Question

Dr. Patel is concerned about the long wait times in his office. The following table presents six random observations for the patient waiting times over a period of 10 days.

	Observations (mins)
Day	1	2	3	4	5	6
1	30	17	18	21	19	33
2	17	11	33	33	39	11
3	19	25	40	17	38	13
4	29	31	29	25	22	21
5	15	34	26	14	14	18
6	8	11	29	33	39	17
7	24	24	26	37	28	20
8	14	33	23	16	40	13
9	27	18	30	11	20	17
10	37	35	12	38	29	8

1. Dr. Patel is willing to use three-sigma limits. Use the given data and the factors from Table 3.1 (page 110) to construct R-chart and -chart.
2. Is the process in statistical control? Explain.
3. If patient surveys indicate that they are willing to wait between 10 and 30 minutes before seeing Dr. Patel, is the process capable of meeting this demand at the three-sigma level?

Table 3.1

Factors For Calculating Three Sigma Limits for the x¯x¯ -Chart and R-Chart

Size of Sample (n)	Factor for UCL and LCL for x¯¯−Chart (A2)x¯-Chart (A2)	Factor for LCL for R-Chart (D3)(D3)	Factor for UCL for R-Chart (D4)(D4)
2	1.880	0	3.267
3	1.023	0	2.575
4	0.729	0	2.282
5	0.577	0	2.115
6	0.483	0	2.004
7	0.419	0.076	1.924
8	0.373	0.136	1.864
9	0.337	0.184	1.816
10	0.308	0.223	1.777

Answer 1

A₂=0.308

D₃=0.223

D₄=1.777

Day	1	2	3	4	5	6	Total	sample Mean	Sample Range
1	30	17	18	21	19	33	138	23	16
2	17	11	33	33	39	11	144	24	28
3	19	25	40	17	38	13	152	25.33333	27
4	29	31	29	25	22	21	157	26.16667	10
5	15	34	26	14	14	18	121	20.16667	20
6	8	11	29	33	39	17	137	22.83333	31
7	24	24	26	37	28	20	159	26.5	17
8	14	33	23	16	40	13	139	23.16667	27
9	27	18	30	11	20	17	123	20.5	19
10	37	35	12	38	29	8	159	26.5	30
						Total	1429	238.1667	225
						Mean		23.81667	22.5
								23.81667	22.5
								UCL	LCL
							mean_chart	30.74667	16.88667
							R_chart	39.9825	5.0175

Control Chart for :

Control Chart for R :

b)

Sample no	sample Mean(m)	Sample Range		Is LCL<m<UCL	IS LCL<R<UCL
1	23	16		Yes	Yes
2	24	28		Yes	Yes
3	25.33333	27		Yes	Yes
4	26.16667	10		Yes	Yes
5	20.16667	20		Yes	Yes
6	22.83333	31		Yes	Yes
7	26.5	17		Yes	Yes
8	23.16667	27		Yes	Yes
9	20.5	19		Yes	Yes
10	26.5	30		Yes	Yes
1429	238.1667	225
	23.81667	22.5
	23.81667	22.5
	UCL	LCL
mean_chart	30.74667	16.88667
R_chart	39.9825	5.0175

Yes the process is in the statistical control. As all the sample means as well as sample ranges are lies in between their respective ranges i.e. LCL and UCL .

c) No This process does not support the patient willingness as UCL for mean chart is more than 30.