A set of 100 subgroups of measurements on productive tomato seedlings has a sum of s values of...

Question:

A set of 100 subgroups of measurements on productive tomato seedlings has a sum of s values of 420.

If the subgroup size 6, calculate the process capability, 6?. (Answer to 3 decimal places)

Process Capability:

The Process Capability Index is a statistical measure and it is used for the Process ability of the output within the specific limits. The value of Process Capability Index should be more for the good ability of the process.

Answer and Explanation:

Given that,

{eq}k = 100\\ \sum{s} = 420 n = 6 {/eq}


{eq}\bar{s} = \dfrac{\sum{s}}{k} = \dfrac{420}{100} = 4.2 {/eq}


The estimate of the process standard deviation, is defined as:

{eq}\hat{\sigma} = \dfrac{\bar{s}}{c_4} {/eq}


The value of {eq}c_4 {/eq} is calculated by the table.

Coefficient Table


{eq}c_4 =0.9213 {/eq}


{eq}\hat{\sigma} = \dfrac{4.2}{0.9213} = 4.56 {/eq}


The process capability index is defined as:

{eq}C_p = \dfrac{USL-LSL}{6\hat{\sigma}} {/eq}


{eq}USL = 100+20 = 120\\ LSL = 100-20 = 80 {/eq}


So,

{eq}C_p = \dfrac{120-80}{6\times 4.56}\\ \color{blue}{C_p = 1.462} {/eq}


Learn more about this topic:

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Process Capability: Definition & Elements

from Business 112: Operations Management

Chapter 4 / Lesson 5
1.1K

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