Statistical Methods for Failure-Time Data

Introduction

In my previous article, I briefly discussed the survival function and the Kaplan Meier method of estimating this function from a given dataset. We applied this method to a vehicle shock absorber dataset to answer questions like “What is the probability that a vehicle shock absorber will last at least 19,000 km?”. The two different modes of failure of a shock absorber (Mode 1 and Mode 2) were ignored and were treated as the same type of failure. In the following post, we will consider the two modes of failures as two competing risks and answer questions like:

“What is the probability that a vehicle shock absorber will experience a Mode 1 failure by 19,000 km and that this failure occurs before it experiences a Mode 2 failure?” [Read more…]

Introduction

I am currently reading the book Survival Analysis: Techniques for Censored and Truncated Data, Second Edition (John P. Klein and Melvin L. Moescheberger). Although the techniques presented in this book focus on applications in biology and medicine, the same statistical tools can also be applied to disciplines ranging from engineering to economics and demography. I have a background in mechanical engineering and am interested in applying survival modeling concepts to data from reliability engineering, manufacturing and quality assurance. This article is the first of, hopefully, many articles that I intend to write as I finish reading different chapters from the book.

The data set(s) that will be analysed are the ones that have been used as examples in another book: Statistical Methods for Reliability Data, Second Edition (William Q. Meeker, Luis A. Escobar, Francis G. Pascual). Both the books I mentioned are excellent resources for anyone who is interested in learning more about this topic.

In this article, we will analyze vehicle shock absorber failure time data Failure time data is also known as survival data, life data, event-time data or reliability data, depending on the field of study. and estimate a few basic survival quantities. The data contains failure times (in kilometers driven) and the mode of failure, first reported by O’Connor (1985) O’Connor, P. D. T. (1985). Practical Reliability Engineering. Wiley. [54, 610]. We will ignore the mode of failure for now and will only consider whether a failure occurred or not, i.e., censored. In a future article, I plan to use the different failure modes to discuss competing risks for time-to-failure data.