This is the sixth in a series of articles about MSA. The focus of this article will be on measurement repeatability and reproducibility for non-replicable measurement systems, commonly called a destructive test.

Okay, what exactly is a non-replicable measurement system and why is it not just called a destructive measurement system? Let’s start with the definition of replicate.

In statistics, a replicable measurement system is one where any given part may be measured multiple times by the same or different operators, and where the result obtained will fall within a predictable range of values.

By this definition, a destructive measurement system is definitely non-replicable. However, there are other situations that are non-replicable that do not result in the destruction of the part.

The following are examples of non-replicable measurement systems:

The part changes on use or test(e.g., rubber parts will soften when flexed, harden when left alone and take a set when compressed; uncured rubber will cure when tested in a rheometer)

The characteristic is dynamic and is sensitive to multiple test conditions that cannot be exactly reproduced(e.g., tests of complex systems such as an automobile)

The characteristic or property measured changes over time(e.g., dimensions of freshly molded plastic parts, viscosity of materials with shelf lives)

The part physically cannot be reintroduced to the test(e.g., in-line measurement devices)

There are some cases where the part itself might be destroyed, but the measurement is still replicable. This may occur if the part must be damaged or destroyed to gain access to the characteristic to be measured. Once access is gained the characteristic may be measured repeatedly.

The part is either physically destroyed(e.g., tensile test) orthe part cannot be re-measured in the same location(e.g., hardness test)

So, now you know you have a non-replicable test. What do you do? The following are several approaches that may work:

Split specimens:The parts or material collected to represent one part are split or sub-divided into smaller units. The smaller units are used for the repeat trials and between operator trials.

Consecutive specimens:Consecutive parts are used to represent one part for the repeat trials and between operator trials. Used when the parts cannot be sub-divided and consecutive parts can reasonable be expected to be homogeneous, such as would occur in an auto-correlated process.

Regression approach:The change in the characteristic over time or activity is known and has a defined relationship [Y=f(x)] (e.g., shrinkage of plastic parts). The subsequent measurements are adjusted using this relationship then analyzed.

We are not through yet. The analysis of a non-replicable MSA is also different. You cannot use the Range method or the standard ANOVA method. Both of these approaches are designed for a “crossed study” where all possible combinations of parts, operators and replicates are possible. A non-replicable MSA is what is called a “nested” study where the parts are nested within the operators and replicates. All possible combinations cannot be run. Some statistical software packages such as Minitab have a Nested MSA option. If this is not available, use the Nested ANOVA option, or the General Linear Model (properly specifying the nesting relationship). The standard deviations can be determined from these analyses, but metrics such as %Tol, %SV and ndc must be manually calculated using the information in the ANOVA table (Repeatability is the error term).

Stabilized parts:Parts or systems are stabilized before testing. This stabilization will depend on the product and characteristic. Some systems may be broken-in versus tested new. Some characteristics may stabilize when pre-tested a number of times.

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# Intro to MSA of Continuous Data – Part 6: R&R for Non-Replicable Measurements

Non-replicable R&R

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