Questions tagged [reliability]

is for Reliability Engineering and Reliability Theory that describes the probability of a system to complete its expected function during an interval of time. The engineering is an area focused on optimising the reliability or the probability of successful functioning, of systems such as graphs, percolations and mechanical systems such as airplanes. Originally a tool for insurance companies but nowadays more general interdisciplinary research area.

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Striking symmetry in series and parallel system mean time to failure and mean time to recovery

I'm looking at the chapter on reliability theory (chapter 9) in the book on Introduction to probability models by Sheldon Ross: https://fac.ksu.edu.sa/sites/default/files/introduction-to-probability-...
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Availability of machines with a particular repair rule.

There is a data center with $n$ servers. The servers have $t_f$ as their mean time between failures. We run some workloads on the $n$ servers. One of the $n$ servers is always kept empty (no workloads ...
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Reliability of an $l$ pod $k$ of $n$ system.

We have $n$ machines that form a system. The system works if $k$ or more of the $n$ machines are running. The machines are hosted in pods. They are evenly distributed across $l$ of the pods (best ...
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probability of 2 elements failure

I am a little bit confused by an exercise. Given a system consisting of 6 elements with reliabilities: $p_2=p_3=p_4=p_5=1/2, p_1 = 2/3, p_6 = 3/4.$ Find a probability of exactly two elements failure ...
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How can we use Birnbaum importance measure for complicated systems in reliability?

Birnbaum importance measure is used when we are provided the survival probabilities of all the components in a coherent system. It is the rate of increase in the system reliability with respect to the ...
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Properties of the derivative of the truncated mean

I have a function $ h\left( x\right) =\frac{E\left( y|y\geq x\right) -\alpha }{x} $ where the underlying density on the unit interval is smooth and log-concave and alpha is some parameter also in ...
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Degradation models with covariates

I am studying reliability for a project and I would like to use a stochastic model that could incorporate many covariates. Do you know if there is any paper or classical technique to do so? I would ...
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14 views

Calculation of Risk Cost using limited data

I am trying to calculate the risk cost due to machine failure. Here is the problem: I have limited data on a machine that has operated between 2010 and 2019, that is 10 years in total. The machine ...
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How did weibull derive the three parameter weibull distribution? Can anybody have a link so that i can see how it is derived.

In the picture above, how did weibull or any other mathematician arrive at this expression, I saw the 1951 but it is not clear to me. In 1939 he have published a book called A Statistical Theory of ...
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Log-Likelihood function of log-Normal distribution with right censored observations and regression

EXERCISE Find the log-likelihood function for the regression model of log-Normal Distribution considering the right-censored observations ATTEMPT: So, we know that the probability density ...
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Reliability and Provability

I have a system of which 700 are out on the field and one of the components is causing an issue. A new component has been sourced and I want to test it to ensure reliability. So the test I've come up ...
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Non parametric plot of $R(t)$

Here is the attached question from the book, introduction to reliability engineering. Here is the attached solution related to it, but i don't know whether it is correct or not. I just want ...
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Proof of likelihood ratio ordering implying hazard rate ordering

This question was originally asked in stats.stackexchange (the link is given below). I'm reposting it here as I did not get any answer to the said post. https://stats.stackexchange.com/questions/...
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Proof of expected time to failure for a “k out of n” system, each component IID exponentially distributed

A "k out of n" system functions if, as the name suggests, k of the n components of the system remain operational, i.e. the system fails upon failure of any n-k+1 components. My A/S/M MAS-I study ...
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How reliable is the linear problems like $ \min \|Ax - b\|^2$?

The following linear optimization is common used $$\min_x \|Ax - b\|^2$$ Here, $A$ is the matrix; $x,b$ are the vectors. I am curious about how reliable is the solution $x$ by solving above ...
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Probability of system failure, as it requires two adjacent component to fail

I am stuck with a problem in probability. It says that the system consists of 16 components distributed in corners and intersections as the following: ...
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75 views

Combined probability distribution for two hazard functions

I have two items with two different failure rates. I need to find the combined hazard function corresponding to both items failing, from which I can find the combined probability distribution. I ...
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71 views

What density distribution could be used for time delays?

I am analyzing a process related with time delays produced in scheduled departures or arrivals of a distribution trucks. The process consists on: The definition of the problem is: Each truck has ...
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What is the expected number of infected people?

I was recently in an interview and got asked an interesting problem which I want to know the answer to. Suppose we're in a party with $n$ people. At minute $t=0$, there is $1$ person who has a ...
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Failure Rate calculation based on manufacturing defects (electronics-capacitor)

Electronics failure rates typically follow the exponential distribution and models like Prism, Mil-Hdbk-217 or 217Plus (newer) are used to predict failure rates. I'm using 217Plus model for ...
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Analytic model for Preventative Maintenance to increase availability?

I would like to create a model that can increase Availability via preventative maintenance. My current model decreases the availability when I include preventative maintenance. Can you suggest a way ...
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1answer
71 views

system reliability, probabilities of rocket launch suspended

A rocket has 3 computers (a,b,c). If a fails than b will take over and so on. Each computer has 0.01 failure rate. These 3 computers are linked to an expensive sensor. If this sensor fails than all 3 ...
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210 views

Finding the conditional probability that a component works given that the system works

I need to find the probability that component 1 works given that the system works. All components fail independently. I have attached the network here: The answer must be in terms of $p_1, p_2, p_3, ...
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Reliability Analysis - Interpretation of constant reliability in blocks of a system

I am trying to understand a phrase on the reliawiki website : Link Close to the end of the page there is a part talking about blocks with static reliability values. It says that: A static block ...
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Perform System Reliability Analysis analytically [closed]

I am trying to calculate probabilistic reliability curves for systems with multiple sub-components with their own probabilistic failure/reliability curves and probabilistic maintainability curves (...
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Information theoretic measures

What is the difference between cross entropy and kerridge inaccuracy measures? I will be thankful if anyone kindly elaborate the same. Rao et al. (2004) introduced the concept of cumulative residual ...
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105 views

Distinguishing between bulbs with long and short exponential lifetimes

Question statement is like this: You brought a box of lightbulbs from a shop. You know that the bulbs are all either short-life bulbs with mean life of 500 hours or long-life bulbs with a mean life of ...
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65 views

Parametric degradation reliability solution needed

Working on a reliability project and ran across this problem of parametric degradation over time relative to a failure threshold. Need to calculate the distribution of failure times $t_{f,i}$ for a ...
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Components in parallel with different reliabilities (redundancy)

There are $n$ components in parallel and at least $m$ of them are required to work (in order for the system to work); so we can have $n-m$ or less failures. The $n$ components are made up of $a$ of ...
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k out of n probability

An engineering system consisting of n components is said to be a k-out-of-n system (k≤n) when the system functions if and only if at least k out of the n components function. Suppose that all ...
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510 views

Wilson Confidence Interval for binomial proportion, 99.9% level yields strange results for p=0.5

Fellow Stackers, I have a formal customer requirement for a mechanism to have a failure rate of 0.1% or less. After some study, I found various methods for estimating the confidence interval of a ...
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47 views

Historically key works on structural reliability theory?

I want to understand better the structural reliability theory. Is it related to the reliability of structures? Where does it originate and what are the most important work for it?
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64 views

Finnish-English Dictionary on Graph Theory and Reliability Engineering?

I need to translate an abstract to Finnish and I need to find a dictionary on Graph theory. Does there exist any canonical reference work in Finnish that could be used as a reference for finding the ...
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Is Site Percolation with Bernoulli variables i.i.d. independent and identically distributed?

I cannot understand the identically distributed part in the i.i.d assumption. Consider a site percolation where each event is a Bernoulli variable. Does this mean ...
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Which Random Graph model on Reliability network when vertices deleted?

The reliability network when edges deleted corresponds to binomial random graph model that is also called Bernoulli Model. The page 3 of Random Graphs book (2000) by Svante Janson, Tomasz Luczak and ...