The chapter discusses the analysis of censored failure times, focusing on the extension of Kaplan and Meier's work to incorporate regression-like arguments into life-table analysis. The hazard function, which represents the age-specific failure rate, is assumed to be a function of explanatory variables and unknown regression coefficients, multiplied by an arbitrary and unknown function of time. The conditional likelihood is derived to infer the unknown regression coefficients. The methods are asymptotic but are relevant for situations with significant sampling fluctuations, making them suitable for industrial reliability studies and medical statistics. The chapter also reviews the product-limit method, which is used to estimate the survivor function and the hazard function in the presence of censored data.The chapter discusses the analysis of censored failure times, focusing on the extension of Kaplan and Meier's work to incorporate regression-like arguments into life-table analysis. The hazard function, which represents the age-specific failure rate, is assumed to be a function of explanatory variables and unknown regression coefficients, multiplied by an arbitrary and unknown function of time. The conditional likelihood is derived to infer the unknown regression coefficients. The methods are asymptotic but are relevant for situations with significant sampling fluctuations, making them suitable for industrial reliability studies and medical statistics. The chapter also reviews the product-limit method, which is used to estimate the survivor function and the hazard function in the presence of censored data.