A process that is considered to be in control measures an ingredient in ounces.
ID: 361350 • Letter: A
Question
A process that is considered to be in control measures an ingredient in ounces. Below are the last 10 samples (each of size n = 5) taken. The population process standard deviation is 1.64
Samples Item 1 Item 2 Item 3 Item 4 Item 5
1 11 10 9 9 11
2 11 9 11 11 10
3 12 8 10 11 10
4 11 10 11 11 10
5 12 11 9 11 9
6 11 9 7 13 8
7 11 10 9 8 10
8 14 10 9 10 7
9 7 8 11 11 10
10 11 12 10 7 13
Standard deviation of the sampling means =?
Based on the 10 samples taken, x double overbar = ? ounces
With z=3, the control limits for the mean chart are:
UCL Subscript x overbar
UCLx =
LCL Subscript x overbar
LCLx =
Based on the 10 samples taken, average range Upper R overbar R =
For the given sample size, Upper Range (Upper D4) =
For the given sample size, Lower Range (Upper D3) =
The control limits for the range chart are:
UCL Subscript Upper R
UCLR =
LCL Subscript Upper R
LCLR =
Explanation / Answer
Given , sample size = n = 5
Following are the relevant values of constants for n = 5 as derived from standard table for Xbar and R chart :
D4 = 2.114
D3 = 0
Now,
Xbar-bar = Mean of sample means = 100.80/10 = 10.08
Rbar = Mean of range values = 38/10 = 3.8
Sample size = n = 5
Control limits for Xbar chart with Z = 3 :
Upper Control Limit = UCLx = Xbar-bar + 3 x ( Sample Standard deviation/ Square root ( n))
Lower Control Limit = LCLx = Xbar-bar – 3 x ( Sample Standard deviation / Square root ( n))
Therefore ,
UCLx = 10.08 + 3 x 0.4341/ Square root ( 5 ) = 10.08 + 3 x0.4341/2.236 = 10.08 + 0.5824= 10.6624
UCLx = 10.08 - 3 x 0.4341/ Square root ( 5 ) = 10.08 - 3 x0.4341/2.236 = 10.08 - 0.5824= 9.4976
Control Limits for R chart :
Upper Control Limit = UCLr = D4. Rbar = 2.114 x 3.8 = 8.033
Lower Control Limit = 0 ( since D3 = 0)
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