Questions tagged [failure-rate]

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Confirming that the failure rate of a new component is less than or equal to the failure rate of the old component with 95% confidence

I have a new component that is meant to replace an old component that has a well-documented failure rate. Both components are buttons, and the failure rate corresponds to the mean number of button ...
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How to relate a time varying variable to a specific date of interest?

I have a dataset where the date of interest is the date where a pipeline failure in a building occurs. Different buildings have different amounts of failures, hence different spacing in time between ...
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Component reliability with an uncertain starting time

I have a lab data analysis challenge which I think can be viewed as a kind of reliability analysis problem. Imagine a warehouse is filled with light bulbs that were installed at some unknown times in ...
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failure rate and probability

I am reading a paper about a Failure Tree Analysis. When I was at university I did a course where the FTA was presented and we worked directly on the probability using the logic gates AND/OR. In this ...
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Lot size acceptance

I have a lot of 1,000 parts. We ran a test on a sample size of 50. We had 12 failures. A colleague did the following calculation in excel: Using a 80% confidence level.... =BETAINV(1-.8,38,12+1) The ...
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How to draw a graph with the following fault and failure data?

a) Draw a graph representing the above data. The graph should include the curves derived from the data, and all labels and legends as needed, and should be sufficiently accurate to enable you to ...
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95 percentile for failure frequency with Poisson process

I am trying to recreate the stats for 'failure frequency' - in this case the 95 percentile - shown in the attached images below. For one set of failure data there are 27 failures over a cumulative ...
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Statistical test on a feature that changes over time

Let me explain my use case with an example. Let's say some phone manufacturer such as apple iphone monitors hardware failure rates. I have a hypothesis that says the latest ios version is resulting in ...
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Interpretation of stress-strength model probability

This is all to settle a methodology debate and neither of us have a good enough grasp of the subject to come to a satisfying solution. We have this Stress-Strength model of a failure : Bascially, the ...
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Right censored data

I have some data that is right censored. A study has recorded data for several years and some units have failed and some units have not failed (right censored). Now, some of the units observe a minor ...
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Identify the confidence of the impact of a proposed improvement initiative

Assume I have a manufacturing process that involves a moving train. It has failures of certain types like brakes and steering and also the weather. However, we can not do anything with regard to ...
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1 answer
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How do I calculate the probability that some system will survive for some years before some event will occur?

I have a failure rate problem involving structural beams. The scenario is that a set of $n$ structural beams are supporting a weight of $W$ kilograms. For the purpose of simplification, we can assume ...
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Failure Rate of a Sum of i.i.d Random Variables

Suppose that $X_1, X_2, \ldots, X_n$ are i.i.d. random variables, with failure rate $r(t)$. Suppose $r(t)$ is increasing. Is it true that the sum $X_1 + X_2 + \ldots + X_n$ also has an increasing ...
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How to apply a t-test for product failure?

Background: I'm trying to determine if there is a difference in the rate of failure between two populations. Population 1 is an engine run on one type of fuel. Population 2 is the same engine run on ...
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Statistical method to study failure rate data

What are the good statistical methods to study failure rates? For example, let's say I manufacture 100 tire models and I sold 3 million units that hit on road. Let's say I have the manufacture date, ...
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Basic question about probabilities and frequency

I wonder about the following situations for a while now and can't quite figure out: You play lottery once, you have a certain probability to win. When you play more than once, your probabilities don'...
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How can I use life-testing to model actual failures?

I am responsible for a large electricity meter fleet and would like to compare and predict the failures of different types electricity meters from existing data. We have the current number of meters ...
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Is it true that for the Weibull distribution a value of $k$ for $ k > 1 $ indicates that the failure rate increases with time?

When describing the Weibull distribution on Wikipedia, it is claimed, among other things, that "A value of $ k > 1 $ indicates that the failure rate increases with time." However, for $ k > 3 ...
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Is there an example that a probability distribution is having an increasing mean residual lifetime(IMRL) but not a Dreasing Failure Rate(DFR)

It is well known in risk theory that a random variable having a Decreasing Failure rate implies the Random Variable has an increasing mean residual lifetime. However, the converse is not true. Is ...
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