Simple interval estimate methods for proportions exhibit poor coverage and can produce evidently inappropriate intervals. Criteria appropriate to the evaluation of various proposed methods include: closeness of the achieved coverage probability to its nominal value; whether intervals are located too close to or too distant from the middle of the scale; expected interval width; avoidance of aberrations such as limits outside [0,1] or zero width intervals; and ease of use, whether by tables, software or formulae. Seven methods for the single proportion are evaluated on 96,000 parameter space points. Intervals based on tail areas and the simpler score methods are recommended for use. In each case, methods are available that aim to align either the minimum or the mean coverage with the nominal 1 -alpha.

/pdf/two-sided-confidence-intervals-for-the-single-proportion-3bv9l3o9do.pdf

Two‐sided confidence intervals for the single proportion: comparison of seven methods

Preface to the Paperback Edition. Preface. About the Author. 1. Overview and Background. 2. Basic Concepts and Distributions for Product Life. 3. Probability Plotting of Complete and Singly Censored Data. 4. Graphical Analysis of Multiply Censored Data. 5. Series Systems and Competing Risks. 6. Analysis of Complete Data. 7. Linear Methods for Singly Censored Data. 8. Maximum Likelihood Analysis of Multiply Censored Data. 9. Analyses of Inspection Data (Qualtal--Response and Interval Data). 10. Comparisons (Hypothesis Tests) For Complete Data. 11. Comparisons with Linear Estimators (Singly Censored and Complete Data). 12. Maximum Likelihood Comparisons (Multiply Censored and Other Data). 13. Survey of Other Topics. Appendix A. Tables. References. Index.

/pdf/applied-life-data-analysis-48iuyi4pne.pdf

Applied life data analysis

How safe are autonomous vehicles? The answer is critical for determining how autonomous vehicles may shape motor vehicle safety and public health, and for developing sound policies to govern their deployment. One proposed way to assess safety is to test drive autonomous vehicles in real traffic, observe their performance, and make statistical comparisons to human driver performance. This approach is logical, but it is practical? In this paper, we calculate the number of miles of driving that would be needed to provide clear statistical evidence of autonomous vehicle safety. Given that current traffic fatalities and injuries are rare events compared to vehicle miles traveled, we show that fully autonomous vehicles would have to be driven hundreds of millions of miles and sometimes hundreds of billions of miles to demonstrate their reliability in terms of fatalities and injuries. Under even aggressive testing assumptions, existing fleets would take tens and sometimes hundreds of years to drive these miles—an impossible proposition if the aim is to demonstrate their performance prior to releasing them on the roads for consumer use. These findings demonstrate that developers of this technology and third-party testers cannot simply drive their way to safety. Instead, they will need to develop innovative methods of demonstrating safety and reliability. And yet, the possibility remains that it will not be possible to establish with certainty the safety of autonomous vehicles. Uncertainty will remain. Therefore, it is imperative that autonomous vehicle regulations are adaptive—designed from the outset to evolve with the technology so that society can better harness the benefits and manage the risks of these rapidly evolving and potentially transformative technologies.

/pdf/driving-to-safety-how-many-miles-of-driving-would-it-take-to-1xvi4a59wq.pdf

Driving to Safety: How Many Miles of Driving Would It Take to Demonstrate Autonomous Vehicle Reliability?

Thirteen methods for computing binomial confidence intervals are compared based on their coverage properties, widths and errors relative to exact limits. The use of the standard textbook method, x/n +/- 1.96 square root of [(x/n)(1-x/n)/n], or its continuity corrected version, is strongly discouraged. A commonly cited rule of thumb stating that alternatives to exact methods may be used when the estimated proportion p is such that np and n(1(-)p) both exceed 5 does not ensure adequate accuracy. Score limits are easily calculated from closed form solutions to quadratic equations and can be used at all times. Based on coverage functions, the continuity corrected score method is recommended over exact methods. Its conservative nature should be kept in mind, as should the wider fluctuation of actual coverage that accompanies omission of the continuity correction.

Confidence intervals for a binomial proportion

This paper is a state-of-the-art review of the literature related to optimal maintenance models of systems subject to failure. The emphasis is on work appearing since the 1976 survey, “A Survey of Maintenance Models: The Control and Surveillance of Deteriorating Systems,” by W.P. Pierskalla and J.A. Voelker, published in this journal.

Optimal maintenance models for systems subject to failure–A Review

Bayesian Reliability Analysis

(1981). Life Testing and Reliability Estimation. Technometrics: Vol. 23, No. 3, pp. 310-311.

Life Testing and Reliability Estimation

In this paper we modify a previously given procedure for testing the equality of the scale parameters of two Weibull populations with common shape parameters. Also presented is a modification of a previously given procedure for selecting the Weibull population with the largest scale parameter (or equivalently selecting the Weibull population with the largest mean). The methods presented here are more powerful than those currently available.

On Procedures for Comparing Two Weibull Populations

In the computation of two-sided confidence intervals for the binomial parameter p (using the binomial mass function), it is known that such intervals achieve a confidence coefficient that in general is not equal to the confidence level 1 – α, say. In this article we present some general results on the confidence coefficient and tabulate them for selected pairs (α, n = number of trials). We treat only the nominal equal tail probability case because it is the most commonly taught and used.

https://www.jstor.org/stable/pdfplus/2683650.pdf

Improved Confidence Statements for the Binomial Parameter

: This report presents the results of a study and investigation of software reliability models. In particular, the purpose was to investigate the statistical properties of selected software reliability models, including the statistical properties of the parameter estimates, and to investigate the goodness of fit of the models to actual software error data. The results indicate that the models fit poorly, generally due to in most part the vagaries of the data rather than shortcomings of the models.

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA072113&Location=U2&doc=GetTRDoc.pdf

Ray E. Schafer

Papers

Bayesian Reliability Analysis

Life Testing and Reliability Estimation

On Procedures for Comparing Two Weibull Populations

Improved Confidence Statements for the Binomial Parameter

Validation of Software Reliability Models