Project Overview
This project was completed for the course Statistical Methods for Counting Processes at TU Dortmund.
The task was to analyze survival times of ice cream machines and investigate how warranty period and
manufacturer influence machine failure risk.
The analysis used censored survival data, meaning that some machines failed during observation while others
were replaced at the end of a year before failure was observed. The project combines non-parametric survival
estimation, semi-parametric Cox regression, time-dependent covariates, parametric relative risk modelling,
hypothesis testing, and simulation.
Research Motivation
For manufacturers, machine reliability is directly connected to warranty costs, customer satisfaction, and
product design. A key question is whether machines show different failure behavior depending on warranty length
and manufacturer. Another important question is whether the failure risk changes after the warranty period ends.
Main research goal: evaluate the effect of warranty period and manufacturer on the survival time
and failure risk of ice cream machines.
Dataset
The dataset contains censored survival times for more than 100 ice cream machines. Machines that were still
functional at the end of a year were replaced, so censoring times occur at multiples of 365 days.
Each machine belongs to one of three manufacturers and has either a standard 2-year warranty or a premium
5-year warranty.
| Variable |
Description |
Role in Analysis |
| id |
Unique identifier for each ice cream machine |
Machine-level index |
| days |
Days until failure or replacement |
Survival time |
| status |
Failed or replaced at the end of the year |
Event / censoring indicator |
| warranty |
Warranty period in years: 2-year standard or 5-year premium |
Main explanatory variable |
| manufacturer |
Manufacturer group coded as 1, 2, or 3 |
Group comparison factor |
Problem Definition
The project treats machine lifetime as a survival analysis problem. The event of interest is machine failure,
while machines replaced before failure are treated as censored observations.
The central statistical question is whether warranty and manufacturer affect the hazard rate, meaning the
instantaneous risk that a machine fails at a given time, conditional on having survived until that time.
Statistical Methods
Several survival-analysis methods were used to understand the failure process from different angles. The project
starts with diagnostic plots, then moves to Cox regression, time-dependent covariates, parametric relative risk
regression, and simulation-based validation.
| Method |
Purpose |
Why It Matters |
| Nelson-Aalen Estimator |
Estimate cumulative hazard non-parametrically |
Used for diagnostics and visual comparison |
| Cox Proportional Hazards Model |
Model hazard as a function of warranty and manufacturer |
Core semi-parametric survival model |
| Breslow Estimator |
Estimate cumulative baseline |