# 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.

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