The following question refers to an injection molding process to make refrigerat
ID: 2926958 • Letter: T
Question
The following question refers to an injection molding process to make refrigerator door handles. The door handle mold has four cavities (forms four handles at a time). A Six Sigma team is investigating premature door handle failures in the field, and suspects variation in thickness a a potential root cause. A snapshot of data from successive cycles is presented below, representing each of the four cavities over time, measured in millimeters (assume this data is representative of a larger sample).
Cycle------Cavity 1------Cavity 2-----Cavity 3-----Cavity 4
1 --------------3.6------------- 3.4----------- 3.7----------- 3.5
2 --------------3.9------------- 4.0----------- 3.7----------- 3.6
3-------------- 4.1------------- 4.4------------4.5----------- 4.3
4-------------- 3.8------------- 3.9----------- 3.6----------- 3.5
Question options:
a)
Subgroup by two cavities with output from multiple cycles.
b)
Subgroup by cavity - include output from multiple cycles.
c)
A. Subgroup by cycle - include output from each cavity.
d)
Subgroup at random from combined output.
e)
Subgroup by cycle and cavity - include all output from several cycles.
a)
Subgroup by two cavities with output from multiple cycles.
b)
Subgroup by cavity - include output from multiple cycles.
c)
A. Subgroup by cycle - include output from each cavity.
d)
Subgroup at random from combined output.
e)
Subgroup by cycle and cavity - include all output from several cycles.
Explanation / Answer
The toal snapshot data consists of 4 cycles data for 4 cavities. The study is regarding Quality Control of thikness of mold of refrigerator handles.
a. We are to include multiple cycles and take 2 cavities. Then 2 cavities are selected at random using a random number table. Consult a 2 digit random number table and choose the cavity according to the below rule:
If random number belong to (00,24) the Cavity1,If random number belong to (25,49) the Cavity2,If random number belong to (50,74) the Cavity3,If random number belong to (75,99) the Cavity4. In this way each cavity gets equal probability. The random numbers from random number table drawn is 78 and 39. So we select Cavity 2 and Cavity 4 and all observations on the cycles.
b. We now choose one cavity and observations from multiple cycles. We draw a random number again and now we obtain 53. So Cavity 3 is chosen and all observations from 4 cycles.
c. Reversing the objective, now we choose 1 cycle with observations from multiple cavities. We draw a random number again and obtain 22. So we choose cycle 1 and all observations from 4 cavities in it in the subgroup.
d. We are to subgroup at random. There are 2 ways to subgroup - by cycle and by cavity. Lets draw a subgroup of size 4. There are 16 observations. We draw random numbers between 01 to 96 and divide just like in (a) the observations in group of 6. i.e. if random number is between 01 to 06 then we select the observation of first cycle first cavity, if random number is between 07 to 12 then we select the observation of the second cycle and first cavity. Now the 4 random numbers drawn are 18,91,33,57. So we select the observations : 4.1, 3.5,4.0 and 3.7.
(Have answered the first 4 parts)
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