64th ISI World Statistics Congress - Ottawa, Canada

64th ISI World Statistics Congress - Ottawa, Canada

Double Sampling Control Charts for Monitoring the Median of Birnbaum-Saunders Distribution


Ming-Che Lu


  • S
    Su-Fen Yang


64th ISI World Statistics Congress - Ottawa, Canada

Format: CPS Abstract

Session: CPS 51 - Statistical methodology III

Tuesday 18 July 4 p.m. - 5:25 p.m. (Canada/Eastern)


The Birnbaum-Saunders (BS) distribution is a lifetime distribution describing fatigue failures and general random wear failures. By means of monitoring the median of BS distribution, the quality control of lifetime of products subject to failures can be performed. Although increasing sample size can improve the detecting power for median shifts and reduce false alarm rates, its disadvantages are not only the increased cost of sampling as well as measurement but also the need to spend more time on analysis and measurement of product's lifetime. Double sampling monitoring schemes may provide better statistical performance and reduce cost without increasing sample size. In this study, we construct a double sampling control chart for monitoring the median of BS distribution to detect if exists any shift of median. The average number of observations to signal (ANOS) is used to measure the out-of-control detection performance. The smaller ANOS under the same specified in-control average run length indicates better out-of-control detection performance. The proposed chart presents smaller out-of-control ANOS than the existing chart, meaning less cost and time spending on monitoring the median of BS distribution. Finally, a real data with BS distribution is given to illustrate the design and implementation of the proposed chart.