Basic Statistical Background: Difference between revisions

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In the case of times-to-failure, our random variable ''X'' can take on the time-to-failure (or time to an event of interest) of the product or component and can be in a range from ''0'' to infinity (since we do not know the exact time ''a priori'').
In the case of times-to-failure, our random variable ''X'' can take on the time-to-failure (or time to an event of interest) of the product or component and can be in a range from ''0'' to infinity (since we do not know the exact time ''a priori'').


In the first case, where the random variable can take on only two discrete values (let's say ''defective =0'' and ''non-defective=1''>), the variable is said to be a ''discrete random variable''. In the second case, our product can be found failed at any time after time ''0'', i.e. at ''12.4 hours'' or at ''100.12 miles'' and so forth, thus ''X'' can take on any value in this range. In this case, our random variable ''X'' is said to be a ''continuous random variable''.
In the first case, where the random variable can take on only two discrete values (let's say ''defective =0'' and ''non-defective=1''), the variable is said to be a ''discrete random variable''. In the second case, our product can be found failed at any time after time ''0'', i.e. at ''12.4 hours'' or at ''100.12 miles'' and so forth, thus ''X'' can take on any value in this range. In this case, our random variable ''X'' is said to be a ''continuous random variable''.


{{ProbabilityDensitynCumulativeDistributionFunctions}}
{{ProbabilityDensitynCumulativeDistributionFunctions}}

Revision as of 16:12, 6 February 2012

New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images, more targeted search and the latest content available as a PDF. As of September 2023, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest reference at help.reliasoft.com/reference/life_data_analysis

Chapter 2: Basic Statistical Background


Weibullbox.png

Chapter 2  
Basic Statistical Background  

Synthesis-icon.png

Available Software:
Weibull++

Examples icon.png

More Resources:
Weibull++ Examples Collection


Statistical Background

In this section provides a brief elementary introduction to the most common and fundamental statistical equations and definitions used in reliability engineering and life data analysis.


Random Variables

In general, most problems in reliability engineering deal with quantitative measures, such as the time-to-failure of a component, or whether the component fails or does not fail. In judging a component to be defective or non-defective, only two outcomes are possible. We can then denote a random variable X as representative of these possible outcomes (i.e. defective or non-defective). In this case, X is a random variable that can only take on these values.

In the case of times-to-failure, our random variable X can take on the time-to-failure (or time to an event of interest) of the product or component and can be in a range from 0 to infinity (since we do not know the exact time a priori).

In the first case, where the random variable can take on only two discrete values (let's say defective =0 and non-defective=1), the variable is said to be a discrete random variable. In the second case, our product can be found failed at any time after time 0, i.e. at 12.4 hours or at 100.12 miles and so forth, thus X can take on any value in this range. In this case, our random variable X is said to be a continuous random variable.

New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images, more targeted search and the latest content available as a PDF. As of September 2023, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest reference at help.reliasoft.com/reference/life_data_analysis

Chapter 2: Basic Statistical Background


Weibullbox.png

Chapter 2  
Basic Statistical Background  

Synthesis-icon.png

Available Software:
Weibull++

Examples icon.png

More Resources:
Weibull++ Examples Collection


Statistical Background

In this section provides a brief elementary introduction to the most common and fundamental statistical equations and definitions used in reliability engineering and life data analysis.


Random Variables

In general, most problems in reliability engineering deal with quantitative measures, such as the time-to-failure of a component, or whether the component fails or does not fail. In judging a component to be defective or non-defective, only two outcomes are possible. We can then denote a random variable X as representative of these possible outcomes (i.e. defective or non-defective). In this case, X is a random variable that can only take on these values.

In the case of times-to-failure, our random variable X can take on the time-to-failure (or time to an event of interest) of the product or component and can be in a range from 0 to infinity (since we do not know the exact time a priori).

In the first case, where the random variable can take on only two discrete values (let's say defective =0 and non-defective=1), the variable is said to be a discrete random variable. In the second case, our product can be found failed at any time after time 0, i.e. at 12.4 hours or at 100.12 miles and so forth, thus X can take on any value in this range. In this case, our random variable X is said to be a continuous random variable.

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Additional Resources

References

See Also

See Also

Notes

Notes


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Additional Resources

References

See Also

See Also

Notes

Notes