# Questions tagged [failure-rate]

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### Compare failure rates across multiple systems

I work in pharmaceutical manufacturing and one part of a process is a filtration step that uses 'clusters' or 'sets' of single-use (disposable) filters in parallel - the product flows into a manifold ...
16 views

### Real-world testing: estimating chance that there's an unknown variable/constraint/relationship

I'm working on a hardware product where reliability is paramount. So, one test I've done is to power-cycle units repeatedly, seeing if they properly start up. Result in 10k power-cycles of a group of ...
98 views

### Statistical test for rates that are very low with low count

I want to know if dataset suitable for test of significance, and if 'no' (which I am suspect) why exactly not as I must report it why not. I have three apples species (Gala, Pink Lady and 'new') and ...
44 views

### Cumulative Incidence Function given no event before time $t_d$

Suppose we have a simple competing risks model and have a calculated $CIF_K$ for two events $\{k_1, k_2\} \in K$. By definition $CIF_{k_1}(t_i)$ gives us the probability that event $k_1$ has occurred ...
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76 views

### Compare reliability / lifetimes/ failures of two different groups

I have two different groups of devices with different failure rates: Group 1: 72 devices, 57 % did not fail during observation. Group 2: 11 devices, no device failed during observation. How could I ...
• 3,473
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### Population reliability based on sample testing [duplicate]

I have a total population of X, and I test Y < X units for a certainly binary reliability test. Of Y units, some y fail the reliability test. Is there a method (oversimplification is ok) that can ...
9 views

### Comparing roof life of two different population of homes

I am trying to compare the initial roof life of two different data sets of homes. I want to know if the data can be said to show a statistical difference in roof life. I have two populations. One ...
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1 vote
65 views

### Calculate failure probability for given time series data

I am trying to find a way to calculate the likelihood that a machine will fail. Specifically, I would like to receive a prediction such as, "There is a 28% chance that this machine will fail ...
239 views

### Relationship between Survival Distributions and Log Linear Regression in Accelerated Failure Time models

The accelerated failure time model (AFT) can be expressed as: $S_{1}(t) = S_{0}(\frac{t}{\gamma})$ where $S_{0}$ is a specified baseline survival distribution and $\frac{1}{\gamma}$ is the accelerant/...
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1 vote
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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 ...
1 vote
23 views

### 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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509 views

### 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 ...
1 vote
95 views

### 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 ...
133 views

### 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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### 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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141 views

### 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 ...
1 vote
28 views

### 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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1 vote
447 views

### 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, ...
33 views

### 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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1 vote
50 views

### 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 ...