Canine Gourmet Super Breath dog treats are sold in boxes labeled with a net weig

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

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.