# Capability Index - Explained

What is the Capability Index?

## What is a Capability index (Cp)?

A process capability index (Cpk) is an arithmetic tool used for quantifying the proficiency of a process to produce products within the customer specification range. It values the producers ability to produce output within the acceptable customer range. Cpk is important in approximating the closeness between you and the target set, and the steadily one is to the mean performance. Cpk portrays the best case situation for the current development.

## How does a Process Capability Index (Cpk) Work?

Cpk is given by this complex equation: [Minimum (mean - LSL, USL - mean)] / (0.5*NT). LSL refers to Lower Specification Limit, and USL stands for Upper Specification Limit.

Normally Cpk is described as the ability of the process in achieving whether or not the mean is located at the middle of the measurement range. Cp and Cpk, these two data share a lot. The lesser the standard deviation, the greater the Cp and Cpk. Under the appropriate situation, Cp and Cpk are the same in value. Cpk is a regular index to illustrate the ability of one procedure. Cpk value is directly proportional to the degree of goodness of a procedure. The higher the Cpk value, the better the procedure. For instance, Machine 1 has a Cpk of 1.7 and machine 2 has a Cpk of 1.1. In regards to the Cpk, one can conclude that machine 1 is better than 2. We can also calculate the yield produced and the ineffectiveness of the machine because Cpk applies the use of the gradation range.

### Relationship to measures of process fallout

The plotting from capability indices like Cpk to quantification of process impacts is forthright. Process fallout measures the number of flows a process results into and id measured by DPMO or PPM. Process output is the supplement of process fallout, and it is estimated similar to the area under the probability density curve. Cpk equal to or greater than 1.33 shows that the process is able and matches specification range. Any value less than 1.33 suggests fluctuation is wider in comparison to the description or the process mean if far from the provision made.

Example 1: Upper specification limit (USL) =16 Lower Specification limit (LSL) = 4 Mean () = 10 & Standard deviation () = 2 Given the formula to calculate Cpk is Cpk = min [USL/3, LSL/3] = min [16-10/6, 10-4/6] = min [1, 1] = 1 Statistical clarification when curve stretches from +3 to -3, it is believed to occupy 99.73% and here the machine is making 99.73% fit parts.

Example 2: Upper specification limit (USL) =18 Lower Specification limit (LSL) = 0 Standard deviation () = 2 Cpk = min [USL/3, LSL/3] = min [18-10/6, 10-0/6] = min [1.33, 1.67] = 1.33 Here at least, 99.99% of the outputs from the machine are good.