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Prediction & Tolerance Intervals; Measurement and Reliability



May 29, 2015 to June 26, 2015

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Prediction & Tolerance Intervals; Measurement and Reliability

taught by Tom Ryan

Aim of Course:

This online course, "Prediction & Tolerance Intervals; Measurement and Reliability" goes beyond the standard coverage of introductory statistics to cover topics important to practicing engineers. Participants will learn how to calculate prediction intervals, confidence intervals, and calibration intervals. Participants will also learn to assess measurement error, and measurement system appraisal to determine whether measurement systems are in control. Measurement system appraisal is critical because the results of any statistical analysis will be compromised if there is substantial measurement error. Similarly, designed experiments (not covered in the course) can be seriously undermined when there is measurement error. The course will also cover life testing, accelerated life testing, and reliability testing.

Course Program:

WEEK 1: Prediction and Tolerance Intervals

  • Tolerance intervals
    • 2-sided
    • 2-sided, asymmetric
    • 1-sided, bounded
    • Distribution-free intervals
  • Prediction intervals
    • Known parameters
    • Unknown parameters, normality assumed
      • Sensitivity to non-normality
    • Non-normal distributions
      • Single observation
      • Number of failures

WEEK 2: Measurement System Appraisal

  • Calibration intervals
  • Components of measurement variability
  • Tolerance analysis
  • Graphical methods
  • Bias and calibration

WEEK 3: Reliability and Life Testing

  • Repairable and non-repairable populations
  • Accelerated testing
    • Arrhenius equation
    • Inverse power function
    • Degradation data and acceleration models
  • Censoring
  • Distributions and models
    • Exponential
    • Weibull
    • Lognormal
    • Extreme value
  • Reliability prediction

WEEK 4: Application of Other Concepts*

  • Improving reliability with designed experiments
    • Sample size determination
  • Regression
    • Measurement Error
    • Calibration
    • Control

*This section provides engineering applications of concepts that are not fully covered here, but are covered in other statistics.com courses: Introduction Design of Experiments, Regression Analysis, and Sample Size and Power Determination. You will probably get more out of these illustrations if you have previously covered this material, but this is not a course requirement. The examples can also serve to provide meaningful context and motivation for further study.


Homework in this course consists of short answer questions to test concepts, guided data analysis problems using software, and guided data modeling problems using software.


In addition to assigned readings, this course also has an end of course data modeling project.

Prediction & Tolerance Intervals; Measurement and Reliability


May 29, 2015 to June 26, 2015

Course Fee: $629

Do you meet course prerequisites? What about book & software? (Click here to learn more)

Tuition Savings:  When you register online for 3 or more courses, $200 is automatically deducted from the total tuition. (This offer cannot be combined and is only applicable to courses of 3 weeks or longer.)

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Add $50 service fee if you require a prior invoice, or if you need to submit a purchase order or voucher, pay by wire transfer or EFT, or refund and reprocess a prior payment. Please use this printed registration form, for these and other special orders.

Courses may fill up at any time and registrations are processed in the order in which they are received. Your registration will be confirmed for the first available course date, unless you specify otherwise.

Prediction & Tolerance Intervals; Measurement and Reliability

taught by Tom Ryan

Who Should Take This Course:

Those involved in monitoring and testing products and processes in industry.



These are listed for your benefit so you can determine for yourself, whether you have the needed background, whether from taking the listed courses, or by other experience.

Some familiarity with ANOVA and regression, as covered in Statistics 3, will also be helpful. (Also note the comments in the outline, session 4, concerning regression, design of experiments, and sample size and power.)

Organization of the Course:

This course takes place online at the Institute for 4 weeks. During each course week, you participate at times of your own choosing - there are no set times when you must be online. Course participants will be given access to a private discussion board. In class discussions led by the instructor, you can post questions, seek clarification, and interact with your fellow students and the instructor.

At the beginning of each week, you receive the relevant material, in addition to answers to exercises from the previous session. During the week, you are expected to go over the course materials, work through exercises, and submit answers. Discussion among participants is encouraged. The instructor will provide answers and comments, and at the end of the week, you will receive individual feedback on your homework answers.

Time Requirement: about 15 hours per week, at times of  your choosing.

Students come to the Institute for a variety of reasons. As you begin the course, you will be asked to specify your category:
  1. You may be interested only in learning the material presented, and not be concerned with grades or a record of completion.
  2. You may be enrolled in PASS (Programs in Analytics and Statistical Studies) that requires demonstration of proficiency in the subject, in which case your work will be assessed for a grade.
  3. You may require a "Record of Course Completion," along with professional development credit in the form of Continuing Education Units (CEU's).  For those successfully completing the course, 5.0 CEU's and a record of course completion will be issued by The Institute, upon request.

Course Text:

The required text for this course is Modern Engineering Statistics by Thomas Ryan.



No specific software is required.

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