Transnational Research Associates

Inexpensive Automobile Tires

The Bathtub Curve, Reliability and Safety

A Brief Inferential Statistical Analysis

Art Madsen, M.Ed.

Executive Summary

The original proposal for this reliability study foresaw the usefulness of studying automobile tire reliability and intended to do so by examining, in some depth, eight models of Goodyear Tires and deriving a price/reliability ratio that might prove valuable to the consumer. However, in the interim, it was felt that the central issue involved should be some aspect of the actual reliability of the manufactured product, rather than exclusive emphasis on pricing policy and consumer satisfaction, which is more of a marketing inquiry. Pricing in relation to reliability is important, however, when calculating manufacturing costs, among other factors, and so it will be mentioned in one of the four items of investigation in this study.

In the Systems Design Analysis section of the paper, an explanation of how reliability pertains to the tire manufacturing industry will be offered. Also mentioned will be the objectives of reliability-engineers and their design strategies. The Design Analysis segment will be followed by the presentation of three hypotheses. The hypotheses will be supported or rejected on the basis of a locally conducted survey of experienced motorists, coupled with engineering findings converted to Likert scores, correlated with results of the motorist survey. Definitions will be provided to enhance uniformity and accuracy, insofar as possible, of data collection and analysis. In standard academic format, Methods, Results, Discussion and Recommendations will follow. These sections will incorporate published, accepted data from engineering journals or their equivalents, which will be statistically analyzed in relation to findings among local motorists to derive coefficients of correlation of the two data sets.

System Design Analysis

The design of this study, with some obvious limitations, will empirically demonstrate whether local motorists reflect in their personal experience certain assumptions of professional tire reliability experts, and, if so, to what degree. Correlation results will be statistically calculated and an attempt to establish significance at the .05 level of confidence will be made.

The majority of reliability engineers base their predictions of product reliability on the supposition that all product-components are linked in a series. Failure of any one component means failure for the entire product. So, the more components or parts of a product there are, the higher is the probability of failure. In most calculations used by reliability experts, it is known that the failure rate in the initial phase of use is 2.8 times as high as during the mature use phase of the product (Punches, K., 1996). This corresponds to the classic "bathtub curve" known well by reliability engineers. However, for tires specifically, it is possible to remove design and manufacturing flaws so that they function properly in the initial stages. The mini-survey outlined below, comparing engineers' assumptions, as expressed in published literature, with motorist experience, may demonstrate that, in fact, the bathtub curve does not apply even to low-price range tires.

When examining the tire industry, reliability is not considered a function of time, but rather of distance. Product warranties are based on mileage, not months of use. Thus, assuming average driving habits and conditions, distance is a vital factor in predicting failure. After a pre-calculated finite distance, up to 63.2% of all products, hence tires, will, in fact, fail, according to the standard Mean Time Between Failures (MTBF) equation (Ebeling, 1997).

The objectives of tire reliability engineers are to ensure the longest possible failure-free operating distance for each manufacturing dollar spent and to do so over the wide range of their products, whether expensive or inexpensive. In order to achieve this objective, they examine each component-part of the tire that will be used and look closely at its function and performance. Qualification tests are conducted and important decisions impacting safety and reliability, are made.

Model Development

By excerpting these types of known reliability principals from the professional literature and by converting these data to a Likert Mean for the same questions asked locally, a correlation coefficient will be derived.

The mini-survey of experienced drivers in the Las Cruces area, mentioned above, will be conducted to determine (Q1, Q2) whether the standard bathtub curve pertains to tires, as engineering literature suggests, or whether modern design and fabrication techniques have eliminated 'early life fails' in inexpensive tire models. This survey will also (Q3) shed light on a small, but statistically valid, sampling of motorists with regard to their experience with the reliability-levels of expensive tires in relation to inexpensive ones. Safety concerns will (Q4) also be addressed by revealing motorist tire-safety experience with inexpensive models.

Three basic hypotheses will be formulated and subsequently supported or rejected by two sets of data to be generated and analyzed. Comparison of results with engineers' reliability findings will then be made under Discussion and Recommendations. Tentative suggestions and insights will be offered in the Recommendations section.




I. Engineering statements will be excerpted from professional reliability literature cited on Table II in Appendix II. Focus will be placed on the four parameters reflected on the survey questionnaire. It is important that engineering data pertaining to the bathtub curve for items one and two be converted to a Likert mean (Agree/Disagree). For questions three and four, similar information will be extracted from existing professional literature and converted to a Likert mean. The mechanism of conversion from the journal article to a numeric Likert figure will rely on the reasonable assumption that at least 50 reliability engineers would stand behind statements made in a published journal. Where actual percentages of support are provided or implied in the literature, the Likert score will reflect that percentage (e.g. 75% certainty will convert to 7.5 on the Likert scale). Where percentages are not available, a high Likert reading will be assigned if the data is phrased convincingly and with certainty in the cited article. The converse would prove the case, as well. This is a 'rule of thumb' principle that can be construed as reasonable for statistical purposes. Detractors, of course, could find fault with this conversion methodology.

II. For the second motorist experiential portion of the study, a simple "1-10 Likert Disagree/Agree" questionnaire has been designed to elicit information from approximately 50 motorists encountered at random within 100 feet of the Las Cruces (NM) WALMART Automotive Garage facility located at 2351 E. Lohman Avenue. To avoid respondent unwillingness to cooperate, only four key questions appear on the questionnaire. The questionnaire (Appendix I) focuses, in simple terminology, on the "bathtub curve" concept in the first two items, and on the experience motorists have had with both expensive and inexpensive tire models in relation to tire failure and general safety, in the final two items. From empirical data generated, certain guarded conclusions as to the accuracy of the reliability engineers' findings, referred to immediately above, can be drawn.

Both data sets, presented in raw form in Appendix II, will be analyzed using a standard Pearson Product-Moment Correlation Model with anticipated validation of results at the .05 level of confidence.


[Raw Data Appended]


Interpretation of Results

Examining the foregoing results indicates that, for three of the four questionnaire items, the driving public's experience with inexpensive tires correlates well with reliability engineers' findings. There is a significant discrepancy on item two. We need to keep firmly in mind in this discussion that "correlation" does not imply "causation." So, perhaps obviously, what reliability engineers may feel is valid or invalid in this study cannot, and did not, influence the Walmart motorist survey results.

In item one, both the public and the engineering community acknowledge that the standard 'bathtub curve' is not an operative concept pertaining to tires. The public strongly disagrees (M = 2.35) with the questionnaire statement that tires fail in the initial period after purchase, and engineering literature suggests the same, since technology has 'built in' the latest design features preventing early product failure. These results call into question the validity of the bathtub curve's left-hand parameter with respect to inexpensive automobile tires.

Interestingly, the first hypothesis (H1) is not supported by these findings. Neither the public nor the engineering specialists seemed to confirm the notion that new tires, even if inexpensive, fail in the initial stages after purchase. The correlation coefficient of r = . 49 demonstrates a moderately high degree of agreement or inter-relatedness between the public and engineers that the bathtub curve does not apply to new tires. These results, which could be readily replicated in any future survey, are found significant at the .05 level of confidence on Australia National University's Doing Psychology Chart, Appendix 2, Table 3, p. 291 (or on any such chart, widely available).

For item two, the public's experience with inexpensive tires indicates that their tires do not fail at the 40,000 mile mark, which would represent the right-hand side of the bathtub curve. However, the cited engineering literature, as reflected in the 7.67 Mean, (indicating moderately strong agreement with the contents of item 2) suggests that engineers agree that tires do reach a wear-point in that approximate mileage range. The negative correlation coefficient of r = - .28 indicates the marked degree divergence between the two respondent groups; it also means that replication of these results is improbable or unpredictable.

This item's relationship to the first hypothesis (H1) is ambivalent. Engineers' support the right-hand side of the bathtub curve, whereas empirical and experiential data from motorists would tend to undermine the wear-point concept. There may be a flaw, of course, in the questionnaire model-construct or in the way the respondents perceived the question, since, obviously, tires fail at some point. The 40,000 mile mark was an arbitrary, but realistic, estimate of where Goodyear's relatively low-cost model (T-Metric) might begin to fail. (In fact, Goodyear representatives in Las Cruces stated that their tire warranty was valid to 40,000 miles.)

For item three, engineers and the public agree that more expensive tire models are likely to be more reliable. The Likert means, respectively, are 7.38 and 7.55, with a convincing degree of correlation, at r =.49, also found significant at the .05 level. The implications involved in this item deal with the notion that higher materials costs produce higher quality products, and that good components have a high reliability quotient. This realization is borne out in the literature, notably in Punches (1996) who addresses cost issues in the field of electronics, but whose findings apply to all manufactured or assembled products such as tires.

For item four, which deals with safety and tire price, positive findings emerged. The public (M=7.21) and the engineering community (M= 8.06) did, in fact, find that safety improved with increases in retail price. There was a distinctly conclusive correlation between these two data sets on this item. Hypothesis three was supported by the findings generated in both data sets. It is interesting that there is an underlying perception that more 'money means more safety', even though Government safety standards must ensure 'bottom-line' safety of the motoring public.

Conversion Method of Engineering Statements

Of the 15 references used for preparation of this paper, it was determined that two, in particular, served to best provide the evidence that was required for responding to the four questionnaire items, i.e. on the engineers' portion of the study. Of course, many more articles and books were consulted to glean relevant information from the field of reliability engineering for drafting of this study. Yet, the Goodyear web-site and the Gorzelany article were found most useful for purposes of substantiating replies to the four survey questions. The method of conversion relied, as indicated earlier, on the reasonable assumption that at least 50 qualified engineers would support these two authoritative, published sources. When calculating Mean Scores and the Correlation Coefficient it was thought best to use a range of Likert scores for each question. That range is indicated on Table II in Appendix II. It spans two or three points and best replicates what might be a random response pattern of engineers to the statements made in the articles cited. Given the lack of certified reliability engineering personnel in the local area surrounding the University during the Holiday Season, the above method best simulates typical responses and values. In future versions of similar studies conducted, it would be recommended that actual survey questions be presented to engineers as they were to Walmart Automotive respondents.

Limitations of Study

This paper is primarily conceptual in nature. Findings are predicated on a limited sampling of public respondents and on engineering statements made in Goodyear and professional reliability articles that sometimes imply, rather than state, certain tire-performance criteria. This must be kept in mind when reviewing data, conclusions and recommendations. Nonetheless, certain guarded assertions as to the non-applicability of the bathtub curve to the tire industry can be considered, on the basis of this inferential study, which falls well within the realm of the 'realistic'.

Formally speaking, this paper does not exclusively reflect technical material dealing with reliability, as such, although it contributes substantially to the confirmation of reliability engineers' facts and figures regarding the safety, failure-rate and underlying assumptions related to product reliability. Under these circumstances, this study, and future efforts along these lines, could act as testing mechanisms for theoretical models to be developed in research institutions associated with major product manufacturers.

Federal Safety Regulations

For inexpensive tires nationwide, Federal Safety Guidelines apply to manufacturing standards. Results of item number four, therefore, in this study's questionnaire might have been influenced to some degree by this recognition on the part of respondents. However, it is noteworthy to point out that all respondents, in both data sets, seemed to feel that there was a perceivable relationship between cost and safety, with both factors increasing in parallel.

Mean Age of Respondents

The mean age of Walmart respondents has not been formally documented in the data tables. However, their age range spanned 16 to 55 years of age, with a probable mean of 30 years, indicating approximately 14 or 15 years of driving experience, and ownership of at least three vehicles, on average, during that period. This observation would tend to further strengthen the findings of this brief correlation-based reliability survey.


There was a mixed pattern of Support and Non-Support of this paper's three Hypotheses. It was found that the bathtub curve, contrary to H1, was not an operative feature of new tires in the inexpensive price range. The right-hand portion of the bathtub curve was, however, partially confirmed in this survey and the significance of these results was noted.

However, the remaining two Hypotheses (H2 and H3) were completely supported, since high reliability was perceived as related to high price. Interestingly, data did not allow us to conclude that low price was or was not necessarily related to unreliability. The safety and price hypothesis (H3) was supported, in spite of probable motorist recognition that, among low-end priced products, government regulations provided the absolute 'floor' for consumer safety parameters.

Lastly, it is largely true that what engineers know about tire reliability is reflected in the local sampling of experienced motorists. However, motorists' empirical data suggest that their tires did not fail at times indicated in the professional literature.

In terms of recommendations, it must be noted that few inexpensive tires seem, under normal driving conditions, to have failed before 2000 miles; therefore, on-going quality control of manufacturing processes is indicated, while redoubled efforts to improve these products are probably not necessary. Design is already adequate at the low-price end of most tire product-lines. Further, government standards have ensured bottom-line safety and reliability. Continued research, however, to keep prices low and reliability/quality high is advised. Surely, new materials and processes could be profitably explored by the tire industry which, already, seems to be providing excellent quality merchandise to the value-conscious consumer. Reliability Engineers are accomplishing their tasks, as well; indeed, motorists are aware of their findings, through publications such as Consumers Digest, and seem to place implicit trust in the judgement of reliability engineers insofar as reliability and safety are concerned.


Reliability Survey Questionnaire

Based on your actual experience:

1. Tires costing less than $100 have failed before 2, 000 miles............1 2 3 4 5 6 7 8 9 10

2. Tires costing less than $100 each begin to fail at 40,000 miles........ 1 2 3 4 5 6 7 8 9 10

3. More expensive tires are more reliable.......................................... 1 2 3 4 5 6 7 8 9 10

4. An expensive tire is safer than an inexpensive tire.......................... 1 2 3 4 5 6 7 8 9 10


A. Engineering Data Based on Cited Sources, Converted to Likert Means / N = 52

(Insert Excel Engineering Table I Here)

Item .................Author.............. Article Name .....Date/Page.... Likert Range.... Random Mean

Question 1   Gorzelany    Tires/C. D.  Nov 98/75     1 to 3       2.10         

Question 2   Goodyear     T-Metric     'tl.html'     7 to 9       7.67         

Question 3   Gorzelany    Best Buys    Nov 98/76     7 to 9       7.55         

Question 4   Gorzelany    Tires/C.D.   Nov 98/76     8 to 10      8.06         
Table II: Summary of Engineering Input Sources 

B. Likert-Based Local Survey Results / N= 52

(Insert Excel Walmart Table Here)


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Bunday, B.D. Statistical Methods in Reliability Theory and Practice, Ellis Horwood, New York, N.Y., 1991.

Calabro, S.R. Reliability Principles and Practices, McGraw-Hill Book Company, Inc., New York, N.Y., 1962.

Continental/General Tire, "Timely delivery of quality tires backed by strong sales 'partners'",

Crowder, M.J. Kimber, A.C., Smith, R.L., and Sweeting, T.J., Statistical Analysis of Reliability Data, Chapman & Hall, London, 1991.

Ebeling, C., An Introduction to Reliability and Maintainability, McGraw-Hill, New York, N.Y., 1997.

Frankel, E.G. Systems Reliability and Risk Analysis, Kluwer Academic Publishers, Dordrecht, 1988.

Goodyear Tire & Rubber Company, "Car and Light Truck Tire School Site", and subsidiary page "T-Metric", 1999.

Gorzelany, J., "Tires" and "Best Buys in Tires", Consumers Digest, November/December 1998, 75-76.

IFA Services, "Statistical Tests, Correlation", UVA, The Netherlands, 1999.

McGarty, C., "Examining Relationships Between Variables: Correlation", Doing Psychology: A Study Guide, Australia National University,

Punches, K., "Designing for Reliability: A Checklist", EDN, Reed Publishing, Boston, November 21, 1996, 149-156.

Saber, R. "Reliability and Stress Methodology for Electronic Card Assemblies", Micronews, 2:4, International Business Machines,

Smith, D.J., Reliability, Maintainability and Risk: Practical Methods for Engineers, Fourth Edition, Butterworth Heinemann, Oxford, 1993.

Smith, D.J., Reliability and Maintainability in Perspective, John Wiley and Sons, New York, N.Y., 1985.