# Graphical Analysis of Repair Data

With the kind permission of Wayne Nelson and Robert Abernathy we are posting an article on the analysis of repair data. As you may know, the assumptions made when using simple time to failure analysis of repairable systems may provide misleading results. Using the analysis method outlined by Wayne is one way to avoid those costly mistakes.

Here is the opening elements of the work by Wayne, followed by a link to the full paper.

Appendix M: Repair Data Analysis of Abernethy, R.B. (2006), The New Weibull Handbook, 5th ed., available from Dr. R.A. Abernethy, weibull@worldnet.att.net, 536 Oyster Road, North Palm Beach, FL 33408. May 5, 2006

# AN APPLICATION OF GRAPHICAL ANALYSIS OF REPAIR DATA

Wayne Nelson, consultant
WNconsult@aol.com, 739 Huntingdon Drive, Schenectady, NY 12309, USA

SUMMARY. This expository article presents a simple and informative non-parametric plot of repair data on a sample of systems. The plot is illustrated with transmission repair data from cars on a preproduction road test.

KEY WORDS: repair data; reliability data; graphical analysis.

## 1. INTRODUCTION

Purpose. This article presents a simple and informative plot for analyzing data on numbers or costs of repeated repairs of a sample of systems. The plotting method provides a non-parametric graphical estimate of the population mean cu¬mulative number or cost of repairs per system versus age. This estimate can be used to:

1. Evaluate whether the population repair (or cost) rate increases or decreases with age (this is useful for sys¬tem retirement and burn-in decisions),
2. Compare two samples from different designs, production periods, maintenance policies, environ¬ments, operating conditions, etc.,
3. Predict future numbers and costs of repairs,
4. Reveal unexpected information and insight, an impor¬tant advantage of plots.

## Overview

Section 2 describes typical repair data. Section 3 de¬fines the basic population model and its mean cumulative function (MCF) for the number or cost of repairs. Sec¬tion 4 shows how to calculate and plot a sample estimate of the MCF from data from systems with a mix of ages. Section 5 explains how to use and interpret such plots.

## Author Bio

Dr. Wayne Nelson is a leading expert on analysis of reliability and accelerated test data. He consults and gives training courses for companies and professional societies. For 24 years he consulted across the General Electric Co. and received the Dushman Award of GE Corp. R&D for developments and applications of product reliability data analysis. He was elected a Fellow of the Amer. Statistical Assoc. (1973), the Amer. Soc. for Quality (1983), the Institute of Electrical and Electronics Engineers (1988) for his innovative developments. He was awarded the 2003 Shewhart Medal and the 2010 Shainin Medal of ASQ and the 2005 Lifetime Achievement Award of IEEE for outstanding developments of reliability methodology and contributions to reliability education. He authored three highly regarded books Applied Life Data Analysis (Wiley 1982, 2004), Accelerated Testing (Wiley 1990, 2004), Recurrent Events Data Analysis (SIAM 2003), two ASQ booklets, and 130 journal articles. He can be contacted via WNconsult@aol.com.
Dr. Robert B. Abernathy, www.bobabernethy.com