Chapter 6 Statistical Intervals for a Binomial Distribution

Objectives and Overview

This chapter describes statistical intervals for proportions or percentages. Such intervals are used, for example, when each observation is either a “conforming” or a “nonconforming” unit and the data consist of the number, or equivalently, the proportion or percentage, of nonconforming units, in a random sample of n units from a population or process. Two examples are:

  • An integrated circuit passes an operational test only if it successfully completes a specified set of operations after a 48-hour “burn-in” at 85°C and 85% relative humidity. Thus, the given data consist of the proportion of the n units that failed or passed the test. The goal is to estimate the proportion of potentially failing (nonconforming) units in the sampled manufacturing process.
  • Federal regulations require that the level of a certain pollutant in the exhaust from an internal combustion engine be less than 10 parts per million (ppm). If an engine fails to meet this standard, it must undergo expensive rework. Management wants to estimate the proportion of units from a specified process that will require such rework. The available data consist of the number of units that needed rework in a random sample of n engines from the manufacturing process.

Our discussion will be mainly in terms of “nonconforming” units to suggest the common quality control application. The applicability of the intervals is, however, much more general. ...

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