# Meena Chavan Corp's computer chip production process yields DEAM chips with an average life of...

## Question:

Meena Chavan Corp's computer chip production process yields DEAM chips with an average life of 1,800 and standard deviation = 100 hrs. The tolerance upper and lower specification limits are 2,400 hrs and 1,600 hrs; respectively. Is this process cable of Producing DRAM chip to specification?

2. The manager of a food processing plant desires a quality specification with a mean of 16 ounces, an upper specification limit of 16.5, and a lower specification limit of 15.5. The process has a mean of 16 ounces and a standard deviation of 1 ounce. Determine the Cpk of the process.

## Capability Index Ratio

The capability index ratio is a statistical measurement. This measurement analyzes whether a product is processed or produced within the given specifications. This helps the managers measure the process and determine if it is satisfactory of if changes need to be made.

## Answer and Explanation:

a)

Given

UCL = 2400

LCL = 1600

Average life (mean) = 1800 hours

Standard Deviation (SD) = 100

Calculation of capability of process

{eq}\begin{align*} &{\rm{Capability}}\; = \dfrac{{{\rm{UCL}} - {\rm{LCL}}}}{{6 \times {\rm{SD}}}}\\ &= \;\dfrac{{2400 - 1600}}{{6 \times 100}}\\ &= \;\dfrac{{800}}{{600}}\\ &= \;1.33 \end{align*} {/eq}

Calculating the minimum capability

{eq}\begin{align*} &{\rm{Minimum}}\;{\rm{Capability}} = \left( {\dfrac{{{\rm{UCL}} - {\rm{mean}}}}{{3 \times {\rm{SD}}}}} \right),\left( {\dfrac{{{\rm{mean}} - {\rm{LCL}}}}{{3 \times {\rm{SD}}}}} \right)\\ \\ &= \;\left( {\dfrac{{2400 - 1800}}{{3 \times 100}}} \right),\left( {\dfrac{{1800 - 1600}}{{3 \times 100}}} \right)\\ \\ &= \;\left( {\dfrac{{600}}{{300}}} \right),\left( {\dfrac{{200}}{{300}}} \right)\\ \\ &= \;2,0.67 \end{align*} {/eq}

The capability for the LCL is less than 1.25 and therefore the process is not capable of producing within the given specifications.

b)

Mean = 16

Standard deviation (SD) = 1

UCL = 16.5

LCL = 15.5

{eq}\begin{align*} &{C_{pk}}\; = \;\left( {\dfrac{{UCL - {\rm{mean}}}}{{3 \times {\rm{SD}}}}} \right),\left( {\dfrac{{{\rm{mean}} - {\rm{LCL}}}}{{3 \times {\rm{SD}}}}} \right)\\ \\ &= \;\left( {\frac{{16.5 - 16}}{{3 \times 1}}} \right),\left( {\frac{{16 - 15.5}}{{3 \times 1}}} \right)\\ \\ &= \;0.16,0.16 \end{align*} {/eq}

The capability index is 0.16

#### Learn more about this topic:

from Business 112: Operations Management

Chapter 4 / Lesson 5