**Abstract**

This paper investigates whether or not the DNF’s (those who ‘did

not finish the race’) due to early life critical part failures are

higher than would be expected in NASCAR vehicles. The hypothesis is that

early 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

have sizeable budgets and use only highly specialized components. In addition,

the extensive mileage typically associated with commercial vehicles is

not required of these parts. This paper develops a reliability model to

test whether the average time of failure for these critical components

is higher than what would be expected of high performance critical components.

**Introduction**

The origins of NASCAR reach back to the days of Prohibition, when cars

used by

moon shiners needed speed to make delivery runs and avoid the authorities

in pursuit. More horsepower was needed but the greater loads put on factory

designed engines had the adverse effect of increasing engine failures.

So began the quest to modify cars with horsepower and reliability. Simultaneously,

the sport of auto racing began. The inaugural auto race at Daytona Beach

took place March 8, 1936 (Felden, 2005).

These early races, however, were not officially organized, so races were

haphazard and drivers tended to show up randomly. Fans were few and driving

stock cars remained a hobby since it didn’t generate enough income

to qualify as a job. Over the next ten years, fan interest increased considerably

and stock car racing evolved from an occasional, hastily organized race

on sand and dirt tracks, to the frequent races in stadiums and paved tracks

we know today. In December of 1947, Bill France, Sr., a driver and race

promoter, developed the idea of NASCAR as organized stock car racing subject

to specific rules. On February 15, 1948 NASCAR ran its first race at the

Daytona Beach road course. The Daytona 500 remains the premier NASCAR

race.

NASCAR vehicles have evolved to become highly sophisticated pieces of

equipment. Parts are designed individually to maximize horsepower and

reliability. However, maximizing horsepower often compromises reliability

and vice versa. This paper has two objectives. First, NASCAR has received

scant attention in sport economics literature and the data available lend

themselves to the development of a body of academic literature on engineering

and economic issues specific to NASCAR. This paper seeks to add to that

literature. Second, this paper examines the question of whether or not

critical part failures are higher than would otherwise be expected in

NASCAR vehicles. The basis for the model presented here is standard in

the reliability engineering literature.

The paper proceeds in five parts. Part II discusses some of the literature

on NASCAR and reliability issues. Part III explains the data used in this

paper. Part IV develops a reliability model and tests it against the empirical

data. Part V presents the results and conclusions of the analysis.

**Current Research**

Scholarly research on NASCAR as a sport in any form is in its infancy.

This is particularly true where quantitative studies on NASCAR vehicle

performance and reliability are concerned. Majety, Dawande, and Rajgopal

(1999) show that in general, the typical reliability allocation problem

maximizes system reliability subject to a budget constraint. They note

that cost is an increasing function of reliability, hence the tradeoff

between dollars spent and system reliability. The latter point is certainly

true but the nature of the budget constraint specific to NASCAR is a crucial

aspect of the question pertaining to maximizing system reliability. By

many anecdotal accounts, NASCAR owners are willing to spend virtually

unlimited amounts of money to earn a spot in Victory Lane (*New York Times*, 2/13/06;

*CBS News*, 10/6/05; Pfitzner, January, 2006).

However, Wachtel (2006) suggests that a budget constraint does exist,

although budgets in NASCAR racing are far more substantial than those

common to commercially produced vehicles.

Pfitzner and Rishel (2005) developed a model predicting order of finish

in NASCAR races based on variables such as car speed, driver characteristics,

and the like. This research is significant because it takes a predictive

and quantitative approach rather than an informal and subjective approach

to predicting NASCAR race outcomes. Such academic research may eventually

become a common source of information for NASCAR teams in their pursuit

of victory. Williamson (1997) views teamwork as the key to reliability

in NASCAR component performance, hence the key to winning. Williamson’s

analysis, however, is limited to a basic management approach and largely

excludes quantitative analysis.

**The Data**

The data used in this paper were obtained from the NASCAR website. Results

were taken from the thirty-six races in each season from 2002-2005. Each

race includes forty-three cars. The data include length of race in hours,

average speed over duration of race, order of finish, laps completed,

and completion condition. Completion condition indicates one of three

outcomes for each car. The vehicle was running when it completed the race,

the vehicle did not finish the race (DNF) due to an accident, or the vehicle

did not complete the race due to critical part failure. The order of finish

statistic for the DNF’s ranks them according to laps completed at

the time of an accident or failure of a non-repairable and therefore,

as this paper defines it, a critical part.

Using 144 races over four seasons, the average time per race was calculated

to be 3.2 hours. The average percentage DNF failure rate due to critical

part failure over the four seasons was calculated to be 9.7%. For purposes

of this paper, those are the two key empirical data points needed.

**The Model**

During a NASCAR race, a certain percentage of cars do not finish the

race. Some of these DNF’s are due to crashes, which are not relevant

to the question here. This paper examines the DNF’s due to critical

part failures. Stock cars, as the term is used in NASCAR, are not “stock”

as the term is used for automobiles purchased by consumers. In the latter

sense, stock simply means that the vehicle comes equipped with factory

made parts common to other vehicles with minor variations based on make

and model. NASCAR uses the term stock in name only. As was discussed earlier,

original NASCAR vehicles were stock in the traditional sense of the word,

although amateur expert mechanics were employed to enhance the vehicular

performance. Since 1947, when NASCAR became official, NASCAR vehicles

have been stock in name only and highly trained engineers and mechanics

are allowed to modify the cars for maximum performance within a set of

rules. Sponsorship money has created budgets to build teams that can create

the winning car.

It is reasonable to assume that NASCAR teams operate with a budget constraint,

but one that is different than is the case for commercially produced vehicles.

Specifically, dollars per part spent on NASCAR vehicles are substantially

higher than dollars per part spent on commercially produced vehicles (Wachtel,

2006). This is because a NASCAR vehicle is essentially custom built, while

a typical passenger car is factory built in mass quantities. The larger

budgets afforded NASCAR teams would suggest that critical part failure

during races should be low. How low? Consider a 500 mile race. We would

expect a regularly maintained commercial vehicle with mid-level mileage

to make a 500 mile trip without a critical part failure. Yet with NASCAR

vehicles, a percentage of DNF’s over the course of a 500 mile race

occur due to critical part failure despite the higher dollar per part

expenditure and the well above average maintenance that goes into these

vehicles. Furthermore, these vehicles are virtually brand new at the start

of every race. For this reason, the model we use here assumes reliability

for critical parts in NASCAR vehicles given average race time to be .99.

This is, in other words, what we would expect from a commercially produced

vehicle.

This paper utilizes the reliability function

R(T) = e^{-λ T}

where T = average race time over the season and λ = the failure

rate (Evans and Lindsay, 1993). The function R(T) then represents the

probability that a part will not fail within T units of time. At this

point, the question we have to pose as theoretical concerns the expected

number of early life critical part failures in NASCAR vehicles. Based

on the theoretical assumptions of the model, we expect this failure rate

to be .01.

Letting T = 3 for average race time in hours and setting R(T) = .99,

we can calculate λ.

(1)

R(T) = .99 = e

^{-λ3}ln .99 = -3λ

λ = (ln .99)/3 = -.003

or λ = 1/3%

This means that if, as is documented, the average NASCAR race lasts three

hours and if we assume, according to our theory, an expected critical

part reliability rate of 99% for critical parts, then the DNF rate per

race due to critical part failure should be 1/3%. This means that 99.7%

of the cars should either finish the race or DNF due to reasons other

than critical part failures. Note that the average race time over the

four season period was slightly higher than three hours, but did not change

the value of λ to an extent that warranted rounding down to three

hours.

Using the NASCAR data described in Section III, we find that the average

critical part failure rate over the four seasons 2002-2005 was, in fact,

9.7%. We can recalculate equation (1) and solve for the time in hours

this generates for first failure. We re- write equation (1) as

(2) R(T) = .99 = e^{-.097T}

and calculate for T. Following the same procedure, we find that T = .1036.

In other words, the average time to the first critical part failure is

1/10^{th} of an hour or six minutes in a NASCAR race. For example, this is

consistent with the data from the 2005 Daytona 500 finishes where the

first car to drop out due to critical part failure was at fourteen laps.

This, at an average speed of 135 mph on the 2.5 mile oval, amounts to

about six minutes.

The graphical depiction of this reliability function, or the failure

rate curve, further illustrates our results.

In general, the failure rate curve shows the expected life of some manufactured

part. The negatively sloped portion depicts early part failure, the flat

portion depicts the useful life of a part, and ordinarily the function

would show a positive slope depicting the wear-out phase of the part.

The above function is a graphical representation of our mathematical equations

where 3.0 shows that we expect 1/3% of commercially manufactured auto

parts in a passenger vehicle to show early life failure, which means,

in this case, not beyond three hours. However, based on empirical data,

NASCAR vehicles show close to a 10% early life critical part failure suggesting

that, other things equal, a driver has a 10% chance of not finishing the

race to a critical part failure.

It should be noted, however, that this analysis assumes a constant failure

rate, which means that different test lengths during a given period of

time should show the same results. This is highly desirable where passenger

cars are concerned and when time is such a crucial element of reliability.

While one would assume this to be desirable for NASCAR vehicles, it is much more likely that the failure

rate will vary from race to race and year to year. In fact, the empirical

data bear that out.

**Results and Conclusion**

This paper hypothesized a reliability rate of 99% for a conventionally

manufactured vehicle over a three-hour time span. We used this as a reasonable

expectation for NASCAR vehicles because of the higher dollar per part

spent on NASCAR as compared to commercially manufactured vehicles, in

addition to the number of highly trained mechanics and engineers devoted

to essentially custom building a new car for each race. However, for thirty-six

races for each of four NASCAR seasons between 2002 and 2005, our results

showed a 9.7% critical part failure rate. The question then becomes, what

accounts for this?

The 9.7% critical part failure rate may be attributable to two factors.

First, under normal driving circumstances, NASCAR vehicles would demonstrate

the same reliability of 1/3% critical part failure rate over a three hour

time period as commercially produced vehicles do, were it not for the

fact that in an effort to increase horsepower and speed, critical parts

in NASCAR vehicles are pushed to their tolerance limits throughout the

race and can be expected to fail at higher rates. Second, NASCAR rules

place restrictions on the critical part reliability improvements that

NASCAR teams can make. For examples, compression ratios must be 12:1,

engine size cannot exceed 358 cubic inches, and the materials composition

of the vehicles and its parts cannot include titanium. These are a few

of the rules designed to prevent certain team specific technological improvements

that would make each race predictable in terms of outcome and thus potentially

reduce competitiveness and fan interest in NASCAR.

Areas for further research in NASCAR and the economics of sports are numerous.

One such application of this particular paper might be an examination

of the specific rules NASCAR places on the use of technology, which may

be useful in re-formulating the reliability function. Another application

might be the inclusion of a specific budget constraint to re-formulate

the problem as one of optimization subject to constraint.

**References**

Evans, James and William Lindsay. *The Management and Control of Quality*,

3^{rd} ed., 1996, West Publishing Company.

Felden, Greg. NASCAR: *A Fast History*, 2005, Publications International

Ltd.

Lorincz, Jim. “CNC machining improves NASCAR Cars,” *Manufacturing Engineering*, vol. 136, no.1, January, 2006.

Majety, Subba Rao, Millind Dawande, Jayant Rajgopal. “Optimal reliability

allocation with discrete cost-reliability data for components,”

*Operations Research*, vol. 47, no.6, Nov-Dec., 1999.

Martin, Mark. *NASCAR for Dummies*, 2005, Wiley Publishing.

“Weather man made to order for NASCAR’s engine tests,”

*New York Times*, February 13, 2006.

Pfitzner, Barry, Tracy Rishel. “Do reliable predictors exist for

the outcomes of NASCAR races?” *The Sport Journal*, vol.

8, no.2, Spring 2005.

Wachtel, Gene. Mechanical Engineer, Hendrick Motor Sports, Personal Interview,

February 10, 2006.

Williamson, Robert. “NASCAR racing teamwork leads to reliable equipment,”

*AFE Facilities Engineering*, July-August, 1997.