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!

A picture is worth thousand words - Part III

Would you prefer reading through the 14 step given below or just viewing the picture of the process?

Picture showing flow of material and information at company "Funplace" that makes toys

Steps describing the flow of information and material in Funplace
1.Funplace electronically sends a 4-week order forecast to XYZ toys. The quantities
are confirmed on a weekly basis and the purchase order is placed.
2.Based on this input, XYZ Toys electronically orders the parts from their
suppliers. XYZ Toys sends a 3-week forecast and confirms the quantity every week.
3.XYZ holds at least 2 days worth of raw material inventory in the warehouse.
4.Production control manually issues finished good quantities required on a weekly
basis. This information is sent to production.
5.Based on the production volumes required each week, the production manager
prepares for manufacturing. He gets his team together and the line leader Nick
plans for production. Per the daily production volume, Nick requests the warehouse
to issue raw material to the assembly line.
6.The assembly process consists of 4 primary steps…
- Gear assembly : putting gears in the plastic body of the toy
- Audio assembly : assembling the audio system in the toy
- Testing
- Packing
7. Everyday a truck shipment of 2000 toys is sent to Funplace.

A picture is worth thousand words - Part II

To convey a message, it is usually recommended to use pictures or diagrams rather than plain words. Are pictures really better than words?

We are used to learning faster with pictures.
Just like small kids learn to read looking at colorful pictures, adults understand better with pictures.

In a corporation, every level uses pictures that make sense to them and communicate what they need to know to do a better job.
Managers look at dashboards giving them information about an area, a location or the overall company.
Staff look at diagrams or charts to track critical process information. People doing the job look at pictures in their work areas as aids to guide them perform a given task.

Pictures enables everyone in an organization get the information they need very quickly. People looking at these pictures only need to be responsive when the picture calls for action.

Do you use pictures for getting critical information about your process, product or service?

A picture is worth thousand words...

I always thought that pictures were more effective and efficient in communicating a message. People around the world come up with more and more innovative ways to present business data as pictures that are easy to read and convey the message quickly.

In the Quality world, I deal with pictures in the form of charts(SPC charts, affinity diagrams, relation diagrams etc) or maps (SIPOC maps, VSM etc). These pictures (charts, diagrams and maps) capture lot of meaningful information about the
quality of the product or service. However, many quality practitioners struggle with proper interpretations of these pictures and fail to take necessary action to improve quality.

Control charts for example are designed to communicate what's happening in the process. They provide signals that indicate the presence of special causes in the process. All we have to do is pick up these signals and act on them!

Rather than looking through paper reams full of data that could take hours, pictures tell us the real story in just a few minutes.
A picture is truly worth a thousand words...but will be effective only if it is looked at by the right people, interpreted correctly and acted upon.

Do quality charts or maps help you find quality problems in your process?
Have you improved a process by acting on signals from SPC charts?

Is my data variable or attribute?

From my training class last week, I had an interesting question from one of my class students who was from the healthcare industry.

The student asked "I measure success of tests conducted by lab personnel. For example, I monitor number of blood tests were conducted every day by each lab assistant. I also monitor how many attempts were required for the assistant to successfully draw blood and complete the test.
I want to plot an SPC chart for the number of successful blood draws in single attempt. Should I use variable or attribute control charts?"

My answer to her was a series of questions..
Question 1: What do want the SPC chart to tell you?
Answer : Number of successful blood draws in single attempt.
Also, success rate of each lab personnel.

Question 2: Are either of the above measurements or counts?
Answer : They are counts.

Question 3: What SPC chart helps chart count data?
Answer: Attribute control charts

My student was able to answer her own question after breaking down her problem in small sections.

Have you struggled with data types?
Do you have questions about type of SPC charts you should use?
Please visit our tutorial on "SPC in healthcare" at www.sybeq.com/Tutorial.aspx