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Failure Data Analysis Tools 2010/7/3

© 2010 by Albert H.C. Tsang 1

Tools forFailure Data Anal sis

Dr. Albert H.C. Tsang

Phone: (852) 2766–6591 Fax: (852) 2362–5267 email: [email protected]

Importance of Maintenance

W h a t p e r c e n t a g e o f y o u r o r g a n i za t i on ’ s t o t a l

o p e r a t i n g b u d g e t i s m a i n t e n a n c e r e l a t e d ?

15 to 40% of total manufacturing costs aremaintenance related

40% of man-hours expended in providing the

© 2010 by Albert H.C. Tsang Failure Data Analysis Tools 2

work — MTR Corporation





Maintenance as a Business Process

process that has not been optimized

Handled well, it pays direct dividends,handled wrongly, it incurs costs

Effective maintenance can brin substantial


savings, both direct & indirect, maximizingefficiency & productivity, and improving thebottom line

Breaks

Maintenance / CleaningEffective Utilization

Types of Losses

planned

Break downs / Repairs

Production change over

Tool change / Adjustments

Start u / Shut down

Run at reduced speeds

Minor stoppages

Idling

Stops

PerformanceLosses

unplanned


Errors / Defects

Scrap

ReworkQuality-Losses





Total Time The OEE is decreased by all non-value adding

Overall Equipment Effectiveness (OEE)

Available Time

Productive Time

Availability

Losses

Performance

Losses

ven s:

- 80

min

Planned- Breaks, Maintenance, Cleaning- Changeover, Adjustment, Tool change

Unplanned- Breakdowns, Repairs

- Run at reduced speeds

- Minor stoppages

- Idling

480 min

400 min


Effective TimeQuality

Losses

- Scrap

- Defects

- Rework

-

min

- 20

min

. .

- Start up and Shut down losses330 min

310 min

OEE (in %) =OEE Calculation

Availability Rate =Total Time - Availability Losses

Total Time

Available Time=

X

Performance Rate =Available Time – Performance Losses

Available Time

=400 min - 70 min

400 min

PR 0,825

Productive Time

Available Time=

AR 0,833

=480 min – 80 min

480 min


= 0,646

= 64,6%

Quality Rate =Productive Time – Quality Losses

Productive Time

= 330 min - 20 min

330 min

QR 0,939

=Effective Time

Productive Time





Prioritization of the Losses

Use a Pareto diagram to visually prioritize

∑ Losses

Adjustments

Break Downs

Minor Stops

Changeovers

OEE

Pareto Analysis


Utilization

C h a n g e o v e r s

M i n o r S t o p s

B r e a k - D o w n

s

A d j u s t m e n t s

Determining Maintenance Priorities

How do you prioritize failure codes?






Optimizing Maintenance Decisions

O timizin E ui ment Maintenance and Re lacement Decisions

ComponentReplacement

InspectionProcedures

Capital EquipmentReplacement

ResourceRequirements


DATABASE (CMM/EAM/ERP System)

Quantitative decision models

Quality of Life Data






Component Replacement

The unscheduled actions taken, as a resultof failure, to restore a system to a specifiedlevel of performance

P r ev e n t i v e R e p la cem e n t

The scheduled actions taken, not as a result


o a ure, o re a n a sys em a a spec elevel of performance by such functions asscheduled replacement of critical items andoverhauls


Is preventive replacement aIs preventive replacement apanacea for optimization of panacea for optimization of maintenance?maintenance?







the risk of failure increases with ageor usage, i.e., wear-out effectoccurring

total cost of a failure replacement isreater than total cost of a reventive


replacement

Optimizing PreventiveReplacement Decisions

Fact-based arguments

(data driven decisions)

NOT


Intuition-based pronouncements

(strength of personalities, # of mechanics’ complaints)





Total Cost Per Week

Preventive Replacement Cost Conflicts

Failure Replacement

Cost per Week

i l C o s t p e r W e e k


0

revenive eplacemen

Cost per Week

Optimal preventive replacement age

Preventive

Replacement Age0

Optimizing Preventive

Replacement Decisions

databases of CMM/EAM/ERP system

A typical scenario:Data Rich, Information Poor


T e ris o ai ure can e eterminefrom analysis of the item’s failuredata – Weibull Analysis





Software & Web Sites

ReliSoft: www.reliasoft.com

MORE tools: http://www.crcpress.com/product/isbn/9780849339660

Maintenance Web Siteshttp://www.pem-mag.com


http://www.plant-maintenance.comhttp://reliabilityweb.com

References

Tsang, Albert H.C., et al. (2000) RCM : A K ey

t o M a i n t e n a n c e Ex c e l l e n c e , CityU Press

Jardine, A.K.S. and Tsang, Albert H.C. (2006)

Ma i n t e n a n c e , R ep l a cem e n t , a n d Re l i a b i l i t y : Th e o r y a n d A p p l i ca t i o n s Taylor& Francis: CRC Press






The Instructor

Albert H.C. Tsang is Principal Lecturer in the Department of Industrial &S stems En ineerin at The Hon Kon Pol technic Universit He has a PhD.from the University of Toronto. Dr. Tsang is a chartered engineer in the UnitedKingdom with working experience in the manufacturing industry coveringfunctions such as industrial engineering, quality assurance, and projectmanagement. He is a founding member, fellow, and past Chairman of the HongKong Society for Quality (HKSQ). Dr. Tsang had provided consultancy andadvisory services to enterprises and industry support organizations inmanufacturing, logistics, public utilities, health care, and government sectors onmatters related to quality, reliability, maintenance, performance managementand assessment of performance excellence.


Dr. Tsang is the author of “WeibullSoft”, a computer-aided self learningpackage on Weibull analysis, and a co-author of 2 books: Reliability-CentredMaintenance: A Key to Maintenance Excellence, and Maintenance, Reliability andReplacement: Theory and Applications.



Tools for Failure Data Analysis Page 1 of 9 17/10/2006

Tools for Failure Data Analysis

Albert H.C. TsangThe Hong Kong Polytechnic University

[email protected]

Abstract

Using knowledge acquired from fact-based analysis to inform decisions is the hallmark of

performance excellence in maintenance management. This paper presents a set of data

mining tools applicable to failure data analysis that will support maintenance and asset

replacement optimization, and prioritization of failure codes. These tools – Weibull analysis,

Laplace trend test, logarithmic scatter plot of MTTR versus count of failures, and jack-knife

diagrams – will enable maintenance, plant, works or planning managers and engineers to:

(1) Characterize the risk of failure of specific assets

(2) Choose between preventive replacement and run-to-failure(3) Detect trends of reliability degradation or improvement

(4) Classify failure codes into reliability, maintainability and availability problems

(5) Determine criticality of failure codes in the context of the business cycle

(6) Visualize maintenance performance trends associated with specific failure codes

Keywords

Maintenance optimization, Weibull analysis, Laplace trend test, plot of MTTR versus failure

counts, Jack-knife diagrams

Introduction

A survey conducted by Plant Engineering & Maintenance Magazine (Robertson & Jones,

2004) indicated that maintenance budgets ranged from 2 to 90% of the total plant operating

budget, with and the average being 20.8%. It can be reasoned that operation and maintenance

(O&M) represent a major cost item in equipment intensive industrial operations. These

operations can achieve significant savings in O&M costs by making the right and opportune

maintenance decisions. Maintenance is often the business process that has not been optimised.

Instead of being a liability of business operations, achieving excellence in maintenance will

pay huge dividends through reduced waste, maximised efficiency and productivity, thereby

improving the bottom line.

Maintenance excellence is concerned with balancing performance, risks and the resource

inputs to achieve an optimal solution. This is not an easy task because much of what happens

in an industrial environment is characterised by uncertainties.

Traditionally maintenance practitioners in industry are expected to “cope” with maintenance

problems without seeking to operate in an optimal manner. For example, many preventive

maintenance schemes are put into operation with only a slight, if any, quantitative approach

to the scheme. As a consequence, no one is very sure just what the best interval between

preventive replacements is and, as a result, these schemes are cancelled because it is said

“they cost too much”. Clearly some form of balance between the preventive replacementinterval and the returns from it is required (for example, maintenance costs are reduced

because items are often replaced before they fail in-service resulting in costly repairs).




Asset managers who wish to optimise the life-cycle value of the organisation’s human and

physical assets must consider four key decision areas: (1) component replacement, (2)

inspection activities, including condition monitoring, (3) replacement of capital equipment,

and (4) resource requirements. (Jardine and Tsang, 2005)

Consider the conflicts involved in decision area (1), i.e., component replacement. If adecision is made to perform repairs only, and not to do any preventive maintenance, such as

overhauls, it may well reduce the budget required by the asset management department but it

may also cause considerable production or operation downtime. Analytical models can help

the maintenance manager to take account of these interactions in order to achieve optimal

solutions, thereby reducing tension that often occurs between maintenance and operations.

Figure 1: Optimal frequency of overhauls

Figure 1.9 illustrates the type of approach taken by using a mathematical model to determine

the optimal frequency of overhauling a piece of plant by balancing the input (maintenance

cost) of the maintenance policy, against its output (reduction in downtime).

Modelling the risk of failure is a crucial step in optimising replacement of components that is

subject to failure in preventive maintenance or condition based maintenance schemes.

Weibull analysis, a powerful tool for modelling such risks, as well as the techniques and tools

available to address complications that may arise in such analysis are presented in the

subsequent section.

Outage incidents and repair times are typically classified according to failure modes, which

are known as failure codes in many organizations. Pareto charts are commonly used to

determine the maintenance priorities by ranking equipment failure codes according to their relative downtime contribution. However, these charts fail to highlight the dominant variables

that contribute to equipment downtime. These variables are frequency of failure, and mean

time to repair (MTTR). The latter part of this paper presents a powerful charting tool that

Cost of time lost dueto breakdowns

Total cost of maintenanceand time lost

Maintenance policy (say, frequency of overhauls)

C o s t / u n

i t t i m e

0

Cost of maintenance policy

Optimal Policy

0




addresses the above mentioned limitation of Pareto analyses. It allows us to classify failures

into acute and chronic problems, and identify problems that affect system reliability,

availability, and maintainability. This type of knowledge is critical in adjusting the focus of

maintenance efforts that takes into account changes in business priorities. The charting

technique can also be extended to visualize maintenance performance trends associated with

specific failure codes

Weibull Analysis

Maintenance decision analyses that consider risks of failure involve the use of the

equipment’s failure time distribution that may not be known. However, observations of

failure times may well be available from maintenance records. We might wish to find a

Weibull distribution that fits these failure observations. The Weibull distribution is named

after Waloddi Weibull (1887 ─ 1979) who found that in general, distributions of data on an

item’s time-to-failure can be modeled by a function of the following form:

The three parameters of a Weibull distribution are: β (Shape parameter), γ (Location

parameter), and η (Scale parameter). β and η have non-negative values. When an item’s

failure time distribution can be modelled by a Weibull distribution, the β value of that

distribution will determine the item’s risk profile. When β is less than, equal to, and greater

than 1, the risk of failure will decrease, remain constant, and increase with age (usage),

respectively. The motivation of replacing an item preventatively is to reduce the risk of in-service failure so as to optimize total preventive and failure replacement costs. Obviously,

there is no justification to do preventive replacement when β is not greater than 1. In such

cases, run-to-failure should be the optimal replacement policy.

The Weibull distribution that models a given set of failure data can be determined graphically

using Weibull analysis. The procedure, which involves plotting cumulative percentage failure

F (t ) versus the observes failure time t on a special probability paper known as Weibull paper,

is given in Jardine and Tsang (2005: 239 – 243).

Figure 2 shows the Weibull plot of a set of lamp failure data. A straight line can be fitted

through the plot, indicating that the Weibull distribution with γ = 0 can be used as the modelof the data set. We can then proceed to estimate the other parameters of the distribution from

the plot. From the estimation point on the top left hand corner of the Weibull paper, we draw

a line perpendicular to the fitted line. The intersection between the perpendicular line and the

β ̂ scale beneath the Estimation Point gives the estimated value of β , which is 1.2 in this case.

Thus, the lamp passes an essential hurdle to justify the adoption of a preventive replacement

policy. The value of t at which the fitted line cuts F (t ) = 63.2% (the η estimation line on

Weibull paper) is an estimate of η .

While a Weibull distribution is completely defined by the values of its γ, β and η parameters,

we may also wish to determine its mean value μ . It can also be determined from the Weibull plot, from the intersection between the perpendicular line and the P μ scale beneath the

γ

γ η

γ

η

γ

η

β β β

≤=

>⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ ⎟⎟

⎠

⎞⎜⎜⎝

⎛ −−⎟⎟

⎠

⎞⎜⎜⎝

⎛ −=

−

t t f

t t t

t f

for 0)(

for exp)(

1




Estimation Point of the Weibull paper. In the example given in Figure 2, P μ = 60%. Thus, the

distribution mean is 40 hours, the time at which the cumulative probability of failure = 60%.

Figure 2: Weibull plot of lamp failure data

Weibull analysis on failure data may get complicated in practice. Commonly encountered

complications include: the Weibull plot is non-linear; not every item observed has been run to

failure, i.e., data set with censored (incomplete) failure data; too many records need to be

analysed; and analysis of data generated from multiple failure modes. Furthermore, additional

information may need to be mined from the Weibull plot, such as determining the confidence

interval on estimates of reliability at specified age, and assessing the goodness of fit between

the hypothesized Weibull model and the data set. A discussion on the techniques and tools todeal with these situations and demands will considerably increase the size of this paper.

Interested readers are referred to Appendix 2 of Jardine and Tsang (2005) for such

information.

Item: Lamps

Age: (hours)

Pμ

β ̂

60%

1.2

60%

μ = 40 hours

η = 43 hours




Identifying Trends of Failure Data

A Weibull analysis involves fitting a probability distribution to a set of failure data. It is

assumed that the process generating the failure times is statistically stable. In reality, this

condition may not apply as in the case of failure times observed from maintenance records of

repairable systems. Fore example, design modifications and improvements made on theequipment in successive life cycles may have the effect of progressively reducing thefrequency of failure. In another scenario, imperfect repair or increasing severity of usage in

successive life cycles may produce a trend of increasing frequency of failure. Conducting aWeibull analysis on time-between-failure data of these cases is inappropriate because the

failure distribution varies from one life cycle to another. The Laplace trend test can be used todetect existence of trends in a data set of successive event times.

Let t i denotes the running time of a repairable item at its i-th failure, where i = 1, … , n; N (t n)

be the total number of failures observed to time t n, and the observation terminates at time T

when the item is in the operational state. In other words, the failure times are obtained from a

time terminated test. Figure 3 shows the notations used.

Figure 3: Time-terminated failure times

Using the Laplace trend test to determine if the failure generating process is stable, the teststatistic for time terminated data is:

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −

⋅=

∑5.0

)()(12 1

n

n

i

nt N T

t t N u …… (1)

If the process is stable, u will be normally distributed with mean = 0, standard deviation = 1.

When u is significantly small (negative), we infer the existence of reliability growth. When

u is significantly large (positive), we infer the existence of reliability deterioration.If we are satisfied that the failure generating process is stable, Weibull analysis can be

performed on the inter-failure times, (t i – t i–1), where i = 1 to n.

In the case where the observation terminates at a failure event, say t n , we have a set of failure

terminated data. The test statistic for failure terminated data is:

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −

⋅=

−

−

−

∑5.0

)()(12

1

1

11

nn

n

i

nt N t

t t N u …… (2)

Worked examples illustrating the use of Laplace trend test can be found in Jardine and Tsang(2005: 268 – 270).

• • • •• •

Running time

0 t 1 t 2 t i-1 t i t n-1 t n

t 1 t i

t n

End of observation

T




Visualization of Maintenance Priorities

Pareto charts are the classical tool used by maintenance analysts to prioritize failure codes.

Depending on the focus of attention, these Pareto charts may help to visualize ranking of

failure codes according to cumulative maintenance downtime (or costs), failure frequency,

and MTTR. The priorities generated from these Pareto charts are often dissimilar to eachother. Given the multiple listings, which failure codes should be given top priority for

improvement effort to maximize impact on business performance? It is also noted that

maintenance downtime, failure frequency, and MTTR are inter-related. Maintenance

downtime is contributed by the combined effects of failure frequency and MTTR. Thus, a

Pareto chart of maintenance downtime that prioritizes availability problems is unable to

identify failure modes that caused brief yet frequent operational disturbances (reliability

problems), or those with long downtime in each instance (maintainability problems). A tool

that can simultaneously identify availability, reliability, and maintainability problems will be

very useful to maintenance analysts. Knights (2004) presents a visualization tool that serves

this purpose. It is a scatter plot of failure codes on a log-log graph paper. The X and Y axes of

the plot indicate “number of failures” recorded and “MTTR”, respectively. Curves of constant downtime will be shown as lines with a slope of -1 on the graph. Figure 4 is an

example of such a plot, with each dot represents a failure code.

Figure 4: Log scatter plot of MTTR versus number of failuresSource: Knights (2004)

Failure codes that result in lengthy repair in each occasion are classified as acute problems,

and those that recur frequently are considered chronic problems. Thus, we can divide the

scatter plot into four quadrants as shown in Figure 5. The threshold limits that define the

boundaries of these quadrants can be determined by company policy, or they can be relative

values, as suggested by Knights (2004).

The determination of maintenance priorities is influenced by business imperatives. When

facilities have to operate at capacity to meet surplus demand for output, or when each unit of

output generates high return, the opportunity cost of lost production will far exceed the directcost of repair and maintenance. In such situation, enhancing equipment availability and




reliability should have higher priority than improving maintainability, and the “Jack-knife”

diagram shown in Figure 6 helps to identify these higher priority problems.

Figure 5: Log scatter plot with limit values

Source: Knights (2004)

Figure 6: Jack-knife diagram for facilities operating at peak capacity





In another scenario, when facilities have lots of idle capacity, or when the return from output

is low, controlling and reducing the direct cost of repair and maintenance will become the

primary focus of attention. Under such circumstances, dealing with equipment availability

and maintainability problems should be given higher priority than resolving reliability

problems, and the “Jack-knife” diagram shown in Figure 7 helps to identify these higher

priority problems.

Figure 7: Jack-knife diagram for facilities with lots of idle capacity


Maintenance performance trends associated with specific failure codes can also be visualized

on the log scatter plot. Figure 8 shows the trends of four failure codes over a period of 3 years.

Figure 8: Trends in unplanned failures for an equipmentSource: Knights (2004)



Concluding Remarks

This paper presents two powerful tools for failure data analysis that support maintenance and

replacement optimization, and prioritization of maintenance problems. The data used in such

analyses are typically maintained in the database of the computerised maintenance

management system (CMMS), enterprise asset management system (EAM), or enterpriseresource planning system (ERP). However, it should be noted that these data are often not

well organized in structure and imperfect (dirty and incomplete) in content. Preprocessing

such data for decision support becomes a challenge. Tsang, et al (2006) discuss issues of data

management for condition based maintenance (CBM) optimization. Some of the common

data quality problems identified in that publication are also relevant for effective application

of the tools presented in this paper.

References

Jardine, A.K.S. and Tsang, A.H.C. (2005) Maintenance, Replacement, and Reliability:Theory & Applications, CRC Press

Knights, P.F. (2004) “Downtime Priorities, Jack-knife Diagrams, and the Business Cycle”,

Maintenance Journal , 17(2), Melbourne, Australia

Robertson, R. and Jones, A. (2004) “Pay Day”, Plant Engineering & Maintenance, 28(9),

pages 18–25

Tsang, A.H.C., Yeung, W.K., Jardine, A.K.S. and Leung, Bartholomew P.K. (2006) “Data

Management for CBM Optimization”, Journal of Quality in Maintenance Engineering,

12(1), 37–51

tools for failure data analysis_section1

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