Your Reliability Engineering Professional Development Site
A discreet distribution useful when counting events within a time period.
It models rates, such as the number of gophers in your garden, paint scratches on your car, or the number of shopping carts that arrive in the 5 minutes before you in line. Essentially it’s the count of something over a time period or defined area. [Read more…]
The exponential distribution is a model for items with a constant failure rate (which very rarely occurs).
If the chance of failure is the same each hour (or cycle, etc.), including the first hour, 100th hour, and 1 millionth hour or use, then the exponential distribution is suitable.
Many practitioners assume the failure rate either is constant or changes so little as to be essential constant in order to make reliability calculations simpler. [Read more…]
A point estimate of the mean of a population is determined by calculating the mean of a sample drawn from the population. The calculation of the mean is the sum of all sample values divided by the number of values. [Read more…]
The basic measures of central tendency are mean, median, and mode.
Given a collection of data, a common question is about where the data resides. Knowing the center or mid-point or average is a starting point as we consider the data. [Read more…]
It may be possible to pass the CRE exam knowing one formula.
The math elements of the exam may take a bit of time to solve, and knowing reliability statistics well is a good plan heading into the exam. Knowing the exponential distribution reliability function is one that you should memorize. [Read more…]
A simple assumption in many experiments is to assume the variable act independently on the response.
This means when I change the temperature a little in a polymer dryer silo that time to achieve a certain dryness goes down. And, changing the humidity or airflow rate or pressure either do not change or as they change has no impact on the relationship between temperature and drying time. [Read more…]
Dr. Nelson created a simple experiment to illustrate the effect of meddling with a stable process. (Dr. Deming did something similar)
While the intent of making small changes to a process may be to make improvements, these perturbations generally increase the variation of the results.
To improve a process requires understanding the source of the variation and often controlled experiments to identify process improvements. [Read more…]
Another variation of the X-bar and R chart, in this case measuring and plotting individual readings instead of a sample average. The range value is obtained from the current reading and a fixed number of previous readings.
This type of control chart is suitable for calibration or testing situations where it is not practical to create subgroups of items for samples. [Read more…]
The s chart replaces the R chart and provides an increase in sensitivity to variation of the spread of the data.
The s-chart works better with 10 or more items per sample in order to obtain the s (standard deviation) estimate. The use of a spreadsheet or calculator expedites the calculation of the sample standard deviation.
Control charts provide an ongoing statistical test to determine if the recent set of readings represents convincing evidence that a process has changed or not from an established stable average.
The test also checks the sample to sample variation to determine if the variation is within the established stable range. A stable process is predictable and a control chart provides the evidence that a process is stable or not.
Some control charts use a sample of items for each measurement. The sample average values tend to be normally distributed allowing straightforward construction and interpretation of the control charts. The center line of a chart is the process average. The control limits are generally set at plus or minus three standard deviations (of the sample means – commonly called the sampling error of the mean) from the grand average.
Every process should operate stably. Every process may have many measurements available to monitor either various aspects to the final product or the assembly equipment. There may be hundreds of possible items to measure and monitor.
We do not have the resources nor time to apply control chart principles to each possible measurement. Control charts do not directly add value and they have a cost to maintain and interpret. While it may be tempting to add a dozen or so control charts, as the cost increases the value quickly decreases.
As stated before, variation happens.
The root cause of the variation for a stable process includes material, environmental, equipment, and so on, changes that occur during the process. No saw cuts the same length of material twice – look close enough there is some difference. [Read more…]
An easy method to monitor and control a process average. It is an alternative to the Shewhart control chart.
Pre-control charts work well with stable and slow process drifts or changes. These charts provide a means to monitor a process and act as a guide for process centering.
They are easier to setup, implement, and interpret the Shewhart charts. [Read more…]
The connection between the specifications or drawings or design requirements and the manufacturing process is the capability of the process to consistently create items within spec.
A ratio of the specification over the spread of measured items provides a means to describe the process capability.
The ratios rely on the standard deviation or spread of the produced items. The index is meaningful only if the process is stable. Thus beyond making sure the measurements have minimal measurement error, check the stability using the appropriate control chart.
In this article we are assuming the measurements are normally distributed, yet knowing that is not always the case, you can calculate capability indices using the actual distribution.
The indices will have similar interpretations yet take care when applying these concepts using other than normal distribution data.
We have statistics to describe the variation that occurs in our world. Statistics is the language of variation.
If each of your produced products were identical in every way to all products produced, with no variability, we wouldn’t be concerned with the effect of variation on the performance and reliability of our designs.
Yet, variation does happen and we have a range of tools to identify and minimize the naturally occurring variation. [Read more…]