Question

Elm Street Medical Hospital has the largest emergency room in the city. Because approximately 85% of the emergency room visits in the city are handled by Elm Street Medical Hospital, the emergency room is often crowded and the staff work longer hours than advised. The hospital administrators and city officials are concerned about patient care and want to assess the level of service the emergency room is capable of providing its patients. Wait time, the time between when a patient checks in and when the patient is first seen by a medical staff member, is one of the key performance indicators the hospital uses to gauge the quality of its services. Elm Street Medical Hospital administrators would like to use statistical process control to monitor patient wait times. The table below contains patient wait time data randomly collected over the course of several days. Sample 4 1 27 2 18 Wait Times (minutes) 3 20 31 23 40 5 19 17 23 2 22 25 22 19 20 12 20 16 45 22 24 22 5 6 - 16 35 21 17 25 15 31 28 15 27 33 15 21 38 26 23 26 30 119 33 T 25 31 8 9 10 23 24 29 35 20 20 32 127 a) Construct both and x-bar and R chart, indicate whether the process appears to be in control, and what criteria you used to make that determination. Round control limits to 3 decimal places. (You may use Excel to create the control charts, however, you must show your work for the control limit calculations and copy and past the control charts into your test document. Make sure the components of your charts are clearly labeled. DO NOT submit the Excel file to demonstrate your work.) b) If Elm Street Medical Hospital is required to have emergency room wait times of 25 minutes = 5 minutes, use the process information from part (a) to compute the process capability measures that can be used to assess whether the process is capable of meeting these requirements. Round each measure to 3 decimal places. State whether each measure indicates the process is capable and why. If the process is not capable, identify on what end of the requirement the wait times are likely to not to comply.

Answer 1

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a)

Sample	x1	x2	x3	x4	x5	X-bar	Range
1	27	18	20	23	19	21.4	9.0
2	22	25	31	40	17	27.0	23.0
3	16	15	22	19	23	19.0	8.0
4	35	27	16	20	24	24.4	19.0
5	21	33	45	12	22	26.6	33.0
6	17	15	22	20	30	20.8	15.0
7	25	21	26	33	19	24.8	14.0
8	15	38	23	25	31	26.4	23.0
9	31	26	24	35	32	29.6	11.0
10	28	23	29	20	27	25.4	9.0
					Avg.	24.54	16.40
						X_double-bar	R-bar
A2	0.577
D3	0
D4	2.114
UCLx	34.003
LCLx	15.077
UCLr	34.670
LCLr	0

The process seems to be in control in that none of the estimates of mean or ranges overshoot the limits.

(b)

R-bar = 16.40

Constant d₂ for n=5 is 2.326

Estimated process standard deviation, σ = R-bar / d₂ = 16.40 / 2.326 = 7.05

The process mean is estimated by the X_double bar, so, μ = 24.54

USL = 25+5 = 30 minutes
LSL = 25 - 5 = 20 minutes

Since the process mean is shifted towards the LSL,

C_pk = (μ - LSL) / 3.σ = (24.54 - 20)/(3*7.05) = 0.215

C_p = (USL - LSL) / 6σ = (30 - 20)/(6*7.05) = 0.236

So, the process in incapacble of producing even 3-sigma quality in that both the parameters are less than 1.0.

To, improve, the major step should be to reduce the variability i.e. the standard deviation.