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In this video, we look at some examples
of applying the process capability ratio.

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The first question aims to understand how
we can adjust the process capability ratio.

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Imagine that our current capability
ratio for a key quality variable is 1.3.

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The average value of the quality
variable being measured was 64 units.

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We are told the process operates closer to
the lower specification limit, which is 56.

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The upper specification limit is 93.

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Which two parameters in the system
can we adjust, and by how much,

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to achieve a desired capability ratio of 1.67?

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For example, recent safety regulations
might just have been put in place.

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We need to improve our capability.

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In the answer where you are
specifying these two parameters,

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assume that you can adjust those
parameters independently of each other.

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The answer will be shown on
the screen in a few seconds.

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The second example shows values of the particle
size, a key critical quality value taken

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from their certificates of analysis.

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Certificates of analysis are a piece
of paper that specify what the upper

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and lower specification limits are
for a product that you are purchasing

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or for a product that you are selling.

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When you are selling the product, you supply
the certificate of analysis to your customer.

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When you are purchasing, you will receive the
certificate of analysis from the supplier.

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Download these data from this link of
20 recent shipments from a supplier

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and calculate what the supplier's capability
ratio is, given that on their certificate

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of analysis it shows the lower
specification limit was 45 microns

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and that the upper specification
limit was 59 microns.

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When you do your calculation, clearly state
all the assumptions that you need to make.

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The answer will be shown on
the screen in a few seconds.

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Here is a final example.

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Plastic sheets are manufactured
on your blown film line.

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The C_p value, in other words, the capability
ratio assuming your process is centered,

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is given as 1.7.

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You sell these plastic sheets to your
customers with a specification limit

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of two millimeters plus and minus 0.4.

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Can you list three important assumptions
you must make to interpret the C_p value?

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Here they are, written for you on the screen.

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Answer the following next.

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What is the theoretical process
standard deviation sigma for this system?

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Answer the following question next.

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What would be the Shewhart
chart limits for this system

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if you had used subgroups of size n equals four?

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To answer this last question, I strongly suggest
you draw an illustration on a piece of paper,

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showing where the specification limits are and
showing where the Shewhart chart limits are.

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Draw this with a diagram of the
normal distribution superimposed.

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If you follow that advice, you would have
had a generic diagram that looked as follows.

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Notice that the lower specification
limits fall below the lower control limit.

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Similarly, the upper spec limit
falls above the upper control limit.

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Notice where sigma for the process lie and
where sigma over root n, the value that's used

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to calculate the control limits,
lie relative to each other.

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Given this, you can then calculate the upper

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and lower control limits as
shown here on the screen.