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One of the very first plots of a string of data is a simple run chart. The plot of the data over time. This plot provides information related to location, trends, patterns, anomalies, and more. A rather informative chart.
You have most likely constructed many run charts and if not, you really should. This short introduction to run charts will cover creating and interpreting them, as well as a few cautions and tips, as well. [Read more…]
A histogram is a graphical representation of a set of data. It is useful to visually inspect data for its range, distribution, location, scale, skewness, etc. There are many uses for histogram, there you should know how to create one.
Let’s explore a set of data and create default histograms using a variety of methods. If you have a way to create a histogram using some other method or software package please send it over and we’ll add it to the article. [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. In this case, you do not know the actual variance of the population, you just have a sample.
This test is often the second one in a textbook that describes hypothesis testing. It is a useful hypothesis test and applies in many situations as we rarely know the population variance. [Read more…]
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…]