Process Capability Index Calculator

Welcome to Omni's process capability index calculator, aka the C_pk calculator! With the process capability index calculator, you can quickly determine whether the products of your process meet specification limits (target values, usually set by customers, in which products or services are relative to customer requirements).

Do you want to determine whether your process is going smoothly, or whether you need to make some improvements for the future? Read on to learn more about:

• How to calculate process capability index (a.k.a. process capability ratio);
• What the meaning of C_pk is; and
• What values of C_pk statistics are satisfactory.

As a bonus, you will learn why people are so excited when their C_pk is 1.33 or larger! 💡

To better explain the process capability index, let's imagine a scenario. You are craving a delicious cappuccino on a Monday morning ☕. You decide to walk to the coffee shop at the corner of your street. That coffee shop is your favorite because the way they make cappuccino meets your requirements, which have certain specifications. You know that if the cappuccino's milk temperature exceeds your specification limits of 55-65 °C, the fluffy foam will not be stable, and it will most definitely ruin your Monday morning.

Unlike other coffee shops that are even closer to your house, the one at the corner of your street is your favorite because you can get a cappuccino with a perfect milk temperature within your specification limits every time.

Now that you have the scenario in mind, let's define the process capability index. Process capability index, process capability ratio, or C_pk, is a measure of the process's capability to produce desired results that meet the customer's specification limits (values within which a product should perform). In the scenario described, the C_pk of preparing milk for cappuccinos would indicate that the coffee shop is consistent with its average performance of producing cappuccinos for customers (i.e., baristas consistently deliver cappuccinos with milk temperature that is 60 °C on average 🥛, and rarely exceeds 55-65 °C).

Before presenting the process capability index (or process capability ratio) formula, it is essential to note that you can apply different process capability indices (C_pk, C_p, C_pm, C_pkm) to different situations.

For example, you can successfully utilize the process capability index formula when you want to observe variation in your process relative to specification limits and determine how the process can perform in the future. C_pk can be used when your process average is not perfectly centered. The formula for C_pk is as follows:

where:

• $C_{pk}$ — Process capability index;
• $\text{USL}$ — Upper specification limit;
• $\text{LSL}$ — Lower specification limit; and
• $\sigma$ — Standard deviation.

If you want to see the potential capability of the process when the process average is centered, you can use the following formula of C_p:

where :

• $C_p$ — Potential process capability;
• $\rm USL$ — Upper specification limit;
• $\rm LSL$ — Lower specification limit; and
• $\sigma$ — Standard deviation. If you're unsure how to calculate standard deviation, feel free to use our standard deviation calculator.

If you want to see the capability of your process around a specific target, you can use the following formula for C_pm below. However, remember that C_pm does not account for the process average that is off-centered.

where:

• $C_{pm}$ — Process capability to be relative to the target process mean. This is also called the Taguchi capability index.
• $C_p$ — Potential process capability;
• $μ$ — Mean; and
• $T$ — Target process mean.

If you're determining the process capability around a target, and you don't have a process that is centered around the target value, you can use the C_pkm formula below:

• $C_{pkm}$ — "Third generation" process capability index; and
• $C_{pk}$ — Process capability index.

Now that you're familiar with the process capability index formula, how to calculate the process capability index, and what C_pk is, let's talk about its interpretation. As mentioned before, the higher your C_pk value, the better your process produces. Experts agree that you want your C_pk index to be at least 1.33. Here is the explanation of why you want to reach this magic number:

Rare events in your process become detectable when the mean moves off-center by 1.5 sigmas (i.e., when normal distribution shifts by 1.5 standard deviations on either side). When C_pk is 1.33, upper and lower specification limits are four standard deviations from the process mean. In this case, there is some (one standard deviation) room for variability within specification limits, and you can consider the process capable. However, a C_pk of 1.33 is not ideal since you want larger variability before defects are displayed.

The process with C_pk of 2 corresponds to a 6-sigma level process; therefore, it can bear a larger process mean shift while having the most process-related output within specifications (has desired room for variability). Therefore, a C_pk of 2 would indicate excellent process capability.

Is it still confusing? Let's discuss an example. Soups at your buffet must be served between 64–80 °C, as per your customer's specifications 🍲. The mean temperature of the soups is usually 72 °C, and the process of reheating has a standard deviation of 1.5 °C. What is the C_pk value of reheating soups?

Since the smallest acceptable C_pk is 1.33, your value of 1.778 is a great result, and we can conclude that your process is capable!