Specifications for scoops of ice cream al a local ice cream parlor are that sing

Question

Specifications for scoops of ice cream al a local ice cream parlor are that single scoops should weigh between 3.75 and 4.25 ounces. Servers generally scoop ice cream with a mean of 4 ounces and a standard deviation of 0.1 ounces. The distribution of the scoops is Normal. What percentage of scoops will not meet the weight specs What is the process capability index CP Is this value good or bad Why What is the adjusted process capability index Cp? Is this value good or bad Why Is CP or Cpk more appropriate in this context Why

Explanation / Answer

a. The percentage of scoops that will not meet weight specs is 0.1/4 = 2.5 %

b. Process Capability (Cp): Process capability is a technique to find out the measurable property of a process to a specification. Generally, the final solution of the process capability is specified either in the form of calculations or histograms

Cp = (USL-LSL) / 6 Std. Dev.

As per question, Cp= (4.25 - 3.75) / 6 * 0.1 = 0.8333

As it falls between the specified limits so a capable process of scooping the ice-cream, so it is good.

c. Process Capability Index (Cpk) : Process capability index (cpk) is the measure of process capability. It shows how closely a process is able to produce the output to its overall specifications.

Cpk = min [ (USL - Mean) / 3* Std. Dev , (Mean - LSL) / 3* Std. Dev ]

As per question, Cpk= min[ (4.25 - 4) / 3 * 0.1 , ( 4 - 3.75) / 3 * 0.1 ]

= min (0.8333 , 0.8333)

Cpk = 0.8333

As it falls between the specification limits so a capable process of scooping the ice-cream, so it is also good.

d. Out of Cp and Cpk , we can say Cpk is more appropriate as it covers both upper and lower limits. A process where almost all the measurements fall inside the specification limits is a capable process.

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