Question

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?

Answer 1

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.