Your Reliability Engineering Professional Development Site
Received a question from a reader this morning that will make a nice tutorial.
A box contains 27 black and 3 red balls. A random sample of 5 balls is drawn without replacement. What is the probability that the sample contains one red ball?
So here’s my thinking and two ways to solve this problem. Instead of red and black balls in an urn type problem, which is pretty abstract, let’s say we know 3 bad parts are in a bin of 30 total parts.
Let’s say you have shipped 1,000 products to your customer on January 1st. All are immediately placed into service. And each month since you have received a few product returns, what we are going to call failures. We also have fitted the data to a Weibull distribution. Then in May, your boss asks you to estimate how many failures to expect in June.
This is a simple example as we’re not shipping units every month, nor changing the product design or assembly process. We also have worked out the fitted Weibull parameters already. That leaves the calculation of how many failures we should expect over the next month. [Read more…]
This is part of a short series on the common distributions.
The Triangle distribution is univariate continuous distribution. This short article focuses on 4 formulas of the triangle distribution.
The distribution becomes a standard triangle distribution when a = 0, b = 1, thus it has a mean at the $- \sqrt{{c}/{2}\;} -$ and the median is at $- 1-\sqrt{{\left( 1-c \right)}/{2}\;}-$. The distribution becomes a symmetrical triangle distribution when $- c={\left( b-a \right)}/{2}\;-$.
The triangle distribution is used to approximate distributions when the actual distribution is unknown and bounded, often useful for Monte Carlo simulations. Other applications include subjective representation when there is evidence of bounds and a mode, or as a substitution to the beta distribution since it is bounded. [Read more…]
This is part of a short series on the common distributions.
The Uniform distribution is a univariate continuous distribution. This short article focuses on 7 formulas of the Uniform Distribution. A common application is as a non-informative prior. Another application is to model a bounded parameter. The uniform distribution also finds application in random number generation. [Read more…]
This is part of a short series on the common life data distributions.
The Poisson distribution is a discrete distribution. This short article focuses on 4 formulas of the Poisson Distribution. It is also known as the rare event distribution. It has application in a homogeneous Poisson princess and with renewal theory. [Read more…]
This is part of a short series on the common life data distributions.
The Pareto distribution is a univariate continuous distribution useful when modeling rare events as the survival function slowly decreases as compared to other life distributions. This short article focuses on 7 formulas of the Pareto Continuous Distribution also known as the Pareto distribution of the first kind (there are three kinds, apparently). [Read more…]
This is part of a short series on the common life data distributions.
The Binomial distribution is discrete. This short article focuses on 4 formulas of the Binomial Distribution.
It has the essential formulas that you may find useful when answering specific questions. Knowing a distribution’s set of parameters does provide, along with the right formulas, a quick means to answer a wide range of reliability related questions. [Read more…]
This is part of a short series on the common life data distributions.
The Birnbaum-Saunders distribution is a univariate continuous distribution. This short article focuses on 7 formulas of the Birnbaum-Saunders Distribution. This distribution was designed to model the Miner’s rule, thus allowing for non-constant fatigue cycles through accumulated damage.
If you want to know more about fitting a set of data to a distribution, well that is in another article.
It has the essential formulas that you may find useful when answering specific questions. Knowing a distribution’s set of parameters does provide, along with the right formulas, a quick means to answer a wide range of reliability related questions. [Read more…]
This is part of a short series on the common life data distributions.
The Beta distribution is a univariate continuous distribution. This short article focuses on 7 formulas of the Beta Distribution.
If you want to know more about fitting a set of data to a distribution, well that is in another article.
The Beta function is not used to describe life data very often yet is used to describe model parameters that are contained within an interval. For example given a probability parameter constrained from 0 ≤ p ≤ 1 the use of the Beta distribution is well suited to model such a parameter.
The Beta distribution is also known as a Pearson Type I distribution. [Read more…]
This is part of a short series on the common life data distributions.
The Logistic distribution is univariate continuous distribution. This short article focuses on 7 formulas of the Logistic Distribution.
If you want to know more about fitting a set of data to a distribution, well that is in another article.
It has the essential formulas that you may find useful when answering specific questions. Knowing a distribution’s set of parameters does provide, along with the right formulas, a quick means to answer a wide range of reliability related questions. [Read more…]
This is part of a short series on the common life data distributions.
The Normal distribution is a continuous distribution widely taught. It is commonly used to describe items, measurements, or time to failure data when there are many additive perturbations that comprise the results. This short article focuses on 7 formulas of the Normal Distribution.
If you want to know more about fitting a set of data to a distribution, well that is in another article.
It has the essential formulas that you may find useful when answering specific questions. Knowing a distribution’s set of parameters does provide, along with the right formulas, a quick means to answer a wide range of reliability related questions. [Read more…]
This is part of a short series on the common life data distributions.
The Lognormal distribution is a versatile and continuous distribution. It is similar to the Weibull in flexibility with just slightly fatter tails in most circumstances. It is commonly used to describe time to repair behavior. This short article focuses on 7 formulas of the Lognormal Distribution.
If you want to know more about fitting a set of data to a distribution, well that is in another article.
It has the essential formulas that you may find useful when answering specific questions. Knowing a distribution’s set of parameters does provide, along with the right formulas, a quick means to answer a wide range of reliability related questions. [Read more…]
On occasion, we want to estimate the reliability of an item at a specific time.
Maybe we are considering extending the warranty period, for example, and want to know the probability of no failures over one year instead of over the current 3 months.
Or, let’s say you talked to a bearing vendor and have the Weibull parameters and wish to know the reliability value over 2 years.
Whatever specific situation, you have the life distributions parameters. You just need to calculate reliability at a specific time. We can do that and let’s try it with three distributions using their respective reliability functions: exponential, Weibull, and lognormal. [Read more…]
Here is an example of a common engineering development task. A design engineer needed a life test plan for a switch verification in a safety system. We jointly developed a plan by taking a system view of the component function, considered corporate and regulatory requirements, customized it to the supplier’s test capabilities, executed the plan, and made design changes to remove product defects. [Read more…]
Most statistics books and the CRE Primer have tables that permit you to avoid calculating the probability for common distributions. The normal distribution requires numerical methods to conduct the calculations and would not be feasible during the CRE exam. [Read more…]