therinzler1825
15.02.2021 •
Mathematics
Components used in a cellular telephone are manufactured with nominal dimension of .3 mm and lower and upper specification limits of .295 mm and .305 mm respectively. the x bar and R control charts for this process are based on subgroups of size 3 and they exhibit statistical control, with the center line on the x bar chart at .3015 mm and the center line of the R chart at .00154 mm.
a) Estimate the mean and standard deviation of this process.
b) Suppose that parts below the LSL can be reworked, but parts above the USL must be scrapped. Estimate the proportion of scrap and rework produced by this process.
c) Suppose that the mean of this process can be reset by fairly simple adjustments. What value of the process mean would you recommend? Estimate the proportion of scrap and rework produced by the process at this new mean.
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Ответ:
Kindly check explanation
Step-by-step explanation:
Xbar = 0.3015 ; Rbar = 0.00154
USL = 0.295 ; LSL = 0.305
For a subgroup size of 3 ; k = 3 ; d2 = 1.693
The mean = xbar = 0.3015 mm
The standard deviation = Rbar / d2 = 0.00154 / 1.693 = 0.0009096
b) Suppose that parts below the LSL can be reworked, but parts above the USL must be scrapped. Estimate the proportion of scrap and rework produced by this process.
P(X < 0.295)
(x - mean) / standard deviation
(0.295 - 0.3015) / 0.0009096 = 0.00003
0.00003 should be reworked.
P(X > 0.305)
1 - P(X < 0.305)
(x - mean) / standard deviation
(0.305 - 0.3015) / 0.0009096 = 3.847
1 - P(Z < 3.847)
1 - 0.99994
= 0.00006
0.00006 should be reworked.
c) Suppose that the mean of this process can be reset by fairly simple adjustments. What value of the process mean would you recommend? Estimate the proportion of scrap and rework produced by the process at this new mean.
Recommended mean = 0.3000 mm
P(X < 0.295)
(x - mean) / standard deviation
(0.295 - 0.3000) / 0.0009096 = 0.00003
0.00003 should be reworked.
P(X > 0.305)
1 - P(X < 0.305)
(x - mean) / standard deviation
(0.305 - 0.3000) / 0.0009096 = 5.497
1 - P(Z < 5.497)
1 - 0.99997
= 0.00003
0.00003 should be reworked.
Ответ:
Step 2 is wrong because they combined like terms incorrectly. The equation should be: 18 = x + 72. Then, in Step 3, you would get x = -54.
Step-by-step explanation:
The given equation is a multi-step equation involving the distributive property. You would first complete the distributive property by multiplying each term inside the parenthesis by the outside term. Step 1 of the problem completes this step correctly. The next step in the problem would be to use inverse operations to combine like terms and isolate the variable - whatever you do to one side of the equation, you must do to the other. In this case, we need to subtract 4x from both sides, not add, to get: 4x - 4x + 18 = 5x - 4x + 72. This gives us 18 = x + 72. To solve for x, we need to subtract both sides by 72: 18 - 72 = x + 72 - 72, or x = -54.