Question

# Question: The time to make beds at a motel should fall into an agreed-on range of...

Question:

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)
Ann 120 90 150
Linda 130 110 140
Marie 200 180 175
Michael 165 155 140

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?

Given

Sample size =4

 Maid Sample1(Sec) Sample2(sec) Sample3(Sec) Mean=sum of 3 samples/3 Range=(Max-Min) Ann 120 90 150 120.00 60 Linda 130 110 140 126.67 30 Marie 200 180 175 185.00 25 Michael 165 155 140 153.33 25 585.00 140.00 Xbar = Sum of means/4= 146.25 Rbar= Sum of Ranges/4 = 35

Xbar = 146.25

Rbar=35

A2 = 0.729 , D3 =0 ,D4=2.282 ( For sample size 4)

(a)

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

(b)

Observations are 180,198,193, 218.

All the readings are above the upper control limit , hence corrective action is needed.

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