{"id":260,"date":"2008-03-14T14:16:38","date_gmt":"2008-03-14T14:16:38","guid":{"rendered":""},"modified":"2016-10-24T11:20:21","modified_gmt":"2016-10-24T16:20:21","slug":"are-there-a-higher-than-expected-number-of-early-life-critical-part-failures-in-nascar-vehicles-a-reliability-studywhat","status":"publish","type":"post","link":"https:\/\/thesportjournal.org\/article\/are-there-a-higher-than-expected-number-of-early-life-critical-part-failures-in-nascar-vehicles-a-reliability-studywhat\/","title":{"rendered":"Are There a Higher than Expected Number of Early Life Critical Part Failures in NASCAR Vehicles? A Reliability Study"},"content":{"rendered":"
Submitted by: Mary Allender<\/div>\n

Abstract<\/strong><\/p>\n

This paper investigates whether or not the DNF\u2019s (those who \u2018did not finish the race\u2019) due to early life critical part failures are higher than would be expected in NASCAR vehicles. The hypothesis is that
\n\tearly life critical part failures are, in fact, higher than would be expected in NASCAR vehicles. This hypothesis is based on the fact that NASCAR teams
\n\thave sizeable budgets and use only highly specialized components. In addition,
\n\tthe extensive mileage typically associated with commercial vehicles is
\n\tnot required of these parts. This paper develops a reliability model to
\n\ttest whether the average time of failure for these critical components
\n\tis higher than what would be expected of high performance critical components.<\/p>\n

<\/p>\n

Introduction<\/strong><\/p>\n

The origins of NASCAR reach back to the days of Prohibition, when cars
\n\tused by
\n\tmoon shiners needed speed to make delivery runs and avoid the authorities
\n\tin pursuit. More horsepower was needed but the greater loads put on factory
\n\tdesigned engines had the adverse effect of increasing engine failures.
\n\tSo began the quest to modify cars with horsepower and reliability. Simultaneously,
\n\tthe sport of auto racing began. The inaugural auto race at Daytona Beach
\n\ttook place March 8, 1936 (Felden, 2005).<\/p>\n

These early races, however, were not officially organized, so races were
\n\thaphazard and drivers tended to show up randomly. Fans were few and driving
\n\tstock cars remained a hobby since it didn\u2019t generate enough income
\n\tto qualify as a job. Over the next ten years, fan interest increased considerably
\n\tand stock car racing evolved from an occasional, hastily organized race
\n\ton sand and dirt tracks, to the frequent races in stadiums and paved tracks
\n\twe know today. In December of 1947, Bill France, Sr., a driver and race
\n\tpromoter, developed the idea of NASCAR as organized stock car racing subject
\n\tto specific rules. On February 15, 1948 NASCAR ran its first race at the
\n\tDaytona Beach road course. The Daytona 500 remains the premier NASCAR
\n\trace.<\/p>\n

NASCAR vehicles have evolved to become highly sophisticated pieces of
\n\tequipment. Parts are designed individually to maximize horsepower and
\n\treliability. However, maximizing horsepower often compromises reliability
\n\tand vice versa. This paper has two objectives. First, NASCAR has received
\n\tscant attention in sport economics literature and the data available lend
\n\tthemselves to the development of a body of academic literature on engineering
\n\tand economic issues specific to NASCAR. This paper seeks to add to that
\n\tliterature. Second, this paper examines the question of whether or not
\n\tcritical part failures are higher than would otherwise be expected in
\n\tNASCAR vehicles. The basis for the model presented here is standard in
\n\tthe reliability engineering literature.<\/p>\n

The paper proceeds in five parts. Part II discusses some of the literature
\n\ton NASCAR and reliability issues. Part III explains the data used in this
\n\tpaper. Part IV develops a reliability model and tests it against the empirical
\n\tdata. Part V presents the results and conclusions of the analysis.<\/p>\n

Current Research<\/strong><\/p>\n

Scholarly research on NASCAR as a sport in any form is in its infancy.
\n\tThis is particularly true where quantitative studies on NASCAR vehicle
\n\tperformance and reliability are concerned. Majety, Dawande, and Rajgopal
\n\t(1999) show that in general, the typical reliability allocation problem
\n\tmaximizes system reliability subject to a budget constraint. They note
\n\tthat cost is an increasing function of reliability, hence the tradeoff
\n\tbetween dollars spent and system reliability. The latter point is certainly
\n\ttrue but the nature of the budget constraint specific to NASCAR is a crucial
\n\taspect of the question pertaining to maximizing system reliability. By
\n\tmany anecdotal accounts, NASCAR owners are willing to spend virtually
\n\tunlimited amounts of money to earn a spot in Victory Lane (New York
\n\tTimes<\/em>, 2\/13\/06; CBS News<\/em>, 10\/6\/05; Pfitzner, January, 2006).
\n\tHowever, Wachtel (2006) suggests that a budget constraint does exist,
\n\talthough budgets in NASCAR racing are far more substantial than those
\n\tcommon to commercially produced vehicles.<\/p>\n

Pfitzner and Rishel (2005) developed a model predicting order of finish
\n\tin NASCAR races based on variables such as car speed, driver characteristics,
\n\tand the like. This research is significant because it takes a predictive
\n\tand quantitative approach rather than an informal and subjective approach
\n\tto predicting NASCAR race outcomes. Such academic research may eventually
\n\tbecome a common source of information for NASCAR teams in their pursuit
\n\tof victory. Williamson (1997) views teamwork as the key to reliability
\n\tin NASCAR component performance, hence the key to winning. Williamson\u2019s
\n\tanalysis, however, is limited to a basic management approach and largely
\n\texcludes quantitative analysis.<\/p>\n

The Data<\/strong><\/p>\n

The data used in this paper were obtained from the NASCAR website. Results
\n\twere taken from the thirty-six races in each season from 2002-2005. Each
\n\trace includes forty-three cars. The data include length of race in hours,
\n\taverage speed over duration of race, order of finish, laps completed,
\n\tand completion condition. Completion condition indicates one of three
\n\toutcomes for each car. The vehicle was running when it completed the race,
\n\tthe vehicle did not finish the race (DNF) due to an accident, or the vehicle
\n\tdid not complete the race due to critical part failure. The order of finish
\n\tstatistic for the DNF\u2019s ranks them according to laps completed at
\n\tthe time of an accident or failure of a non-repairable and therefore,
\n\tas this paper defines it, a critical part.<\/p>\n

Using 144 races over four seasons, the average time per race was calculated
\n\tto be 3.2 hours. The average percentage DNF failure rate due to critical
\n\tpart failure over the four seasons was calculated to be 9.7%. For purposes
\n\tof this paper, those are the two key empirical data points needed.<\/p>\n

The Model<\/strong><\/p>\n

During a NASCAR race, a certain percentage of cars do not finish the
\n\trace. Some of these DNF\u2019s are due to crashes, which are not relevant
\n\tto the question here. This paper examines the DNF\u2019s due to critical
\n\tpart failures. Stock cars, as the term is used in NASCAR, are not \u201cstock\u201d
\n\tas the term is used for automobiles purchased by consumers. In the latter
\n\tsense, stock simply means that the vehicle comes equipped with factory
\n\tmade parts common to other vehicles with minor variations based on make
\n\tand model. NASCAR uses the term stock in name only. As was discussed earlier,
\n\toriginal NASCAR vehicles were stock in the traditional sense of the word,
\n\talthough amateur expert mechanics were employed to enhance the vehicular
\n\tperformance. Since 1947, when NASCAR became official, NASCAR vehicles
\n\thave been stock in name only and highly trained engineers and mechanics
\n\tare allowed to modify the cars for maximum performance within a set of
\n\trules. Sponsorship money has created budgets to build teams that can create
\n\tthe winning car.<\/p>\n

It is reasonable to assume that NASCAR teams operate with a budget constraint,
\n\tbut one that is different than is the case for commercially produced vehicles.
\n\tSpecifically, dollars per part spent on NASCAR vehicles are substantially
\n\thigher than dollars per part spent on commercially produced vehicles (Wachtel,
\n\t2006). This is because a NASCAR vehicle is essentially custom built, while
\n\ta typical passenger car is factory built in mass quantities. The larger
\n\tbudgets afforded NASCAR teams would suggest that critical part failure
\n\tduring races should be low. How low? Consider a 500 mile race. We would
\n\texpect a regularly maintained commercial vehicle with mid-level mileage
\n\tto make a 500 mile trip without a critical part failure. Yet with NASCAR
\n\tvehicles, a percentage of DNF\u2019s over the course of a 500 mile race
\n\toccur due to critical part failure despite the higher dollar per part
\n\texpenditure and the well above average maintenance that goes into these
\n\tvehicles. Furthermore, these vehicles are virtually brand new at the start
\n\tof every race. For this reason, the model we use here assumes reliability
\n\tfor critical parts in NASCAR vehicles given average race time to be .99.
\n\tThis is, in other words, what we would expect from a commercially produced
\n\tvehicle.<\/p>\n

This paper utilizes the reliability function<\/p>\n

R(T) = e-\u03bb T<\/sup><\/p>\n

where T = average race time over the season and \u03bb = the failure
\n\trate (Evans and Lindsay, 1993). The function R(T) then represents the
\n\tprobability that a part will not fail within T units of time. At this
\n\tpoint, the question we have to pose as theoretical concerns the expected
\n\tnumber of early life critical part failures in NASCAR vehicles. Based
\n\ton the theoretical assumptions of the model, we expect this failure rate
\n\tto be .01.<\/p>\n

Letting T = 3 for average race time in hours and setting R(T) = .99,
\n\twe can calculate \u03bb.<\/p>\n

(1)<\/p>\n

\n

R(T) = .99 = e-\u03bb3<\/sup><\/p>\n

ln .99 = -3\u03bb<\/p>\n

\u03bb = (ln .99)\/3 = -.003<\/p>\n

or \u03bb = 1\/3%<\/p>\n<\/blockquote>\n

This means that if, as is documented, the average NASCAR race lasts three
\n\thours and if we assume, according to our theory, an expected critical
\n\tpart reliability rate of 99% for critical parts, then the DNF rate per
\n\trace due to critical part failure should be 1\/3%. This means that 99.7%
\n\tof the cars should either finish the race or DNF due to reasons other
\n\tthan critical part failures. Note that the average race time over the
\n\tfour season period was slightly higher than three hours, but did not change
\n\tthe value of \u03bb to an extent that warranted rounding down to three
\n\thours.<\/p>\n

Using the NASCAR data described in Section III, we find that the average
\n\tcritical part failure rate over the four seasons 2002-2005 was, in fact,
\n\t9.7%. We can recalculate equation (1) and solve for the time in hours
\n\tthis generates for first failure. We re- write equation (1) as<\/p>\n

(2) R(T) = .99 = e-.097T<\/sup><\/p>\n

and calculate for T. Following the same procedure, we find that T = .1036.
\n\tIn other words, the average time to the first critical part failure is
\n\t1\/10th<\/sup> of an hour or six minutes in a NASCAR race. For example, this is
\n\tconsistent with the data from the 2005 Daytona 500 finishes where the
\n\tfirst car to drop out due to critical part failure was at fourteen laps.
\n\tThis, at an average speed of 135 mph on the 2.5 mile oval, amounts to
\n\tabout six minutes.<\/p>\n

The graphical depiction of this reliability function, or the failure
\n\trate curve, further illustrates our results.<\/p>\n

\"Graph\"<\/p>\n

In general, the failure rate curve shows the expected life of some manufactured
\n\tpart. The negatively sloped portion depicts early part failure, the flat
\n\tportion depicts the useful life of a part, and ordinarily the function
\n\twould show a positive slope depicting the wear-out phase of the part.
\n\tThe above function is a graphical representation of our mathematical equations
\n\twhere 3.0 shows that we expect 1\/3% of commercially manufactured auto
\n\tparts in a passenger vehicle to show early life failure, which means,
\n\tin this case, not beyond three hours. However, based on empirical data,
\n\tNASCAR vehicles show close to a 10% early life critical part failure suggesting
\n\tthat, other things equal, a driver has a 10% chance of not finishing the
\n\trace to a critical part failure.<\/p>\n

It should be noted, however, that this analysis assumes a constant failure
\n\trate, which means that different test lengths during a given period of
\n\ttime should show the same results. This is highly desirable where passenger
\n\tcars are concerned and when time is such a crucial element of reliability.
\n\tWhile one would assume this to be desirable for NASCAR vehicles, it is much more likely that the failure
\n\trate will vary from race to race and year to year. In fact, the empirical
\n\tdata bear that out.<\/p>\n

Results and Conclusion<\/strong><\/p>\n

This paper hypothesized a reliability rate of 99% for a conventionally
\n\tmanufactured vehicle over a three-hour time span. We used this as a reasonable
\n\texpectation for NASCAR vehicles because of the higher dollar per part
\n\tspent on NASCAR as compared to commercially manufactured vehicles, in
\n\taddition to the number of highly trained mechanics and engineers devoted
\n\tto essentially custom building a new car for each race. However, for thirty-six
\n\traces for each of four NASCAR seasons between 2002 and 2005, our results
\n\tshowed a 9.7% critical part failure rate. The question then becomes, what
\n\taccounts for this?<\/p>\n

The 9.7% critical part failure rate may be attributable to two factors.
\n\tFirst, under normal driving circumstances, NASCAR vehicles would demonstrate
\n\tthe same reliability of 1\/3% critical part failure rate over a three hour
\n\ttime period as commercially produced vehicles do, were it not for the
\n\tfact that in an effort to increase horsepower and speed, critical parts
\n\tin NASCAR vehicles are pushed to their tolerance limits throughout the
\n\trace and can be expected to fail at higher rates. Second, NASCAR rules
\n\tplace restrictions on the critical part reliability improvements that
\n\tNASCAR teams can make. For examples, compression ratios must be 12:1,
\n\tengine size cannot exceed 358 cubic inches, and the materials composition
\n\tof the vehicles and its parts cannot include titanium. These are a few
\n\tof the rules designed to prevent certain team specific technological improvements
\n\tthat would make each race predictable in terms of outcome and thus potentially
\n\treduce competitiveness and fan interest in NASCAR.<\/p>\n

Areas for further research in NASCAR and the economics of sports are numerous.
\n\tOne such application of this particular paper might be an examination
\n\tof the specific rules NASCAR places on the use of technology, which may
\n\tbe useful in re-formulating the reliability function. Another application
\n\tmight be the inclusion of a specific budget constraint to re-formulate
\n\tthe problem as one of optimization subject to constraint.<\/p>\n

References<\/strong><\/p>\n

Evans, James and William Lindsay. The Management and Control of Quality<\/em>,
\n\t3rd<\/sup> ed., 1996, West Publishing Company.<\/p>\n

Felden, Greg. NASCAR: A Fast History<\/em>, 2005, Publications International
\n\tLtd.<\/p>\n

Lorincz, Jim. \u201cCNC machining improves NASCAR Cars,\u201d Manufacturing
\n\tEngineering<\/em>, vol. 136, no.1, January, 2006.<\/p>\n

Majety, Subba Rao, Millind Dawande, Jayant Rajgopal. \u201cOptimal reliability
\n\tallocation with discrete cost-reliability data for components,\u201d
\n\tOperations Research<\/em>, vol. 47, no.6, Nov-Dec., 1999.<\/p>\n

Martin, Mark. NASCAR for Dummies<\/em>, 2005, Wiley Publishing.<\/p>\n

\u201cWeather man made to order for NASCAR\u2019s engine tests,\u201d
\n\tNew York Times<\/em>, February 13, 2006.<\/p>\n

Pfitzner, Barry, Tracy Rishel. \u201cDo reliable predictors exist for
\n\tthe outcomes of NASCAR races?\u201d The Sport Journal<\/em>, vol.
\n\t8, no.2, Spring 2005.<\/p>\n

Wachtel, Gene. Mechanical Engineer, Hendrick Motor Sports, Personal Interview,
\n\tFebruary 10, 2006.<\/p>\n

Williamson, Robert. \u201cNASCAR racing teamwork leads to reliable equipment,\u201d
\n\tAFE Facilities Engineering<\/em>, July-August, 1997.<\/p>\n","protected":false},"excerpt":{"rendered":"

Submitted by: Mary Allender<\/div>\n

Abstract<\/strong> <\/p>\n

This paper investigates whether or not the DNF’s (those who ‘did
\n not finish the race’) due to early life critical part failures are
\n higher than would be expected in NASCAR vehicles. The hypothesis is that
\n early life critical part failures are, in fact, higher than would be expected
\n in NASCAR vehicles. This hypothesis is based on the fact that NASCAR teams
\n have sizeable budgets and use only highly specialized components. In addition,
\n the extensive mileage typically associated with commercial vehicles is
\n not required of these parts. This paper develops a reliability model to
\n test whether the average time of failure for these critical components
\n is higher than what would be expected of high performance critical components.<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true,"jetpack_social_options":[]},"categories":[290,291],"tags":[27,76,77,8],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p4btio-4c","jetpack-related-posts":[{"id":335,"url":"https:\/\/thesportjournal.org\/article\/the-role-of-driver-experience-in-predicting-the-outcome-of-nascar-races-an-empirical-analysis\/","url_meta":{"origin":260,"position":0},"title":"The Role of Driver Experience in Predicting the Outcome of NASCAR Races: An Empirical Analysis","date":"April 15, 2009","format":false,"excerpt":"Submitted by: Mary Allender - Pamplin School of Business - University of Portland Abstract As national interest in NASCAR grows, the field of sports economics is increasingly addressing various aspects of this sporting contest. 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