Your Reliability Engineering Professional Development Site
The prior article, MSA 3: Gage Bias, focused on defining and calculating a point estimate of gage bias. A method was presented to determine if the bias was statistically significant. If significant, the bias would be applied to the data as a correction factor.
This article discusses gage bias linearity over a measurement range.
In my prior article, Measurement Systems, the total variation in the measurement data was partitioned into part variation (PV), assessor variation (AV), and equipment variation (EV). GR&R is the square root of the sum of the squares of AV and EV. If the ratio of GRR/TV is less than 10%, then the measurement system variation was acceptable.
In addition to variation, data bias needs to be considered. This bias is created by systematic measurement errors.
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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?
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When it is necessary to check 100% of parts for one or more characteristic?
There are situations where 100% of manufactured parts are checked. These include visual inspection, measurements of a part characteristic, and a reaction to low process capability. These may be accomplished manually or an automated process.
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Many companies use SPC to control their manufacturing and assembly processes. Other companies use 100% inspection and some companies do nothing. How can one choose between these three alternatives?
To make a rational choice, some questions need to be answered.
In my prior article, the assumptions behind SPC were discussed in detail except for the analysis. There are two types data that may be analyzed, Counts and Measurement variables. This article focuses on normally distributed measurement variables, and the construction and usage of $-\bar{X}-$ and R charts.
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Statistical Process Controls (SPC) is a suite of methods that can be employed to control a manufacturing or assembly process. It has a wide range of potential applications ranging from consumer products to defense. It can be employed at the lowest element of component manufacturing or an assembly operation.
This article discusses the assumptions necessary to understand SPC.
Quality Costs for manufacturing or services can be categorized as prevention and appraisal costs, and internal and external failure costs. Control occur in prevention and appraisal activities, both of which rely on data. However, when data is collected, it shows variation. One must understand variation to know how to react.
Dr. Deming indicated that 94% of variation is from common causes and about 6% is from special causes. So what are the common and special causes of variation?
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Businesses, to be competitive, need to control all costs. Product or service failure can result in large uncontrolled costs. As product development proceeds, the cost of failures increases. The concept is shown in figure 1.
Figure 1
A state variable is a parameter that is categorized into a countable number of defined states. Examples would include transmission gear states, PRNDL positions, ignition switch states, and others. Sometimes continuous variable, like pedal positions, may be binned into discrete states to be displayed as a histogram. State change timing is unpredictable since vehicle operation is highly variable. A way to deal with this data is Markov Analysis.
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.