Canine Gourmet Super Breath dog treats are sold in boxes labeled with a net weig
ID: 364050 • Letter: C
Question
Canine Gourmet Super Breath dog treats are sold in boxes labeled with a net weight of 12 ounces (340 grams) per box. Each box contains 8 individual 1.5-ounce packets. To reduce the chances of shorting the customer, product design specifications call for the packet-filling process average to be set at 43.5 grams so that the average net weight per box of 8 packets will be 348 grams. Tolerances are set for the box to weigh 348+/- 14 grams. The standard deviation for the packet-filling process is 1.03 grams. The target process capability ratio is 1.33. One day, the packet-filling process average weight drifts down to 43.0 grams. Is the packaging process capable? Is an adjustment needed?
Since the process capability index Cpk is___ The process ( is capable or is not capable). (Enter
your response rounded to three decimal places.)
Explanation / Answer
Given:
Standard deviation of Packet filling process = 1.03 grams
Hence standard deviation of 8 packets in each box , Sd
= Standard deviation of packet filling process x Square root ( Number of packets in each box)
= 1.03 x Square root ( 8)
= 2.913
Given Upper Specification Limit of each box containing 8 packets = USL = 362 grams
Lower Specification limit of each box containing 8 packets = LSL = 334 grams
Therefore process capability ratio, Cp
= ( USL – LSL) / 6 X Sd
= ( 362 – 334 ) / 6 x 2.913
= 1.602
Above is > 1.33 and satisfies the condition of target process capability ratio of 1.33. Higher the Cp is , better it is .
When the packet filling process average weight = 43 grams
Average weight of the packet of 8 = m = 43 x 8 = 344 grams
Thus, Process Capability Index, Cpk
= Minimum ( (USL – m)/ 3 x Sd , ( LSL – m)/3 x Sd )
= Minimum ( ( 362 – 344)/( 3 x 2.913) , ( 344 – 334)/ ( 3 x 2.913) )
= Minimum ( 2.059 , 1.144)
= 1.144
A process is considered capable when Cpk > 1 . Since derived value of Cpk > 1.144 , the process is capable.
SINCE THE PROCESS CAPABILITY INDEX Cpk IS 1.144, THE PROCESS IS CAPABLE
SINCE THE PROCESS CAPABILITY INDEX Cpk IS 1.144, THE PROCESS IS CAPABLE