Years ago I had the opportunity to assess the reliability programs of two organizations. They made similar products for different segments of the market, and they both had about the same size an organization. Two years previously, both organizations lost the reliability professional from their staffs. Furthermore, both teams were located in one building, one upstairs and the other downstairs, which made scheduling the assessment interviews convenient.
Musings on Reliability and Maintenance Topics
I write quite a bit about reliability and have plans to write quite a bit more. I have looked to prolific authors in our field with admiration and respect: Wayne Nelson, Patrick O’Connor or Terrence O’Hanlon, they all share so much knowledge. They make the subjects and material clear and accessible. They have in large part helped me all throughout my career by enabling my ability to solve problems and create value.
Of course, there are many others that have contributed to my career and my approach to engineering. My colleagues, managers, and mentors have each helped to educate and develop my skills and approach. Every single client has also contributed. As many of you have heard from me, I learn from every encounter and feel very fortunate to have a career that enables such wonderful exploration and learning as part of my day-to-day work. [Read more…]
Degradation Hypothesis
This week I received a question from the ASQ Librarian concerning a person’s question about one of the CRE Question bank questions. It was a nice two-part question concerning a hypothesis test of a sample means value and degradation.
Here’s the question as sent over for consideration. [Read more…]
Binomial Cumulative Density Function
Last week I posted about the Binomial probability density function, and it is useful when calculating the probability of exactly x successes out of n trials given p probability of success for each trial.
Well, what happens if you want to know the probability of 2 or more successes for example? [Read more…]
Binomial Probability Density Function
There are many cases where the results of an experiment (or trial) are either it works or it doesn’t, pass/fail, success/failure. Only two possible outcomes one of which we define as success the other outcome as failure. The binomial distribution is suitable if the random variable (the set of experimental or trial outcomes) when
- the number of trials is fixed, and
- the probability of success is equal for all trials.
Common Formulas
Running through a couple of practice CRE exams recently (yeah, I know I should get out more…) found a few formulas kept coming up in the questions. While it is not a complete list of equation you’ll need for the exam, the following five will help in many of the questions. They seem popular maybe because the relate to key concepts in the body of knowledge, or they are easy to use in question creation. I do not know why. [Read more…]
Reliability from Hazard Step Function
Received a sample problem from someone preparing for the CRE exam saying it was a tricky one.
The hazard rate function for a device is given by
0.001 if t ≤ 10 hours and 0.01 if t > 10 hours
What is the reliability of this device at 12 hours?
I first draw the hazard function [Read more…]
Exponential Reliability
Down to the last week of preparation for the exam on March 2nd. Good luck to all those signed up for that exam date. Time to focus on preparing your notes, organizing your references and doing a final run through of practice exams. [Read more…]
Reliability with Confidence
There are rare situations when we would like to estimate the reliability at the lower confidence level after estimating the mean from a sample (often a test result). And, to make even more rare of a situation, we know the population standard deviation. [Read more…]
OC Curve with Hypergeometric Method
The operating characteristic curve is used to understand lot sampling plan. It graphically provides a relationship between the unknown lot’s defect rate (or total) and the probability of the specific sampling plan to accept the lot. Very good plans discriminate between good and bad lots. Poor plans may accept bad lots or reject good lots to easily. [Read more…]
Z Value
A skill needed for the CRE exam is the ability to look up probabilities given a z-value using a standard normal table. It’s old school, I know, yet without software, you most likely will have to find a few values in this manner.
A z-value is the number of standard deviations from the mean at least that’s how I think of it. The area under the curve to the right or left of the z-value is then the probability of interest. Of course, I’m talking about the normal distribution probability density function or what we commonly all the ‘bell-shaped’ curve. [Read more…]
Stress Strength Normal Assumption
Ideally, in every design of every component, the stress – strength relationship looks like this figure. The stress is well below the strength. [Read more…]
Mann Reverse Arrangement Test
In the analysis of repairable equipment, one may need to make the assumption of constant failure rate. In my opinion, anytime one wants to make the assumption of constant failure rate, it should be validated. [Read more…]
Statistical Confidence
An error that I see on occasion is the use of statistical confidence with a goal or target value. For example, we want 95% reliability at five years with 90% confidence. What does that mean? [Read more…]
Hypothesis Test Sample Size
Hypothesis testing permits us to compare two groups of items and determine if there is a significant difference or not. There are many types of hypothesis tests depending on the specific question, type of data, and what is or is not known when designing the test. [Read more…]
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