Hazard rate estimation for call center customer patience time

Han Ye, Lawrence D. Brown, Haipeng Shen

Research output: Contribution to journalArticlepeer-review


Estimating the hazard function of customer patience time has become a necessary component of effective operational planning such as workforce staffing and scheduling in call centers. When customers get served, their patience times are right-censored. In addition, the exact event times in call centers are sometimes unobserved and naturally binned into time intervals, due to the design of data collection systems. We develop a TunT (Transform-unTransform) estimator that turns the difficult problem of nonparametric hazard function estimation into a regression problem on binned and right-censored data. Our approach starts with binning event times and transforming event count data with a mean-matching transformation, which enables a simpler characterization of the heteroscedastic variance function. A nonparametric regression technique is then applied to the transformed data. Finally, the estimated regression function is back-transformed to yield an estimator for the original hazard function. The proposed estimation procedure is illustrated using call center data to reveal interesting customer patience behavior, and health insurance plan trial data to compare the effect between treatment and control groups. The numerical study shows that our approach yields more accurate estimates and better staffing decisions than existing methods.

Original languageEnglish (US)
Pages (from-to)890-903
Number of pages14
JournalIISE Transactions
Issue number8
StatePublished - Aug 2 2020


  • Human patience
  • bandwidth selection
  • competing risk
  • hazard rate
  • local polynomial regression
  • queueing system
  • survival analysis

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering


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