## Module 11 Repairable Systems Analysis

## Lesson M11-05

### Duration: 9 minutes

In the final lesson, the concepts of Maintainability and Availability are described.

Reliability Reference Textbook â€“ Section 11, Pages 34-37

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In the final lesson, the concepts of Maintainability and Availability are described.

Reliability Reference Textbook â€“ Section 11, Pages 34-37

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An example using Reliasoft is presented.Â Â This example fits a parametric model (Power Law) to the repair data.Â Â The Restoration Factor is estimated from the data (by specifying the 3-parameter model).Â Several plots are generated and used to answer specific questions (Cumulative Failures vs. Time, Failure Rate (or Intensity) vs. Time, and Conditional Reliability vs. Time (both varying the start time for a given mission time and varying the mission time for a given start time).Â Â The QCP is also utilized to find estimates.Â Â Finally, an exercise is assigned and reviewed.Â

2 Exercises

Exercise 1 Solution

Exercise 2 Solution

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This lesson introduces the General Renewal Process (GRP) used in Reliasoft to analyze repairable systems data (more generally referred to as recurrent data analysis or RDA).Â Â The key aspects of the GRP model are described including theÂ *action effectiveness factor*Â (or alternatively theÂ *restoration factor*).Â Â This content will enable us to understand the examples and exercises in the next lesson.Â Â

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As in the non-repairable case, we can fit parametric models to the time between failure data. Two categories of parametric models are presented: the Homogeneous Poisson Process (HPP) and the Non-Homogeneous Poisson Process (NHPP). The HPP implies that the failure rate (ROCOF) is constant over time. The usefulness of the Mean Time Between Failure statistic (MTBF) depends on the type of parametric model used. An HPP model fit is demonstrated using Minitab software since Reliasoft only uses a more general approach. The Power Law (or Power ROCOF) model is introduced, and this model handles non-constant failure rates. An example of a Power Law model is shown using Reliasoft.

Reliability Reference Textbook â€“ Section 11, Pages 10-22

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In Lesson 1, we introduce repairable systems and the utility of the analyses. We define some of the key functions including the Mean Cumulative Function (MCF) which is a non-parametric estimate of the cumulative number of failures over time and the Rate of Occurrence of Failure (ROCOF) which is a failure rate. Improving and deteriorating systems are described.

Reliability Reference Textbook â€“ Section 11, Pages 1-9

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Reliasoft is used to complete the exercise.Â Â A model will be fit to the binary response data and some reliability estimates will be made.Â Â

Exercise Solution

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In this lesson, we illustrate the use of Reliasoft to analyze binary response data and estimate reliability statistics. We also present an example that compares two different formulations with binary response data.

Reliability Reference Textbook â€“ Section 13, Pages 3-19

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In Lesson 1, Binary response data is defined and illustrated with an example. A probit model is also presented.

Reliability Reference Textbook â€“ Section 12, Pages 1-3

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In the last lesson, we discuss how non-normal data for either the stress or strength (or both) distribution. We also discuss some practical issues with the stress strength modeling approach.

Reliability Reference Textbook â€“ Section 13, Pages 18

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Here we work through an example where both distributions are normally distributed. We then solve the problem using simulation as well as with the Reliasoft software.

Reliability Reference Textbook â€“ Section 13, Pages 16-17

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In this lesson, we show how to find the mean and standard deviation of theÂ *Strength â€“ Stress* distribution assuming that both distributions are well described by a normal distribution.Â Â From this, we can use the standard normal cumulative distribution function to find the probably that a unit will encounter a stress that exceeds its strength (probability of failure).Â Â Â

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In Lesson 1, the Stress Strength Model is introduced along with some sample applications.

Reliability Reference Textbook â€“ Section 13, Pages 12-13

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Here, we present some general guidelines for planning ALTs. We discuss the number of stress levels, sample sizes, etc. Based on the specification of planning information (assumptions) we present some calculations for optimizing the allocation of units across the various test combinations. We also explore the impact that the estimate precision (bounds ratio) has on the sample size needed. An example in Reliasoft is presented and an exercise is available for practice.

Reliability Reference Textbook â€“ Section 10, Pages 71-77

Exercise

Exercise Solution

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Several potential pitfalls of the ALT methodology are presented. These include the introduction of new failure modes at stress conditions that would not be present at normal use conditions, oversimplification of the life-stress relationship, masked failure modes, and others.

Reliability Reference Textbook â€“ Section 10, Pages 68-70

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As discussed previously, degradation models are revisited but in the context of an ALT. Here degradation models are used to predict the eventual failure times in an ALT. Then those failure times are handled in the normal way in the ALT modeling. Options for handling both non-destructive and destructive measurements (of degradation) are discussed.

Reliability Reference Textbook â€“ Section 10, Pages 63-66

Exercise

Exercise Solution