kim, J. G.; Chun, Y. R., Design of failure-censored accelerated life tests sampling plans for lognormal and weibull Distribution, Engineering Optimization, 21, 197-212 (1993)
[2] Bai, D. S.; Chun, Y. R.; Kim, J. G., Failure-censored accelerated life tests sampling plans for Weibull distribution under expected test time constraint, Reliability Engineering and System Safety, 50, 61-68 (1995)
[3] Balasooriya, U., Failure-censored reliability sampling plans for the exponential distribution, Journal of the Statistical Communication and Simulation, 52, 337-349 (1995) · Zbl 0842.62085
[4] Balasooriya, U.; Low, C. K., Competing causes of failure and reliability tests for Weibull lifetimes under type I progressive censoring, IEEE Transactions on Reliability, 53, 29-36 (2004)
[5] Balasooriya, U.; Saw, L. C., Reliability sampling plans for the tow-parameter exponential distribution under progressive censoring, Journal of Applied Statistics, 25, 707-714 (1998) · Zbl 0933.62105
[6] Balasooriya, U.; Saw, L. C.; Gadag, V., Progressively censored reliability sampling plans for the Weibull distribution, Technometrics, 42, 160-167 (2000)
[7] Fertig, K. W.; Mann, N. R., Life-test sampling plans for two-parameter Weibull populations, Technometrics, 22, 165-177 (1980) · Zbl 0462.62080
[8] Hiergeist, P.; Spitzer, A.; Rohl, S., Lifetime of oxide and oxide-nitro-oxide dielectrics within trench capacitors for DRAM’s, IEEE Transactions on Electron Devices, 36, 913-919 (1989)
[9] Hsiesh, H. K., Accelerated life test sampling plans for exponential distribution, Communication in Statistics-Simulation, 23, 27-41 (1994) · Zbl 0825.62017
[10] Kockerlakota, S.; Balakrishnan, N., One- and two-sided sampling plans based on the exponential distribution, Naval Research Logistics Quarterly, 33, 513-522 (1986) · Zbl 0605.62117
[11] Li, P. C.; Ting, W.; Kwong, D. L., Time-dependent dielectric breakdown of chemical-vapour-deposited \(SiO_2\) gate dielectrics, Electric Letters, 25, 665-666 (1989)
[12] Meeter, C. A.; Meeker, W. Q., Optimum accelerated life tests with a nonconstant scale parameter, Technometrics, 36, 71-83 (1994) · Zbl 0800.62624
[13] Nelson, W., Accelerated Testing-Statistical Models, Test Plans, and Data Analysis (1990), John Wiley & Sons: John Wiley & Sons New York · Zbl 0717.62089
[14] Nelson, W.; Kielpinski, T. J., Theory for optimum censored accelerated life tests for normal and lognormal life distributions, Technometrics, 18, 105-114 (1976) · Zbl 0318.62081
[15] Schneider, H., Failure-censored variable-sampling plans for lognormal and Weibull distributions, Technometrics, 31, 199-206 (1989)
[16] Yum, B. J.; Kim, S. H., Development of life-test sampling plans for exponential distribution based on accelerated life testing, Communications in Statistics-Theory and Methodology, 19, 2735-2743 (1990)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.