Your Reliability Engineering Professional Development Site
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…]
There are a number of different methods to calculate confidence intervals for a proportion. The normal approximation method is easy to use and is appropriate in most cases.
Clopper and Pearson describe the Clopper-Pearson method also called the exact confidence interval and we’ll describe it in a separate article.
There are other methods, which again will find a description in separate articles. [Read more…]
As with other point estimates, we often want to calculate the confidence interval about the estimate. The intent is to determine the range of reasonable values for the true and unknown population parameter. For MTBF, this no different.
When using a sample to calculate a statistic we are estimating a population parameter. It is just an estimate and the sample due to the nature of drawing a sample may not create a value (statistic) that is close to the actual value (parameter). [Read more…]
Control charts help us monitor and stabilize a process. A little graphics along with statistics provides a tool to identify when something has changed. Some changes are abrupt and obvious, other a little more subtle, yet the out of control signals each have approximately the same chance of alerting us to a change.
A little graphics along with statistics provides a tool to identify when something has changed. Some changes are abrupt and obvious, other a little more subtle, yet the out of control signals each have approximately the same chance of alerting us to a change. [Read more…]
As you may recall the probability density function describes the behavior of a random variable.
Like a histogram, the PDF when plotted reveals the shape of the distribution. The PDF also has the property that the area under the curve for is one. Another property is the PDF is defined across the entire sample space. [Read more…]
It seems that anytime we draw a sample, it should be taken randomly. Statistics books and papers regularly advise using a random sample. The adverse effect on results drawn from the experiment may hinge on the randomness of the selection of samples. [Read more…]
This nonparametric test evaluates if two continuous cumulative distributions are significantly different or not.
For example, if the assumption is two production lines producing the same product create the same resulting dimensions, comparing a set of samples from each line may reveal if that hypothesis is true or not.
There is a lot of probability, statistics and data analysis involved with reliability engineering. Why is that? Have you considered why our field of endeavor includes the use of these tools?
Let’s say there were no statistical tools. We would not be able to accurately infer a conclusion based on an observation of a few samples. We might react to everything that we observe – constantly spinning our wheels on minor issues. We might make decisions based on factors that did not include the random variation of the items. We might track failure rates, yet not really know how to determine if the few failures we observe were an indication of a major issue or not. [Read more…]
You use your calculator or spreadsheet, or even a statistics software package to calculate standard deviation, which is an estimate of the population standard deviation. Yet, understanding how one could calculate standard deviation without such advanced tools may prove useful. The knowledge of basic sum of squares methods provides a foundation for ANOVA and DOE analysis techniques. [Read more…]
Before computers and statistical software, we relied on tables to determine values for common integration problems – the normal distribution in particular. There is no closed form solution for the integral of the normal distribution probability density function, it requires advanced numerical methods to estimate the area under the curve. [Read more…]
There are two basic ways to consider the central limit theorem. First consider a random variable, X, which has a mean, μ, and variance σ2. If we take a random sample from f(X) of size n and calculate the sample mean, X̄, then as n increases the distribution of the sample means, X̄’s approaches a normal distribution with mean, μ, and variance σ2/√n̄. The original data, X, may have any distribution and when n is suitably large the distribution of the averages will approach a normal distribution. [Read more…]
A continuous distribution is useful in many statistical applications such as process capability, control charts, and confidence intervals about point estimates. On occasion time to failure, data may exhibit behavior that a normal distribution models well. [Read more…]
Similar to the Weibull distribution yet with slightly heavier tails. While not as easy to interpret if the data shows early life or wear out features, the lognormal distribution often fits time to repair data accurately.
Transform the data by taking the natural log of each data point. The resulting values tend to be normally distributed if the original data fits a lognormal distribution.
You can use base 10 or base 2 or any base and the results will still tend to be normally distributed. It is common to use natural log, ln(). [Read more…]