Your Reliability Engineering Professional Development Site
One of the first things to do when faced with a set of numbers is to plot them. A histogram is often the first choice, maybe a dot plot. Up your data plotting skills and let your data provide a bit more information by using a box plot. [Read more…]
Graphs contain information and often tell a story. Our interpretation of the graphic can be aided or hindered by the design or style of the plot. Cleveland and McGill (1984) studied graphical perception and found the use of dot plots to aid viewers to understand the data’s message clearly.
The nature of a dot plot is like a bar chart, yet without the bars. Less ink, just a dot to indicate count or position along an axis permits conveying information simply. Due to its simplicity, it also permits adding additional information useful for comparisons or spotting trends, and more. [Read more…]
You may have heard of the 80/20 rule. The idea is that 80% of the wealth is held by 20% of the population. As an Italian economist, Vilfredo Pareto made this observation that became generalized as the
Pareto Principle: 80% of outcomes are due to 20% of causes
For field returns, for example, we may surmise that 80% of the failures are due to 20% of the components, for example. This principle helps us to focus our work to reduce field failures by address the vital few causes that lead to the most, or most expensive, failures. [Read more…]
There is a type of error when conducting statistical testing that is to work very hard to correctly answer the wrong question. This error occurs during the formation of the experiment.
Despite creating a perfect null and alternative hypothesis, sometimes we are investigating the wrong question. [Read more…]
A common question when setting up a hypothesis test is concerning sample size. An example, might be: How many samples do we need to measure to determine the new process is better than the old one on average?
While this seems like a simple question, we need a bit of information before we can do the calculations. I’ve also found that the initial calculation is nearly always initiated a conversation concerning the balance of sample risks, the ability to detect a change of a certain size and the constraints concerning the number of samples. [Read more…]
We use a sample to estimate a parameter from a population. Sometimes the sample just doesn’t have the ability to discern a change when it actually occurs.
In hypothesis testing, we establish a null and alternative hypothesis. We are setting up an experiment to determine if there is sufficient evidence that a process has changed in some way. The Type II Error, $-\beta-$ is a measure of the probability of not concluding the alternative hypothesis is true when in reality it is true.
The power, $-1-\beta-$, reflects the ability of the sample to correctly lead us to the conclusion that an actual change has occurred when in reality it actually has. [Read more…]
In hypothesis testing, we set a null and alternative hypothesis. We are seeking evidence that the alternative hypothesis is true given the sample data. By using a sample from a population and not measuring every item in the population, we need to consider a couple of unwanted outcomes. Statisticians have named these unwanted results Type I and Type II Errors. [Read more…]
In the situation where you have a sample and would like to know if the population represented by the sample has a mean different than some specification, then this is the test for you. Oh, you also know, which is actually rather rare in practice, the actual variance of the population you drew the sample. [Read more…]
In system modeling and fault tree analysis (FTA) we use a set of similar calculations based on Boolean logic, the AND and OR gate probability calculations. Within FTA, the AND and OR gates are just two of many possible ways to model a system. Within system modeling, often reliability block diagrams (RBD) we model parallel and series elements of a system.
In order to do these basic calculations, we need to consider a few assumptions then proceed to the math.
When confronted with a stack of data, do you think about creating a histogram, too? Just tallied the 50th measurement of a new process – just means it’s time to craft a histogram, right?
There isn’t another data analysis tool as versatile. A histogram (bar chart) can deal with count, categorical, and continuous data (technically, the first two graphs would be bar charts). It like a lot of data yet reveals secretes of even smaller sets. A histogram should be on your shortlist of most often graphing tools. [Read more…]
Sometimes we just need a simple plot of a few data points. When there is scant data a histogram or box plot just is not informative. This is a great use for a one dimensional scatter plot, dot plot, or a what is called a strip chart in R.
The basic idea is to see where the data lines along a line. For example, let say we have 20 times to first failure. A table of numbers is not all that helpful. We could explore using a cumulative distribution plot (Weibull analysis), yet it would be difficult to fit a distribution with so little data.
Let’s turn to a strip chart to get a look at the data. [Read more…]
In a meeting the other day, the presenter was talking about a range of different failures for the product in question. She talked about each issue, a bit about the failure analysis, yet didn’t reveal which failures occurred more or less often.
She did provide a handout with a listing of the problems in order of the product field age and listing of the failure name (component or system involved). So, I grabbed a piece of paper to create a frequency table so I could quickly determine which problems occurred more often than others. [Read more…]
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.
Most of us rely on accurate measurements. If these measurements are unreliable, then our decisions could be based on false information. How can we have confidence in our measurements?
The purpose of a measurement system analysis is to determine if a gauge is fit for use. This means that we can rely upon the measurements to give us a true indication of the parameter being measured. Our decisions will not be affected by erroneous data. So how can we know the quality of our measurements?
[Read more…]