Cp and Cpk are related. Really?

Process capability analysis plays an important role in quality. It helps determine whether the process is capable of consistently producing parts conforming to customer requirements. Cp and Cpk are the two most popular capability indices used to find process capability. Cp and Cpk are related to each other. Whenever I say this most people around me are surprised, some think I am insane. But it is true. Cp and Cpk are related by the equation. Refer to chapter 6 in the NIST/SEMATECH e-handbook of Statistics Handbook

Cpk = (1-k) Cp
where k is the distance between the process mean and the midpoint of specification range.



where
m = midpoint of the specification range or tolerance
mu = process mean
USL and LSL – upper and lower specification limits.

k has a value between 0 and 1.
When k is 0, Cpk is equal to Cp.
When k is less than 1, Cpk < Cp

That is why Cpk ≤ Cp.

Data versus Facts

Taiichi Ohno said "Data is of course important in manufacturing, but I place the greatest emphasis on facts".
Ohno believed that data served as mere indicators of what's going on in the process.
Actually verifying on the scene facts of the situation is key to knowing exactly what's happening.

The Ohno circle requires people to stand in the circle drawn on the floor of a plant for hours to observe the process. This helps the person to gather facts first hand, thoroughly understand the actual situation, then evaluate and analyze what's going on. This is "Go and See the actual situation for yourself" principle practised at Toyota.

At Toyota, nothing is taken for granted. What one sees in person first hand may never show up in reports.
Data in reports may measure results however, it misses out to reveal the details of the actual process that is being followed on a daily basis.
Data can be manipulated, but facts remain hard facts!

Food labels: Informing or misinforming consumers?

It is over the news since 20th October '09 that "The FDA is warning food manufacturers about false claims on food labels that may mislead consumers". Food manufacturers are touting their products for healthy or smart choices using all kinds of colorful logos, symbols to attract consumers.
Even though the primary purpose of these labels is to communicate health related information. Many food companies are using it as a marketing tool.

Labels like American Heart Association's heart shaped logo, Smart Choices check mark and many others appear on the front of food packages that contain large amount of sugar, salt and other ingredients that may be unhealthy.

Busy consumers shop for groceries by looking at the signs and symbols that indicate the food is healthy. Many consumers may not read the ingredients on the package before deciding to purchase the product. As rightly said "the devil is in the details", ingredients, nutritional information from the label would give the consumers better idea about the quality of food inside the package. It pays to take the time to read the label information.
FDA has warned consumers to read food labels before buying food products.

So the next time you go grocery shopping, plan to spend some extra time in the food aisles to look at those labels on food packages before buying them!

Can Cp be used for unilateral tolerances?

When I go through the topic of capability indices for unilateral tolerances in my training class or consulting sessions, I usually get surprised looks from quality practitioners searching for Cp values. The common reaction is where is the Cp index? How come it doesn’t show on the chart or on my capability report?

For unilateral tolerance, Cp does not apply.
Why?
Because, by definition Cp is estimates process capability for a centered process. For unilateral tolerances the target may not be at the center of the specification limits.
The formula for calculating Cp is USL - LSL / 6σ
For unilateral tolerances, we have either the upper or lower specification limit.
That is why Cp cannot be calculated.

So what capability indices can be used for unilateral tolerances?
Cpk, Cpkm can be used. For details on these indices, please download our white paper on capability indices.
Cpk is Cpu for upper specified unilateral tolerance and it is Cpl for lower specified.

How do you track capability of your processes?

Does sample size affect Cpk?

This was a question from one of my training class participants.
I found the question interesting and answered using the formula of Cpk.

Cpk = Minimum of [USL - Overall Average]/3sigma or [Overall Average - LSL]/3sigma
For Xbar-R chart,
Sigma = Rbar/d2
d2 increases as sample size increases.
So for the same Rbar, sigma reduces as sample size increases.

Cpk increases as sigma reduces.
That means for the same overall process average and range, Cpk will change as sample size changes. In fact as sample size increases, Cpk will be larger.

Example

Outside diameter of a pipe has specifications of 9 and 11. Design target is 10

For a dataset, let's say that...
Overall average = 9.3 and Rbar = 0.5

We will now calculate Sigma and Cpk for two different sample sizes - 5 and 7

For sample size 5, d2 = 2.326
sigma = 0.5/2.326 = 0.215
Cpk = Min [ 10 - 9.3] / 3 x 0.215 or [9.3 - 9] / 3 x 0.215
Cpk = Min of 1.09 or 0.465
Cpk = 0.465

For sample size 7, d2 = 2.704
sigma = 0.5/2.704 = 0.185
Cpk = Min [ 10 - 9.3] / 3 x 0.185 or [ 9.3 - 9] / 3 x 0.185
Cpk = Min of 1.26 or 0.54
Cpk = 0.54

For the same data set, sigma and Cpk change based on the sample size selected. As sample size increases, sigma reduces and Cpk increases.
If a smart quality engineer wants to trick the system and project good process capability, he/she can simply do that by increasing the sample size.

What is the sample size you use? Have you tried finding process capability with different sample size?
Drop us a line at info@sybeq.com and tell us about your process and capability calculations. We would love to hear from you.

Top 10 Trends in Quality

Since we are on the topic of pictures and videos, I thought it would be a good time to talk about emerging trends in quality.
Most trends including those emerging in quality are driven by technology and making use of intelligent systems to get accurate information quickly.

We live in the world where abundant data/information is available and users have little time to look at it.
The challenge is to present data in formats that are easy to understand in a short span of time.
These are the key factors driving the trends that are emerging in quality

Based on our experience in the manufacturing industry, the top 10 trends in the field of quality are:
1) Use of Real time systems in Quality is increasing
2) Quality practitioners need accurate data presented in the form of charts
3) Charts should be designed to tell them the story of their process and product quality in a few minutes
4) Practitioners need to be alerted about problems in real time
5) Quality Engineers have to generate reports for customers and management. Systems should have an easy way to create reports as and when required.
6) Managers and executives need color coded dashboards that tell them about the quality of the parts that are being produced/shipped, overall process capability, production losses, downtime etc.
7) Quality professionals analyze data for finding root causes of problems. They need to slice and dice the data many different ways. Systems should allow them to do this in every possible way
8) All information/reports/analysis should be available on the web. That way quality practitioners can access this information from anywhere in the world.
9) Tracking and correlating data about quality throughout the supply chain should be possible.
10) Information should be available not only on PCs but also on mobile devices like phones, PDAs

And a video is worth ten thousand!