Statistical Intervals, 2nd Edition

Chapter 18 Advanced Case Studies

Objectives and Overview

This chapter contains seven advanced case studies that illustrate the broad applicability of the general methods presented in Chapters 15–17. The following applications are discussed:

• The case study in Section 18.1 shows how to construct, and contrasts, likelihood, bootstrap, and Wald-approximation confidence intervals on the proportion of defective integrated circuits from a manufacturing process, when the consequence of the defect is a product failure during the (early) life of the product operation and the available information is limited time-to-failure data.
• Gauge repeatability and reproducibility studies are used to assess the capability of a measurement process and to estimate components of variance attributable to different sources of variability. The case study in Section 18.2 shows the use of generalized pivotal quantity and Bayesian methods to compute confidence intervals for quantities of interest calculated from such studies.
• Naive computation of a tolerance interval when the data contain measurement errors will result in an interval that is too wide. The case study in Section 18.3 shows how to compute a tolerance interval on actual product performance that corrects for measurement error in the data, using parametric bootstrap and Bayesian methods.
• The case study in Section 18.4 illustrates the use of Bayesian and parametric bootstrap methods for computing a confidence interval on the probability of meeting ...