Your Reliability Engineering Professional Development Site
When time is short and you just want a rough estimate of the standard deviation, turn to the range rule to quickly estimate the standard deviation value.
The standard deviation is approximately equal to the range of the data divided by 4. That’s it, simple. [Read more…]
There are times when you do not have a computer available and would like to visualize the distribution of a small set of data. With paper and pencil, you can create a representation that is similar to a probability density function plot. [Read more…]
This nonparametric hypothesis test tests the equality of population medians. While not as powerful as the Kruskal-Wallis Test, it is useful for smaller sample sizes, when there are a few outliers or errors in the data as it focuses only on the median value. [Read more…]
In statistics and reliability, we use distributions to describe time to failure patterns. The four functions commonly used in reliability engineering include
We often use terms like, mean, variance, skewness, and kurtosis to describe distributions (along with shape, scale, and location). The mean is defined as the use of a moment generating function. First though let’s first back up to the concept of center of gravity (cog) from mechanics. [Read more…]
Here’s an overview of the non-parametric test to evaluate if a set of samples have the same variance. If the variances are equal they have homogeneity of variances.
Some statistical tests assume equal variances across samples, such as analysis of variance and many types of hypothesis tests. It is also assumed for statistical process control purposes to determine stability (often done with range (r chart) or standard deviation (s charts). [Read more…]
A contingency table, as in the chi-squared test of independence, reveals if two sets of data or groups are independent or not. It does not reveal the strength of the dependence. The contingency coefficient is a non-parametric measure of the association for cross-classification data. [Read more…]
The chi-square ( $- \chi^2 -$) test provides a means to determine independence between two or more variables. In this case, it works for count data.
Contingency table or row and column (r x c) analysis are other common names for this analysis. It is useful when comparing results from different treatments or processes. [Read more…]
Here’s an overview of a distribution-free approach commonly called the Kaplan-Meier (K-M) Product Limit Reliability Estimator.
There are no assumptions about underlying distributions. And, K-M works with datasets with or without censored data. We do need to know when failures or losses (items removed from the evaluation or test other than as a failure. Censored items). [Read more…]
This is a non-parametric test to compare ranked data from three or more groups or treatments. The basic idea is to compare the mean value of the rank values and test if the samples could are from the same distribution or if at least one is not.
The null hypothesis is the data from each group would receive about the same mean rank score. We are comparing rank values, not the actual values. [Read more…]
This non-parametric analysis tool provides a way to compare two sets of ordinal data (data that can be rank ordered in a meaningful manner). The result, rs, is a measure of the association between two datasets.
You may want to know if two reviewers have similar ratings for movies, or if two assessment techniques provide similar results. [Read more…]
Let’s say we have data that is only rank order from two or more evaluators (people, algorithms, etc.) and we want to determine if the evaluators agree or not.
The agreement here meaning the results from one person or another are in agreement, or they are concordant. This is typically done with this non-parametric method for 3 or more evaluators. For a comparison of two evaluators consider using Cohen’s Kappa or Spearman’s correlation coefficient as they are more appropriate. [Read more…]
Detecting a change or difference is often the aim of an experiment or set of measurements. We want to learn which vendor, process, or design provides a better result.
When we use a sample to estimate a statistic for a population we take the risk that the sample provides values that are not representative of the population. For example, if we use a professional basketball team to sample men’s height. We may conclude that the height of men in the general population is taller than the true population value. [Read more…]
The U test permits the comparison of two samples to determine if they came from the same population or not. This non-parametric test can use ordinal data, meaning it is in some rank order without containing information about relative distances between ranks. [Read more…]
A test to determine if the homogeneous Poisson model (HPP) is applicable given the data from an individual system is subject to the non-homogeneous Poisson model (NHPP).
This is an alternative test to using the Kendall-Mann Reverse Arrangement Test. [Read more…]
When something fails, what should we do?
A natural question when something fails is
Why did it fail?
The answer is not always obvious or easy to sort out.
One of my favorite examples was on a circuit board that had a small burn mark where a component exploded off the board. The customer didn’t notice that missing part, our engineering team did that. [Read more…]