Exploring Reliability with JMP: Recurrence Analysis...Analysis of repairable system data using...

Copyright © 2009, SAS Institute Inc. All rights reserved.Copyright © 2009, SAS Institute Inc. All rights reserved.

Exploring Reliability with JMP: Recurrence AnalysisDavid C. Trindade, Ph.D.March 2010

Copyright © 2009, SAS Institute Inc. All rights reserved.

Topics

Reliability Concepts and Terminology

Life Distribution Fitting

Competing Cause Analysis

Accelerated Life Testing

Recurrence Analysis

Degradation Studies


3

The usual assumptions we make for non-repairable components is that the times to failure are a true random sample from a single population. Consequently, the observations are independent andidentically distributed.

The implication is that individual failure times can be combined for analysis, neglecting any order of occurrence in the original data.

Are these assumptions valid for repairable systems?

Non-Repairable Vs. Repairable Systems


4

Case Study Example

New Production Equipment:System used in manufacturing which contained a single, replaceable board. Upon failure, repairs were made by replacing failed board with new board from the same population in stockpile.

Analysis: Engineers wanted to model the reliability of the system based on failure data obtained during the first 1000 hours of operation.


5

System Repair History

Repairs were done at system ages (in hours)108, 178, 273, 408, 548, 658, 838, and 988.

A dot plot of repair times is shown below.


6

Case Study Weibull AnalysisThe engineers analyzed the system data by taking the time

for each replacement board to fail, that is, the times between repairs, and treating those times as a group of independent and identically distributed (iid) observationsarising from a single population of failure times.

The actual order in which these times occurred (age of system at repair) was ignored.

Analysis methods used were:Weibull probability plotting of data, parameter estimation, model fitting.


7

Weibull Analysis of DataThe times between repairs are called the interarrival times and calculated below:

For Weibull analysis, the order of interarrival times is not considered.


8

JMP Data Table and Analysis Platform

We run the Life Distribution Platform using Times Between Failures for Y, Time to Event


9

JMP Life Distribution Analysis

The Weibull distribution appears to be a good fit to the data.


10

JMP Life Distribution Analysis

Weibull probability plot shows data points falling close to a straight line.


11

Weibull StatisticsThe Weibull parameters show a characteristic life α ≈ 136 hours and a shape parameter β ≈ 4.3.

For the Weibull distribution, β > 1.0 indicates an increasing hazard rate.


12

Weibull Hazard ProfilerHazard Profiler shows increasing hazard rate.


13

Engineering View of AnalysisEngineers concluded times between repairs followed

a Weibull distribution.

Of concern was that the estimated Weibull shape parameter, β, indicated an increasing “failure rate.”

The equipment engineers thus felt the machine needed to be brought down for additional repair and maintenance before “things got much worse”.

Were these conclusions justified or misleading based on analyzing the boards as non-repairable components?


JMP Recurrence Analysis PlatformData Table

Recurrence Analysis Input Box


MCF Plot of Number of Repairs Vs. Age

No evidence of system reliability getting worse with time.

MCF is Mean Cumulative (or Cost) Function

= average number of repairs per

system versus age

MCF plot for a single system is

called a cumulative plot

= cumulative number of

repairs versus system age


Plot of Times Between Repairs Vs. Age

Graph shows times between repairs actually becoming longer. System reliability is improving!


Misleading Weibull Analysis

Analysis of repairable system data using non-repairable Weibull analysis methods produced misleading conclusions.

Wrong interpretation caused by the neglect of the occurrence order of failures in Weibull analysis.

With correct analysis, engineers avoided expensive maintenance actions that were not necessary.


Analysis of Multiple Repairable Systems We’ll use JMP sample data file Engine Valve Seat.jmp

which records valve seat replacements in locomotive engines (Nelson, 2003). Partial table shown.


Analysis of Valves as Non-Repairable Components (Replacements)

Partial Table of Original and Replacement Times to Failure.

Censor = 1 and Failure Time = 0.

Two Zero Times Excluded from Analysis.


Event Plot for Valves as Non-Repairable Components (Replacements)

Arrow Indicates Censored Observation

X Indicates Repair

Two Zero Times Excluded from Analysis.


Lifetime Distribution Platform

Lognormal distribution appears to fit data very well.


Hazard Rate Profiler

Profiler shows hazard rate increasing early in life, peaking around 100 days, and then decreasing thereafter.


Analysis of Valves on Locomotive as Repairable Systems

MCF plot shows repair rates sharply increasing at 500 days. Wearout occurring?


Lessons LearnedAnalysis of repairable system data using non-repairable

analysis methods can produce misleading results.

For repairable systems, the time order in which failures occur can be a very important factor for analysis.

For individual systems, a cumulative plot shows the repair history graphically. For multiple systems, the MCF plot can reveal trends in the collective behavior of a group of systems.

In addition to failure counts, MCF for costs can provide valuable insight into repair expenses as systems age.


Review of AR-1 Continued

• Accelerated Testing (continued)• Activation Energy• Eyring Models• Determining Model Parameters• Matrix Reliability Studies and Example• Planning Guidelines• Degradation Modeling• Sample Sizes for Accelerated Testing

• System Models• Series System• Parallel System• Analysis of Complex Systems• Standby Redundancy

• Defective Subpopulations

Exploring Reliability with JMP: Recurrence Analysis...Analysis of repairable system data using...

Documents

Transcript of Exploring Reliability with JMP: Recurrence Analysis...Analysis of repairable system data using...