Bill Smith came up with an efficient method (six sigma) to enhance a process. A process is a set of independent instructions, procedures, and stages. They ingest resources and transform them into products. A process capability measures the potential of a process. That is its ability to produce a product within set limits. Cp and Cpk are such process capability indices.

**Cp vs Cpk**

**The main difference between Cp and Cpk is that Cp analyzes the ability of a process to justify the structured specification for a product. While Cpk portrays the deviation of a process from the center within the tolerance range. Cp is termed as Process Capability. Cpk is Process Capability Index. **

Cp also known as Process capability is the statistical calculation of a process’s ability to produce a product within a given set limit. It is the ratio of the total specification to the total effective range. The least value of a Cp is 1 to produce a good capability product.

Cpk is the Process Capability Index. The capability of a process is proportional to its magnitude. The higher the Cpk, the higher is the efficiency of the process. Unlike Cp, it covers how well a process is centered within the specified range. Cpk is never higher than Cp. It can be equal to Cp.

**Comparison Table Between Cp and Cpk**

Parameters of Comparison | Cp | Cpk |

Name | Process Capability. | Process Capability Index. |

Definition | Cp is the capacity of the process to abide by the strategic classification for a product. | Cpk estimates the variation of the process from the center inside the tolerance range. |

Magnitude | Cp is either equal to Cpk or greater than Cpk. | Cpk is always less than Cp. |

Formula | Cp = (USL-LSL)/6 | Cpk = (Xdbar- LSL)/3 ORCpk = (USL-Xdbar)/3 |

The minimum value (for a capable process) | 1.0 – 1.33 | 2.00 |

**What is Cp?**

Cp is one of the process capability indices. It is called Process Capability. Process capability (Cp) is a statistical evaluation of a process’s capability to produce products within a determined limit.

Cp is the ratio of the ‘voice of the customer’ to the ‘voice of the process. It depicts the range of the process and lets us judge its effectiveness. It is measured within six standard deviations ( or 6).

Evaluation of Cp

Cp = Total specification (or Tolerance)/ Total effective range (or natural variability)

Cp = (USL-LSL)/6, here USL = Upper Specification Limit; LSL = Lower Specification Limit; = standard deviation.

The specification limits are the operating range for a given process. Here the upper specification limit is three standard deviations that are 3. The lower specification limit is also three standard deviations. They sum up to a total range of 6 .

Each product has specific demands, the specifications are set to meet those expectations. For instance, if you are preparing a canvas, its width and breadth must be considered. To be precise products must have a specific measurement or structure.

If the magnitude of Cp equals 1, the process is capable.

If the magnitude is lesser than 1 the process is not capable.

If the Cp value is greater than 1 the process has a good capability.

**What is Cpk?**

Cpk is the process capability index. It is the measure of how well a process is centered within the specified limit. It implies the capability of a process. The specific range denotes the expectations of customers. If a process exceeds the given range it does not meet the customer expectancy. Mature processes use Cpk to monitor the variation in a process.

Cpk calculates the variation of standard deviation within the applied specification. It depicts the localization of the process as well. Cpk is the minimum of Cpl, Cpu. Cpl and Cpu are process potential (one-sided).

Cpl = – LSL/3, Cpu = USL-/3. Here is the target of the process. A good process has a larger Cpk. Negative Cpk means the process has exceeded the given specification. Cpk gives us two values, the lower value is considered. It tells us how much the process has shifted from the center. The process capability index keeps the track of the consistency of a process.

Cpk value that equals one implies the process is perfectly centered within the customer’s specification. And the process is capable. A Cpk value can be equal to Cp (process capability) but never more than that.

Condition for a perfectly centered process is

Cp = Cpk .

**Main Differences Between Cp and Cpk**

- Cp is process capability and Cpk is process capability index.
- Cp gives an overall idea about the capability of the product. Cpk lets us know how centered a process is within the range.
- Cp is greater than equal to Cpk. Cpk is always lower than Cp.
- Cp is the difference between USL and LSL divided by 6. Cpk equals to (Xdbar- LSL)/3. or (USL-Xdbar)/3.Here USL is Upper Specification Limit. LSL is Lower Specification Limit.
- Cp must be at least 1, Cpk must have a minimum value of 2

**Conclusion**

In 1920 Walter A Shewhart formed a control chart to monitor the variations. That included improvement of quality, efficient productivity, and reduction of the cost price. These initiated the statistical technique.

There are two types of variations namely common cause variation and special cause variation. Common cause variations are inherent in the process while special cause variations are caused due to external factors.

Bill smith introduced six sigma. Soon it became widely accepted. It is a statistical tool that enhances a given process. Cp and Cpk are process capability indices. There is a condition while calculating Cp and Cpk, that is it should be a stable process. We must analyze Cp and Cpk simultaneously. The reason is Cp ensures the capability of the process whereas Cpk analyzes the performance of the process. Cp judges the variation only. Cpk analyzes both the variation and location of the process.

**References**

- https://onlinelibrary.wiley.com/doi/abs/10.1002/qre.990
- https://www.cps.org.tw/issues/file/201412192253180.pdf

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