Building a Frequency Table

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…]

by Fred Schenkelberg Leave a Comment

5 Steps to Create a Measles Chart

Measles Chart Basics

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.

[Read more…]

by Fred Schenkelberg Leave a Comment

Calculating the Probability of a Sample Containing Bad Parts

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.

[Read more…]

by Dennis Craggs Leave a Comment

Measurement Systems

Introduction

Most of us rely on accurate measurements. If these measurements are unreliable, then our decision 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…]

by Fred Schenkelberg Leave a Comment

The Non-parametric Friedman Test

The Friedman test is a non-parametric test used to test for differences between groups when the dependent variable is at least ordinal (could be continuous). The Friedman test is the non-parametric alternative to the one-way ANOVA with repeated measures (or the complete block design and a special case of the Durbin test). If the data is significantly different than normally distributed this becomes the preferred test over using an ANOVA.

The test procedure ranks each row (block) together, then considers the values of ranks by columns. The data is organized in to a matrix with B rows (blocks) and T columns (treatments) with a single operation in each cell of the matrix. [Read more…]

by Fred Schenkelberg 2 Comments

How to Estimate the Number of Failures Next Month

Let’s say you have shipped 1,000 products to your customer on January 1^st. All are immediately placed into service. And each month since you have received a few product returns, what we are going to call failures. We also have fitted the data to a Weibull distribution. Then in May, your boss asks you to estimate how many failures to expect in June.

This is a simple example as we’re not shipping units every month, nor changing the product design or assembly process. We also have worked out the fitted Weibull parameters already. That leaves the calculation of how many failures we should expect over the next month. [Read more…]

by Fred Schenkelberg Leave a Comment

Data Outliers and Questions

When looking at a pile of data, sometimes there is a data point that is not like the others. It attracts attention as it is different than the rest of the data.

When I spot something odd in a dataset, I wonder if there is something to learn here. Is this an opportunity to make a discovery or improve a process?

All too often it is tempting to remove the outlier as a mistake. Or to drop the outlier as it doesn’t make any sense and ‘messes up’ the analysis. [Read more…]

by Fred Schenkelberg Leave a Comment

McNemar Test

The NcNemar Statistical Test

The McNemar test is a nonparametric statistical test to compare dichotomous (unique) results of paired data.

If you are comparing survey results (favorable/unfavorable) for a group of potential customers given two ad campaigns, or evaluating the performance of two vendors in a set of prototype units, or determining if a maintenance procedure is effective for a set of equipment, this test permits the detection of changes.

The McNemar test is similar to the χ² test. The McNemar only works with a two by two table, where the χ² test works with larger tables. The χ² test is checking for independence, while the McNemar test is looking for consistency in results.

Let’s examine an example where a group of people are surveyed about a prototype design, before and after a presentation. [Read more…]

by Fred Schenkelberg Leave a Comment

The 3 Parameter Triangle Distribution 4 Formulas

This is part of a short series on the common distributions.

The Triangle distribution is univariate continuous distribution. This short article focuses on 4 formulas of the triangle distribution.

The distribution becomes a standard triangle distribution when a = 0, b = 1, thus it has a mean at the $- \sqrt{{c}/{2}\;} -$ and the median is at $- 1-\sqrt{{\left( 1-c \right)}/{2}\;}-$. The distribution becomes a symmetrical triangle distribution when $- c={\left( b-a \right)}/{2}\;-$.

The triangle distribution is used to approximate distributions when the actual distribution is unknown and bounded, often useful for Monte Carlo simulations. Other applications include subjective representation when there is evidence of bounds and a mode, or as a substitution to the beta distribution since it is bounded. [Read more…]

by Fred Schenkelberg Leave a Comment

The 2 Parameter Uniform Distribution 7 Formulas

This is part of a short series on the common distributions.

The Uniform distribution is a univariate continuous distribution. This short article focuses on 7 formulas of the Uniform Distribution. A common application is as a non-informative prior. Another application is to model a bounded parameter. The uniform distribution also finds application in random number generation. [Read more…]

by Fred Schenkelberg 1 Comment