Your Reliability Engineering Professional Development Site
The clever Dr. John Snow mapped cholera cases during the epidemic of 1854 on a street map of the area. This type of mapping now called a measles chart, or defect location check sheet, or defect map, is useful when exploring the effect of location data.
The name measles chart may have come from the habit of using an image of drawing of a product and adding small red dots to signify defect locations.
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.
The Friedman test is a non-parametric test used to test for differences between groups when the dependent variable is at least ordinal (could be continuous). The Friedman test is the non-parametric alternative to the one-way ANOVA with repeated measures (or the complete block design and a special case of the Durbin test). If the data is significantly different than normally distributed this becomes the preferred test over using an ANOVA.
The test procedure ranks each row (block) together, then considers the values of ranks by columns. The data is organized in to a matrix with B rows (blocks) and T columns (treatments) with a single operation in each cell of the matrix. [Read more…]
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…]
When looking at a pile of data, sometimes there is a data point that is not like the others. It attracts attention as it is different than the rest of the data.
When I spot something odd in a dataset, I wonder if there is something to learn here. Is this an opportunity to make a discovery or improve a process?
All too often it is tempting to remove the outlier as a mistake. Or to drop the outlier as it doesn’t make any sense and ‘messes up’ the analysis. [Read more…]
The McNemar test is a nonparametric statistical test to compare dichotomous (unique) results of paired data.
If you are comparing survey results (favorable/unfavorable) for a group of potential customers given two ad campaigns, or evaluating the performance of two vendors in a set of prototype units, or determining if a maintenance procedure is effective for a set of equipment, this test permits the detection of changes.
The McNemar test is similar to the χ2 test. The McNemar only works with a two by two table, where the χ2 test works with larger tables. The χ2 test is checking for independence, while the McNemar test is looking for consistency in results.
Let’s examine an example where a group of people are surveyed about a prototype design, before and after a presentation. [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…]