Role of Sigma in Cpk and Ppk calculations

Cpk and Ppk are calculated using the same formula.
So what’s the difference between the two?
The difference between Cpk and Ppk is the way sigma is estimated.

For Cpk, sigma is estimated using the formula…
Rbar/d2 for Xbar-R chart where Rbar is the average Range and d2 is a statistical constant
Sbar/c4 for Xbar-S chart where Sbar is the average standard deviation and c4 is a statistical constant

For Ppk, sigma is estimated using the formula



Where
X – Individual reading

- Process average

n – Sample size

So why use two separate indices?
Cpk and Ppk are designed for use under specific conditions.

Sigma used in the Cpk calculation explains inherent variation in the process which is caused by common causes. The control chart for such a process would be statistically stable.

On the other hand, sigma used in Ppk calculation explains the total variation caused by common as well as special causes. Control charts for this process would have points out of control i.e. the process is unstable.
New process design or pre production (pilot) runs for new products would typically have special and common causes present. Ppk is used for determining capability of such processes.

Food Quality and Safety go hand in hand

The food and beverage industry has to deliver high quality product that satisfy the consumer needs like any other industry. In addition the food and beverage industry has to comply with the safety and regulatory requirements. Food safety and regulatory compliance are some of the key elements that food and beverage manufacturers track to prevent non compliance issues or recalls.

High quality of the food products in manufacturing plants usually results in high safety. Manufacturing plants that pay close attention to quality of the food products they make typically comply with the safety and regulatory requirements too.
Such plants will typically monitor the food products for regulatory compliance.
Regulatory checks like MAV or net weight/volume of the food products are monitored in real time. Actions are initiated as soon as violations are uncovered.

Let's think about it in using a simulation food plant X that makes ice cream.
Company X is operating at small rejection levels or high quality in production. They conduct the metal detection and other safety checks as part of their routine checks everyday.
Regulatory checks for MAV and net weight violations are tracked and controlled using automated systems.
Mistake proofing is in place using poka yoke devices. There are poka yokes that check box labels, match the box to the correct lid, check ingredients among many other checks.
Poka yoke devices themselves are regularly validated for accuracy.
Everyone in the plant considers quality and safety to be their responsibility.
Ice cream from this plant is high quality which is good for the company and safe for consumers which ultimately results in customer satisfaction.

Safe Quality food program from SQFI (Safe Quality Food Institute) is a food safety program. This program has different levels that start with basic food safety going through certified HACCP food safety plans finally requiring implementation of a comprehensive Quality Management System. Food safety is the primary focus of this program and quality being the secondary requirement. Even though food quality comes after safety, it plays an important role. Safe food products will usually have high quality in the manufacturing plants.

So much information, so little time!

Consumers shopping for food are busy and have very little time to read through all the information on food labels. Most consumers look for the best deal and quickly look at symbols before they purchase food products. Very few take the time to read nutrition facts or ingredient information on labels. Many consumers even misinterpret the symbols used on food products.

Food labels that use words like “organic”, “all natural” imply that the food is healthy. There is a lot of debate on the two terms natural and organic. Is natural the same as organic? Different? Is organic better than natural food? Does natural imply that there are no artificial ingredients or has minimum/no processing?

This leaves the poor consumer wondering how to make sense of these labels on food packages. Some even think if they made the right choice while shopping for food items. The consumer can always turn to the food and drug administration (FDA) for assistance.
FDA has provided food labeling guidelines and the requirements for claiming the food to be ‘healthy’ (please see N49 on this page).

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?