Chapter 3. There are no two things in the world that are exactly the same… And if there was, we would say they’re different. - unknown. Measurement concepts. Measurement terms. Discrimination The smallest unit of measurement on a measuring device. Resolution
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And if there was, we would say they’re different.
- unknownMeasurement concepts
The smallest unit of measurement on a measuring device.
The capability of the system to detect and faithfully indicate even small changes of the measured characteristic.
Half of the accuracy.
Tolerance, specification limits
Acceptable range of a specific dimension. Can be bilateral or unilateral
A graphical representation of a group of numbers based on frequency.
The difference between things.
Set of all possible values.
A subset of the population.
Any individual item in a set has the same probability of occurrence as all other items within the specified set.
One or more samples randomly selected from the population.
Any sample that is more likely to be chosen than another.
Success depends upon the ability to measure performance.
Rule #1: A process is only as good as the ability to reliably measure.
Rule #2: A process is only as good as the ability to repeat.
Gordy Skattum, CQE
We only want normal variation in our processes
Each unit of measure is a numerical value
on a continuous scale
Variation common and special
Pieces vary from
But they form a pattern that, if stable, is called a distribution
There are three terms used to describe distributions
Cost at lower spec
Cost at upper spec
Cost at mean
Lower Specification Limit
Upper Specification Limit
We need to calculate process capability
Using only 50% of the tolerance or less
** 100k is the mean because it is the middle weighted value.**
Remember - Average and Mean are synonymous!!!
If there are an odd number of data values, there will be just one value in the middle when the data are ordered, and that value is the median.
If there is an even number of values, order the values and average the two values that occur in the middle.
** 100k is the median because after the data is arranged in order it is exactly half way to both ends.**
** 100k is the mode because it occurs more than the others in the data table.**
R = range
H = highest value
L = lowest value
Although the method we just used to calculate standard deviation is accurate, it is also very time consuming. Because time is money in industry, we find that it becomes more cost effective to estimate standard deviation rather than calculate the exact number. This gives us a number very close to the exact number, but in a very short time period.
The following formula is used to estimate standard deviation:
= Estimate of Standard Deviation
= the average range among the samples in each subgroup and,
= a constant based on the number of samples in each subgroup
An Individuals X and Moving Range chart, which we will discuss in detail later, uses subgroup sizes of two. The d2 value for subgroups of size two = 1.128.
Therefore, we can easily calculate an estimate of standard deviation for IX & MR charts by dividing the average of all range values by 1.128. The numbers are .3472, .3476, .3478, .3479, .3474, .3472:
Your book also calls this “s”
See Table B.1 for d2 values
An operator is running a job on a lathe. The tolerance is .656-.657. The following values were documented. Complete the calculations and answer the questions that follow.