# Process Capability Indices Cp and Cpk Calculation

## What are the process capability indices Cp and Cpk used for?

The Cp and Cpk are used to measure process capability based on the weight of the bags produced by a process.

## What are the given values for Cp, Cpk, Lower Specification Limit, and Standard Deviation?

The given values are Cp = 1, Cpk = -5, Lower Specification Limit = 1.4 lbs, and Standard Deviation = 0.1 lbs.

## What is the value for the mean of the process?

What is the value for the mean of the process based on the given values using the Cp and Cpk calculations?

## Value for the Mean of the Process

The value for the mean of the process is A) 1.5 lbs.

To calculate the value for the mean of the process based on the given values of Cp = 1, Cpk = -5, Lower Specification Limit = 1.4 lbs, and Standard Deviation = 0.1 lbs, we can use the Cp and Cpk equations.

The process capability indices Cp and Cpk are defined as follows:

**Cp = (Upper Specification Limit - Lower Specification Limit) / (6 * Standard Deviation)**

**Cpk = min((Upper Specification Limit - Mean) / (3 * Standard Deviation), (Mean - Lower Specification Limit) / (3 * Standard Deviation))**

Given that Cp = 1 and Cpk = -5, and the Lower Specification Limit is 1.4 lbs, we can plug in the values and solve for the Mean:

Solving for the Upper Specification Limit:

Upper Specification Limit - 1.4 = 6 * 0.1

Upper Specification Limit = 1.4 + 0.6 = 2.0 lbs

Using the value of the Mean in the Cpk equation:

-5 = (2.0 - Mean) / (3 * 0.1)

Solving for the Mean:

-5 * 3 * 0.1 = 2.0 - Mean

-1.5 = -Mean

Mean = 1.5 lbs

Therefore, the value for the mean of the process is A) 1.5 lbs.