Statistical Process Control (13+15 = 28 Questions) - ENGG381-14A Engineering Statistics (Task A, B, C) - 15 Questions done twice

Management 2070Y - Fall 2013 - Assignment #1 Page 2 of 5

1. “Leave Without Treatment” Analysis (10 marks) Periodically, an individual will check-in at a walk-in-clinic, but leave without ever

receiving treatment. Employees notice this when they call the individual’s name, but the

individual is no longer in the waiting area. It is thought that some of this behaviour can

be explained by the individual “feeling better” and deciding to leave, though

management fears that individuals are leaving because they have waited too long. These

cases are of concern because the individual did not receive treatment which may lead to

more extensive health problems, but also because the individual may “bounce around”

to various walk-in-clinics creating increased demands on health care staff.

In an effort to reduce the frequency of individuals “leaving without treatment”, the local

health region has sampled data from the registration system at their walk-in clinics.

They selected data from 150 registrations each day for 15 days that they defined as

“normal operations” and thus they would like quality control chart(s) to be prepared

with control limits based on that data. Furthermore, management would like to see

recent sample data (150 registrations per day for the last 15 days) plotted against these

control limits. If an out-of-control condition is found, registration data can be used to

contact the individuals to research the specific cause of why they left without receiving

treatment.

Calculate the relevant control limits and prepare relevant ±3σ quality control chart(s).

Provide an analysis of the performance over the past 15 days. (Do not round standard

deviation values. Control limit values should be rounded to four decimals.)

“Normal”

Day # leaving without

treatment

“Recent” Day

# leaving without

treatment

1 6 1 6

2 8 2 9

3 5 3 6

4 7 4 11

5 8 5 15

6 6 6 5

7 7 7 8

8 8 8 8

9 7 9 6

10 5 10 5

11 8 11 8

12 5 12 9

13 8 13 8

14 6 14 10

15 7 15 9

Management 2070Y - Fall 2013 - Assignment #1 Page 3 of 5

2. Wait Time Analysis (15 marks) The primary performance measure for health care services is waiting time. For walk-in-

clinics, waiting time is the time between when an individual registers (check-in) and

when the individual is admitted for treatment.

Since “wait time” is critical for health services (customer satisfaction, government

mandates, etc.), management has tracked historical performance at their walk-in clinics

and found that the average wait time is 30 minutes and the historical range has been 15

minutes.

The local health region believes that government mandated wait times are likely to be in

place very soon and thus they want to identify and eliminate causes of inconsistent wait

times. Specifically, they would like these recent wait time samples to be analyzed:

Calculate the relevant control limits and prepare relevant ±3σ quality control chart(s).

Provide an analysis of the “time in system” performance based on the recent samples,

specifically identifying what, if any, action is recommended. (Use 4 decimals for

control limit values)

Sample

#

Observation

#1 #2 #3 #4 #5

1 32 22 33 28 18

2 42 28 34 24 25

3 27 40 28 24 26

4 24 13 19 21 20

5 29 31 24 36 25

6 26 32 43 17 38

7 31 35 25 39 27

8 31 26 25 32 27

9 29 54 26 38 37

10 38 33 42 34 40

Management 2070Y - Fall 2013 - Assignment #1 Page 4 of 5

3. Process Capability (10 marks) One of the current government’s campaign promises was to reduce wait times at health

services. Correspondingly, a committee was created and has been working on

establishing wait time targets for various health services. With walk-in clinics

impacting the greatest portion of the voters, the government has been keen to implement

wait time specifications in this area of health services first.

The local health region has received a draft of the government’s wait time specifications

that they plan to make effective on January 1 st , 2009. The specification is that 95% of

individuals must have a wait time of less than 60 minutes at a walk-in-clinic. Only

health regions that meet this specification will be eligible for a new program where

private donations are matched by the government.

In preparation for adhering to wait time specifications, the local health region has

researched various improvement alternatives (all with similar costs), including running

software simulations to obtain statistical data on how each alternative would perform

regarding wait times (see below).

Process Description Mean Wait Time Wait Time

Standard Deviation Current Continue as-is

45 15

Alternative #1 Hire additional

doctors / nurses

40 12

Alternative #2 Build additional

assessment rooms

37 15

Alternative #3 Purchase portable

diagnostic equipment

39 9

Prepare a chart that shows how effectively each process would address the government’s

new specifications (6 marks)

Note: Add columns to the above table to calculate z-values, probability, and to comment

on the capability. Show all calculations to receive full marks.

Z-Value Probability Comment

15-10 = 1.00

5

.8413 Not capable –

not even close

In addition to the calculated values, management is looking for further insights. They

would first like to know how capable their current process is of meeting the new

specification. Management would also like to know which of the alternatives you

recommend, if any, they undertake considering the government’s new specifications and

why. (4 marks)

Management 2070Y - Fall 2013 - Assignment #1 Page 5 of 5

4. Pareto Analysis (10 marks) Research into causes of excessive wait times has revealed data on the most common

causes. Prepare a Pareto Analysis graph of the following data (the Microsoft Excel

graph type of “Line – Column on 2 axes” is recommended) (6 marks)

Cause Details # of occurrences

Doctor calls in sick Fewer doctors available to

service individuals

4

Assessment rooms full Staff available, but no

assessment rooms available

39

Supplies not available Assessment room ran out of

supplies

16

Individual Missing Individuals called for

treatment but not in the

immediate vicinity

48

Registration system

issues

Software “crashes” and bugs

delay administration

12

Do you have any suggestions to help address the two most common causes? (4 marks)

5. Cost of Quality (5 marks) The local health region has been piloting a “healthphone” service, where nurses field

calls and provide a preliminary assessment for individuals with health concerns. This

form of “inspection” has proven to be valuable in reducing wait times at walk-in-clinics,

while improving customer satisfaction. Many individuals receive sufficient over the

phone guidance to deal with their health concern and thus do not go to a walk-in clinic.

Thanks to extensive use of information technology (healthphone nurses can answer calls

in their own homes while connected to the healthphone database over the internet),

operating costs for the service are considerably less than the operating costs at a walk-in

clinic.

The healthphone Operations Manager would like to expand their service by hiring more

nurses, however the health region’s finance department is adamant that the current

budget is “very tight” and that there is “no new money” for such expenditures.

Prior to approaching the accounting department for budgetary approval, healthphone’s

Operations Manager has asked you to prepare a clear and concise summary explanation

of how the “cost of quality” concept can be applied to this scenario. It is hoped that

your summary will help to get the expenditure approved even though “there is no new

money available”. Can include conceptual graph, but apply the concepts to this scenario for written points