The time to make beds at a motel should fall into an agreed-on range of times. A sample of four maids was selected, and the time needed to make a bed was observed on three different occasions:
|Maid||Sample 1 (sec)||Sample 2 (sec)||Sample 3 (sec)|
a. Determine the upper and lower control limits for an X-bar chart and R-chart with a sample size of four.
b. After the control chart was established a sample of four observations has the following times in seconds: 180, 198, 193, and 218. Is corrective action needed?
Sample size =4
|Maid||Sample1(Sec)||Sample2(sec)||Sample3(Sec)||Mean=sum of 3 samples/3||Range=(Max-Min)|
|Xbar = Sum of means/4=||146.25|
|Rbar= Sum of Ranges/4 =||35|
Xbar = 146.25
A2 = 0.729 , D3 =0 ,D4=2.282 ( For sample size 4)
For X-bar chart
UCL = Xbar + A2* Rbar = 146.25+0.729*35 =146.25 + 25.51 =171.76
LCL = Xbar - A2* Rbar = 146.25 - 0.729*35 =146.25 - 25.51 =120.74
For R-bar chart
UCL=D4*Rbar =2.282*35 =79.87
LCL =D3*Rbar = 0*35 =0
Observations are 180,198,193, 218.
All the readings are above the upper control limit , hence corrective action is needed.
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