Your Reliability Engineering Professional Development Site
Reliability and durability are essential in today’s competitive market place. However, component reliability verification tests and system durability tests take a long time, cycles, or miles to complete. This puts these tests in direct conflict with program timing, product development budgets, and limited testing resources. To minimize this conflict, it is essential to accelerate these tests.
Extended bogy testing builds on test to bogy (TTB), discussed in a prior article. TTB focused on calculating the number (N) of parts tested to one life bogy, with 0 failures allowed, to a specified reliability (R) and confidence (C) levels.
Using TTB to verify conformance to high reliability and confidence targets requires very large sample sizes, increasing testing cost. The capacity to test large samples may require large facility capital expenditures. Also, the zero failures allowed paradigm removes the opportunity to learn about product failure modes and the opportunity to improve the product through design or manufacturing process changes.
This article focuses on extended bogy test plans as an alternative to TTB.
Test To Bogy Sample Sizes
Introduction
Reliability verification is a fundamental stage in the product development process. It is common for engineers to run a test to bogy (TTB). What sample size is required for a TTB?
Reliability Testing
Reliability is the probability of a part successfully functions under specified life, duty cycle and environmental conditions. Many functions are specified during the design process. Each reliability test will be focused to validate a specific function. The targeted verification level depends on the criticality of the function and potential failure modes. The life could be specified as a count of cycles, an operating time, or perhaps a mileage or mileage equivalent. The duty cycle is a description of how the device is used. Environmental stresses are generally included in the test.
Introduction
When planning a test on a continuous variable, the most common question was “How many should I test”? Later, when the test results were available, the questions were “What is the confidence?” or “How precise was the result?” This article focuses on planning the measurements of a continuous variable and analyzing the test results.
In some of my articles, I have referred to The Central Limit Theorem, a development in probability theory. It can be stated
“When independent identically distributed random variables are added, their normalized sum tends toward a normal distribution (informally a “bell curve”) even if the original variables themselves are not normally distributed.”
We can apply this principle to many practical problems to analyze the distribution of the sample mean. In this article, I provide graphical and mathematical descriptions and a practical example.
How many responses are needed for a survey? This question requires specifying the desired confidence and the accuracy of the survey results.
A Bernoulli trial is an event that has two possible outcomes. Consider the case where the only possible outcomes are success or failure. Let the probability of a success is p and the probability of failure equals q. The probabilities of all possible events must equal 1, so q = 1-p. These relationships are expressed mathematically as
In prior articles on process capability, sample statistics and SPC statistics were assumed to be population parameters and ignored sampling variability. This article reviews the analytic methods that can be used to develop confidence bounds on the process capability indices.
The Pp index calculation requires an estimate of the parameter σ. The index is calculated as:
You have a process that is not capable because sample measurements or SPC data indicate that some characteristics have too much variability. The calculated Cpk’s are too small. What do you do?
Assuming the data is correct, a course of action is to review the assumption is that the measurements are normally distributed. For most situations, this is a reasonable assumption, but other statistical distributions may provide a better description of the data variation.
In the prior article, Process Capability IV, vehicle wheel toe alignment showed excessive variation. Because the vehicle assembly process is very long and involves many steps, the toe alignment problem required brainstorm which serial production steps, factors, and levels could be responsible for the variation. The most likely process steps were examined and the problem area identified as a wheel alignment machine that needed maintenance and calibration.
This post provides a list of my process capability articles, a short description and a link. The goal is to make it easy for the reader to locate any of the articles. It is recommended to read these articles in the order presented. This post will be updated when additional posts are written on the Process Capability topic.
This post provides a list of my telematics analytics articles, a short description and a link. The goal is to make it easy for the reader to locate any of the articles. It is recommended to read these articles in the order presented. This post will be updated when additional posts are written on this topic.
In prior articles of this series, the process was not capable. The Cp ~0.46 so even if centered, a high percentage of parts would be non-conforming! In industry, it is common to see a Cp of about 1. The paradigm is that if the process range is just contained within the tolerance range, it is satisfactory. Such processes are marginally capable. A process mean shift away from the target or an increase in variation significantly increases the number of non-conforming parts. Process Capability needs to be increased. At a minimum, Cp should be greater than 1.33, but larger is better.
There are two approaches to improving process capability. One is to center the process and the other is to reduce variation. Both need to be accomplished.
In the article “PCA I”, the main process performance indices were defined. In the article “PCA II”, ways to calculate the percent defective were introduced. In this article, the mathematical connection between the Cp index and percent defectives is made.
In my prior article, PCA was defined for prototype samples and serial production. It’s application to one and two sided distributions was discussed. The Pp, Ppk, Cp, and Cpk indices were defined. This article provides methods to estimate the percent defective.
The engineering tolerance for a critical characteristic is 10±0.2. So the lower specification limit (LSL) is 9.8 and the upper specification limit (USL) is 10.2. A sample of 30 parts provided measurements of the critical characteristic. The sample mean ($-\bar{x}-$) was 9.951 and the sample standard deviation (s) was 0.1825.
How is a manufacturing process determined to be capable of producing parts that meet engineering requirements? Some, like the finish of a gear tooth are critical, while the roughness of a non-contact surface isn’t critical. The critical characteristics need to be identified and checked to determine if the process is capable.
This article defines the analysis concepts and indices.
Process capability assessments (PCA) start during the product development process and continue into series production. Prototype parts are created by a variety of methods, ranging from hand-crafted parts to short term manufacturing in a production intent process under factory conditions. The methods that are closest to series production are the most realistic.