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Life test sampling plans for Weibull distributed lifetimes under accelerated hybrid censoring

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Abstract

Life test sampling plans (LSPs) for the Weibull distribution are usually developed under the assumptions that the shape parameter is known and the life test is conducted at an accelerated condition for which the acceleration factor (AF) is known. However, the sensitivities of a plan to the assumed shape parameter and AF have been rarely investigated. This paper considers the case where the life test is hybrid censored and develops attributes LSPs under the above assumptions. Then, sensitivity analyses are conducted to assess the effects of the uncertainties in the assumed AF and shape parameter on the actual producer and consumer risks. A method is also developed for constructing LSPs that can accommodate these uncertainties.

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Abbreviations

T U , T A :

lifetimes at the use and accelerated conditions, respectively

F U (t U ), F A (t A ):

cumulative distribution functions of T U and T A , respectively

m :

shape parameter (assumed known)

m * :

true shape parameter. \({\in [{m_{\min}^\ast , m_{\max}^\ast}]}\)

η U , η A :

scale parameters at the use and accelerated conditions, respectively

AF:

acceleration factor (assumed known)

AF* :

true acceleration factor. \({\in [{{\rm AF}_{\min}^\ast , {\rm AF}_{\max}^\ast}]}\)

τ A :

censoring time at the accelerated condition

ηU0, ηU1:

scale parameter values at the use condition specified in H 0 and H 1, respectively. η U0 > η U1.

ηA0, ηA1:

scale parameter values at the accelerated condition specified in H 0 and H 1, respectively. η A0 > η A1. η A0 = η U0/AF and η A1 = η U1/AF

n :

sample size

c :

rejection number

q0, q1:

probabilities that a unit survives until the censoring time at the accelerated condition under H 0 and H 1, respectively.

\({q_0^\ast , q_1^\ast}\) :

q0 and q1, respectively, when m = m* and AF = AF*.

α, β:

producer and consumer risks required to be satisfied, respectively.

α*, β*:

producer and consumer risks, respectively, when m = m * and AF = AF*

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, KAIST, Daejeon, 305-701, Korea

    Min Kim & Bong-Jin Yum

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  1. Min Kim
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  2. Bong-Jin Yum
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Correspondence to Bong-Jin Yum.

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Kim, M., Yum, BJ. Life test sampling plans for Weibull distributed lifetimes under accelerated hybrid censoring. Stat Papers 52, 327–342 (2011). https://doi.org/10.1007/s00362-009-0233-9

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