TY - JOUR

T1 - Estimation of field reliability based on aggregate lifetime data

AU - Chen, Piao

AU - Ye, Zhi Sheng

PY - 2017/1/2

Y1 - 2017/1/2

N2 - Because of the exponential distribution assumption, many reliability databases recorded data in an aggregate way. Instead of individual failure times, each aggregate data point is a summation of a series of collective failures representing the cumulative operating time of one component position from system commencement to the last component replacement. The data format is different from traditional lifetime data and the statistical inference is challenging. We first model the individual component lifetime by a gamma distribution. Confidence intervals for the gamma shape parameter can be constructed using a scaled χ2 approximation to a modified ratio of the geometric mean to the arithmetic mean, while confidence intervals for the gamma rate and mean parameters, as well as quantiles, are obtained using the generalized pivotal quantity method. We then fit the data using the inverse Gaussian (IG) distribution, a useful lifetime model for failures caused by degradation. Procedures for point estimation and interval estimation of parameters are developed. We also propose an interval estimation method for the quantiles of an IG distribution based on the generalized pivotal quantity method. An illustrative example demonstrates the proposed inference methods. Supplementary materials for this article are available online.

AB - Because of the exponential distribution assumption, many reliability databases recorded data in an aggregate way. Instead of individual failure times, each aggregate data point is a summation of a series of collective failures representing the cumulative operating time of one component position from system commencement to the last component replacement. The data format is different from traditional lifetime data and the statistical inference is challenging. We first model the individual component lifetime by a gamma distribution. Confidence intervals for the gamma shape parameter can be constructed using a scaled χ2 approximation to a modified ratio of the geometric mean to the arithmetic mean, while confidence intervals for the gamma rate and mean parameters, as well as quantiles, are obtained using the generalized pivotal quantity method. We then fit the data using the inverse Gaussian (IG) distribution, a useful lifetime model for failures caused by degradation. Procedures for point estimation and interval estimation of parameters are developed. We also propose an interval estimation method for the quantiles of an IG distribution based on the generalized pivotal quantity method. An illustrative example demonstrates the proposed inference methods. Supplementary materials for this article are available online.

KW - Aggregate data

KW - Confidence interval

KW - Gamma distribution

KW - Generalized pivotal quantity (GPQ)

KW - Inverse Gaussian distribution

UR - http://www.scopus.com/inward/record.url?scp=85011341313&partnerID=8YFLogxK

U2 - 10.1080/00401706.2015.1096827

DO - 10.1080/00401706.2015.1096827

M3 - Article

AN - SCOPUS:85011341313

VL - 59

SP - 115

EP - 125

JO - Technometrics: a journal of statistics for the physical, chemical and engineering sciences

JF - Technometrics: a journal of statistics for the physical, chemical and engineering sciences

SN - 0040-1706

IS - 1

ER -