On efficient use of censored data and covariate factors in survival analysis and maintenance scheduling
Abstract: This thesis deals with survival analysis and maintenance scheduling, two important issues to achieve efficient use of different production systems. In survival analysis of failure time data, the survival function and the cumulative hazard function are important reliability characteristics. One common problem in survival analysis is that the available data is incomplete. In estimating the reliability characteristics for censored data, the number of censored failure times between two observed failure times are often the only information of censoring considered. An important problem is therefore to develop new techniques which in an efficient way takes care of censored data. A better estimator of reliability characteristics may be obtained if the exact times for censoring between two observed failure times are considered, which is the case for the piecewise exponential estimator (PEXE) proposed by Kitchin (1980). In this thesis the PEXE is used in a number of situations, and in some cases also compared with the Kaplan-Meier estimator (KME). For example is the TTT-plot based on the PEXE compared with the TTT-plot based on the KME in model identification. A simulation study indicates that a variant of the PEXE is preferable over the KME. Maintenance scheduling of systems can be time-based. Two basic time-based maintenance schedules are the age replacement policy and the block replacement policy with minimal repair. Based on TTT-plotting, the interval between two preventive maintenance actions for the age replacement policy which gives the minimum cost for maintenance in the long run can be estimated. In a simulation study, the PEXE proves to be better than the KME in estimating the length of this interval. For the block replacement policy with minimal repair, the PEXE equals the Nelson estimator in the same mission. Graphically, the length of the interval can be estimated based on the hazard plot. In real life, the failure times are often not sufficient to properly explaining the reliability characteristics of a system. Operating conditions and other factors such as vibration, environmental conditions and material may influence the reliability of the system as well. These factors are referred to as covariates. The effect of the covariates can be estimated using regression models. In this thesis, the effect is estimated using the proportional hazard model (PHM) and the proportional intensity model (PIM). By adding the effect of the covariates, the reliability characteristics of the system can be explained in a better way. The proportional hazards model estimates the effect of the covariates assuming a proportional and time-independent hazard rate over time. Different variants of the PHM-concept has been proposed during the years, and some variants are reviewed in this thesis. New applications of the PHM in maintenance scheduling are given, where the effect of the covariates are considered in addition to the failure times when graphical methods are considered. The applications are illustrated with real life data. The approach is also extended for estimating the threshold values of monitored parameters. To test the goodness-of-fit of the PHM graphical methods can be used. Under the PHM the effect of the covariates is assumed to be timeindependent. A linear regression model is proposed to be a supplement to the PHM, as the estimated effect of the covariates based on the linear regression model can be plotted against time. Drastic changes or increasing/decreasing curves are indicating time-dependence. By plotting the residuals against time, the proportionality assumption in the PHM can be tested. In order to calculate the residuals, the cumulative hazard rate must be estimated. Based on the PEXE, new estimators of the cumulative hazard rate are proposed. These estimators are useful in the case of small sample sizes and/or highly censored data.
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