From HRW, 2004-05 Worldwide Hydro Directory, 2004 - © HCI Publications, www.hcipub.comReproduced with permission.

Most hydropower plants inthe world have been inservice for 40 years ormore, an age at whichreliability typically declines. As a result,preparation for life extension and mod-ernization of assets has become a keybusiness process in many hydroelectricutilities. Because a plant’s reliability is asource of competitive advantage, hydro-power business planners need to quan-tify the relationship between reliabilityimprovement and financial gain. Amethodology for accomplishing thisanalysis, described in this article, is eas-ily within the reach of hydroelectricsystem planners and engineers.

Does reliability equalprofitability?

Researchers have found that 80 to 90percent of plant life cycle costs can beattributed to decisions made in thedesign and planning stages.1 Gettingreliability right at the start of a newproject or refurbishment is important,but high reliability does not alwaysmean high profits. Generally, the higherthe reliability target placed on a design,the greater the design effort and capitalexpense required to achieve it. A higherachieved reliability normally results inlower life costs associated with opera-tions and maintenance. The total lifecost is the sum of the design and capitalcosts and the lifetime operation andmaintenance costs.

The relationship between a plant’sreliability and the revenue it can earnfollows a “law of diminishing returns.”There is a limit to how much an assetcan earn for a business, no matter howreliable it is. Therefore, extreme levels ofreliability do not necessarily produce thebest financial performance.

Figure 1 illustrates the net returns, orrevenue less total costs, for a typical hy-dro plant. The net revenue curve showsa level of reliability at which financialreturns are optimized. Improving relia-bility beyond this point will incur coststhat exceed the revenue increase.

Conversely, failing to allocate the nec-essary resources to maintain reliabilityalso will hurt profitability through in-creased maintenance and operating costsand decreased revenues. Quantifying thisrelationship allows engineers and busi-ness planners to redefine reliability issuesas profitability issues.

Quantifying reliability:understanding the basics

There are three essential steps in deter-mining whether a particular reliabilityimprovement will lead to financial gain.First, the extent of the reliability im-provement must be quantified. Second,the lost value associated with doingnothing about the reliability issue mustbe quantified. Third, the first two analy-ses must be combined to determinewhether the change will create value.

When dealing with reliability, plantlife can be divided into three character-istic periods: a period of early failures

A S S E T M A N A G E M E N T

Plant Reliability Improvement and Financial Gain:What’s the Connection?

By Marcus B. Punch

As hydro plant owners modernize and replace generating equipment, they are con-sidering how decisions about reliability will affect the plant’s value in a competitiveelectricity market. A methodology is available for quantifying reliability and itseconomic benefits.

Marcus Punch, a reliability engineer-ing consultant in Brisbane, Australia,worked for two years for a hydroutility in southeastern Australiaspecializing in hydro plant reliabilityand maintenance. He also has experi-ence applying reliability techniquesto communications and controlsystems, defense electronics, navalshipbuilding, and mining facilities.

This article has been evaluated and edited inaccordance with reviews conducted by two ormore professionals who have relevant expertise.These peer reviewers judge manuscripts for technical accuracy, usefulness, and overallimportance within the hydroelectric industry.

Application of Weibull Analysis-to-Failure Data Set

Time atFailure Failure Median (hours) Order Rank*

1,000 1 7.42,000 2 18.13,000 3 28.7 4,000 4 39.44,700 5 50.05,500 6 60.66,100 7 71.36,700 8 81.87,300 9 92.6*The median rank is calculated as 100 x (rankorder - 0.3)/(number of failures + 0.4)

Table 1

with a rapidly decreasing failure rate, aperiod when the failure rate is fairlyconstant, and a wear-out period whenthe failure rate rises rapidly. Because ofthe rapid increase in failure rate duringthe wear-out period, one cannot expectan aging plant to continue to providethe same levels of reliability that it hasin the past. Quantifying future lossesusually involves a statistical analysis ofplant utilization, the plant’s productmix, and market valuation of the prod-ucts supplied.

Reliability engineers must projectfuture failure trends and cost impactswhen determining the optimal refur-bishment or replacement option for theplant. A statistical technique known asWeibull analysis has proven to be apowerful tool for estimating future fail-ure rates of plant equipment based onplant history.

Why Weibull?

Weibull analysis is a technique for dis-covering trends in data. It involves fit-ting a failure data set to the followingcumulative distribution function:

Equation 1:

F(t) = 1-e-[th]

b

where F(t) is the probability of sur-vival until time t.

The Weibull “characteristic life,” h,is a measure of the spread in the data. It

indicates the time at which approxi-mately 63 percent of a population ofidentical items are expected to havefailed. The Weibull “shape parameter,”b, indicates whether the failure rate isincreasing, constant, or decreasing. A bof 1.0 indicates that the failure rate isconstant. If b is less than one, the itemhas a decreasing failure rate, typical ofthe early life failure period. If b isgreater than one an increasing failurerate is present, which is typical ofequipment that is wearing out.

The Weibull distribution was firstdescribed in 1949, and is now one ofthe most widely used distributions forfailure data analysis.2 An Internet web-site, www. weibull.com, contains de-tailed information on many of theprocedures discussed in this article.3

The main advantage of the Weibull dis-tribution is its versatility. It is equallyuseful in detecting increasing, constant,and decreasing failure rates. It canapproximate exponential, log-normal,and normal distributions, which alsohave been used to trend failure data.Weibull analysis also provides reasonablyaccurate reliability forecasts with verysmall data samples, and has been shownto adequately model mechanical, elec-trical, and electronic failures. It is a fun-damental component of the reliability-centered maintenance process.4

Weibull analysis, step by step

The essence of Weibull analysis is todetermine the parameters h and b for agiven set of failure data. These parame-ters are obtained by plotting failure dataand performing some simple calcula-tions. Before the advent of statisticalsoftware packages, failure data wereplotted on special Weibull plottingpaper from which the parameters couldeasily be estimated. Today, several soft-ware packages are available that plot thedata, estimate the Weibull parameters,and display the underlying failure ratetrends. One such package, includingthe programs RCMCost and AvSim+,is available from Isograph ReliabilitySoftware of Warrington, United King-dom. It is also possible to perform

2 HRW / 2004-05 Directory HRW / 2004-05 Directory 2

Figure 1: For a typical hydro plant, increased reliability yields improvedrevenues, but beyond a certain opti-mum point the costs of increasing reli-ability outweigh the revenue gains.

Figure 1

Figure 2: In Weibull analysis, the cumulative frequency of failure through timeis computed and plotted on a specially scaled graph. The Weibull parametersh and b can be determined graphically or analytically from this procedure.

Figure 2

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Weibull analysis using MS Excel spread-sheets.5

As an example of applying theWeibull distribution to failure data, con-sider a failure data set consisting of aseries of times at which failures of a spe-cific type, or “failure mode,” occurredin a population of identical equipment.These times to failure are ranked bymagnitude and a “median rank” is cal-culated for each, as shown in Table 1 onpage 1. A probability graph is then con-structed by plotting the median ranksagainst the times to failure. Figure 2 onpage 2, a plot developed using theAvSim+ software, illustrates the proce-dure. In a manual analysis, a line of bestfit is drawn through the data points plot-ted on Weibull paper, and the Weibullparameters h and b can be determinedgraphically.

The Weibull parameters in this ex-ample are h=5,259 hours and b=1.66.Therefore, this particular failure modeis exhibiting an increasing failure rateand approximately 63 percent of a pop-ulation of items exhibiting this failuremode will fail within 5,259 hours ofservice life. The AvSim+ software alsocalculates that 10 percent of the itemswill have failed within 1,358 hours.This is known as the “B10” life, a mea-sure that is often quoted on compo-nents such as bearings.

Weibull analysis is a highly versatile

technique for evaluating the reliabilityof hydropower plant components. Fig-ure 3 shows data collected on a partic-ular type of hydraulic system failure ex-perienced in a recently installed set ofturbine governors. In this example,h=10,236 hours and b=0.81. This fail-ure mode is exhibiting a decreasing fail-ure rate. The relatively high initialfailure rate may be related to the qual-

ity of the installation. However, the datapredict that those items that have sur-vived the initial period will continue tooperate with a low constant failure rate.The problem is not getting worse.

Reliability and competitiveadvantage

To understand how reliability affectsprofit, some investigation of market

Figure 3: For this data set on failures of a recently installed hydraulic governorsystem, the b parameter of 0.81 suggests that the initial high rate of failure willnot persist into the future.

Figure 3

Figure 4: This production profile for a pumped-storagehydro station illustrates how often a given number of units

are dispatched (left), and what the product mix is for eachdispatch scenario (right).

Figure 4

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supply-demand interaction is necessary.Revenue earned by electricity suppliersin deregulated markets is largely deter-mined by the timing and placement ofproduction with respect to market de-mands. A production profile effectivelyexpresses how equipment is used togain profit. The profile describes howoften various dispatching unit capacitiesare utilized, and the product-mix of dif-ferent operating modes for each level ofcapacity utilization.

For example, consider a typicalpumped-storage power station, com-prising six generating units. The stationis capable of providing generation, fre-quency control, and voltage controlproducts to the market, using pumped

storage to take advan-tage of energy marketprice differentials andtrading its standbycapacity with othergenerators.

Figure 4 shows thatalmost 40 percent ofproduction scenariosinvolve utilizing fourunits or more, and al-most 20 percent in-volve utilizing fiveunits or more. At low

capacities, the units are mainly instandby with some voltage control andpumped storage, whereas at high capac-ities production is dominated by gener-ation and voltage control. Next, thevalue that the market places on theproducts from this station during thevarious capacity utilization scenariosmust be determined. Trading recordscan be correlated with productionrecords to determine the average pricepaid for the station’s products in each ofthe capacity utilization levels.

By combining capacity utilization,product mix, and market values for allmarkets and products, a station utiliza-tion-to-earnings relationship can bedetermined. Figure 5 shows that earn-

ings are nonlinear in relation to capac-ity utilization. Most of the station rev-enue is earned during high capacityutilizations, even though the proportionof time spent in high capacity utiliza-tion is small.

For this station, unavailability of onegenerating unit when the market de-mands six units results in a much greaterloss of revenue opportunity than itwould during a lower-demand period.This is why reliability is such an impor-tant source of competitive advantage forhydropower businesses, which oftenseek to obtain revenues from peak gen-eration, rapid generator unit loading, orunderwriting the generation contractsof other producers.

Bringing it all together: a case study

Quantifying the financial benefits ofsustaining or improving reliability isessential to gaining management sup-port for reliability initiatives. A casestudy of an aging generator excitationcontrol system illustrates how quantita-tive analysis can support a proposal forreliability improvements. The produc-tion profile used in this case study is thesame as that in the previous example.

Maintenance staff had reported anincreasing rate of failure in a set of exci-tation system circuit boards. As theboards were no longer supported by themanufacturer, on-board repairs wererequired each time a failure occurred.The reliability engineer obtained failuredata for the past 25 years and plottedthem according to the Weibull formula.The plotted data formed a “kink” thatcould not be well represented by astraight line fit. Further investigationsshowed why: the failure data actuallyrepresented multiple underlying failuremodes. For a lengthy period of time thefailure rate was almost random(b=1.15), apparently due to failures ofvarious components on the circuitboards. Then, the failure rate suddenlyincreased rapidly (b=5), which maint-enance engineers attributed to compo-nent aging and degradation of thecircuit board materials and solder joints.

Probability of Being Unable to Deliver Multiple-Unit Capacity over a Ten-Year Period

Number of Percent Probability That Not All Units Will Be AvailableUnits Needed Year 1 Year 2 Year 3 Year 5 Year 10

1 0.00 0.00 0.00 0.00 0.002 0.00 0.00 0.00 0.00 0.003 0.00 0.00 0.00 0.00 0.004 0.00 0.00 0.00 0.00 0.035 0.00 0.00 0.01 0.04 0.886 0.12 0.60 1.19 2.96 14.09

Table 2

Figure 5: Revenues from a pumped-storage plant’s six units are not propor-tional to the level of utilization. The simultaneous use of five or six units ac-counts for about 40 percent of plant revenue, although this mode of operationoccurs only about 25 percent of the time.

Figure 5

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The “Bi-Weibull” distribution, a vari-ant on the Weibull distribution, wasapplied to this data set using AvSim+software. Then, using the Weibull para-meters for the recent wear-out trend,the failure rate curve for the past fouryears and a prediction for the next tenyears was plotted (Figure 6).

If the duration of each failure outageis known, it is possible to predict theunavailability of single generating unitsusing the relationship shown in the fol-lowing Equation 2:

Unavailability = 1 - MTBF/(MTBF+MTTR)

where:l MTBF is the mean time between

failures; andl MTTR is the mean time to repair

(in this case, the MTTR was eighthours).

The probability that multiple unitswill be simultaneously unavailable canbe calculated from the single unitunavailability using a standard equationfor standby redundant systems.3 Table 2shows the predicted probability that thestation will be unable to utilize variouslevels of capacity over the next ten years.

Over time, the rapidly increasing fail-ure rate substantially reduces the abilityof the station to utilize six units and alsoaffects its ability to utilize five units. Thisis significant because utilization of five orsix units accounts for more than 40 per-cent of the station’s revenue. Annual rev-enue losses can be calculated using thepercentages from Table 2 and the utiliza-tion-revenue chart. In this example, therevenue lost due to excitation systemfailures would rise from 0.02 percent inthe first year to 2.6 percent by year ten.

Evaluating costs, benefits of reliability improvements

Revenue loss is not the only cost of de-creasing reliability. There are also in-creased maintenance costs due to higherfailure rates, and there may be costsrelated to the increased risk of conse-quential damage to the plant, safetyconcerns, and environmental effects.For simplicity, only revenue is consid-ered in this case study.

To understand how reliability under-writes financial gain or wealth creation,we can compute the financial benefit-cost ratio achieved if a refurbishmentprogram were implemented in each ofthe next ten years. Expenditures mayinclude replacement of plant equip-ment, improved maintenance plans andcompliance, logistics systems, training,and increased component reliabilities.

For simplicity, “cost” is the capitalexpenditure on the program, and isassumed to be $1 million. “Benefit” is

the revenue losses averted and cost sav-ings in the years preceding the reliabil-ity improvement, less the opportunitycost of capital for the remainder of theten years. It is assumed that reliability isreturned to Year 1 levels. The results ofthis analysis suggest that despite recentfailure rate trends, the most prudenttime for project implementation is notimmediately (Figure 7). The optimalintervention would be in two to fouryears’ time. Indeed, capital expenditurecan be delayed for six years without a

Figure 6: The single-unit failure rate for the next ten years has been projectedusing Weibull analysis and based on the last four years of record.

Figure 6

Figure 7: The benefit-cost ratio for generating unit refurbishment has beencomputed from the projected future reliability of the units and the productionprofile for the plant. The graph suggests that the benefit-cost ratio would bemaximized by delaying refurbishment for two to four years.

Figure 7

2Weibull, W., “A Statistical Repres-entation of Fatigue Failures in Solids,”Transactions of the Royal Institute ofTechnology, No. 49, Stockholm,Sweden, 1949.

3www.weibull.com, ReliaSoft Corp-oration, Tucson, Ariz., USA, 1992-2003.

4Nolan, S.F., and H.F. Heap, ReliabilityCentered Maintenance, National Tech-nical Information Service, Depart-ment of Commerce, Springfield,Virginia, USA, 1978.

5Dorner, W.W., “Using MicrosoftExcel for Weibull Analysis,” QualityDigest, www.qualitydigest.com/jan99/html/weibull.html January,1999.

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ness planners might be bridged if engi-neers and technical staff found a newparadigm — that, in the final analysis,despite the technical intricacies of theirjobs, they are still managers of risk andcreators of value. s

Mr. Punch may be contacted at ARMSReliability Engineers Pty Ltd., Level 5,320 Adelaide St, Brisbane, QLD 4001,Australia; (61) 7-30109487; E-mail:mpunch@reliability.com.au or mar-cuspunch@hotmail.com.

Notes1Gatenby, D., and G. Foo, “Designing

for X: Key to Competitive, Prof-itable Markets,” AT&T TechnicalJournal, Volume 69, No. 3, 1990,pages 2-13.

substantial threat to the calculatedfinancial benefits.

Conclusion

Engineers and managers need to under-stand the importance of reliability andits relationship to profitability. Althoughthe qualitative value of reliability iswidely recognized, hydropower plantowners typically have not applied thenecessary level of resources nor em-powered their staff to develop a quanti-tative understanding of the financialimplications of reliability.

Many engineers complain that busi-ness decision-making is dominated byshort-term, cost-cutting agendas to thedetriment of long-term sustainability.This gap between engineers and busi-