statistical process control

statistical process control

1.

a) There are two types of variation in a process – common causes of variation and special causes of variation. Discuss what are they and what effect do they have on a process. Illustrate the answer with examples from your own experience.

(10 marks)

b) Control charts can be used to monitor both attribute and variable data. Explain the differences between variable data and attribute data. Support your answer with examples from your own experience.
(10 marks)
2.
A call centre receives hundreds of customer calls every day. The manager of the call centre intends to measure the quality performance of its service by counting the rate of incoming telephone calls that are not picked up by operators after 4 rings. 25 samples of 400 calls are taken and the number of telephone calls not responded after 4 rings are recorded below.

Sub-group 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
n 400 400 400 400 400 400 400 400 400 400 400 400 400 400 400
np 8 24 16 20 18 22 28 28 16 20 22 14 24 26 22

Sub-group 16 17 18 19 20 21 22 23 24 25
n 400 400 400 400 400 400 400 400 400 400
np 34 26 18 26 28 28 24 42 26 24

n: no. of calls sampled
np: calls not responded after 4 rings

a) Calculate the control limits (UCLnp and LCLnp) and average number of call not responded of the np-chart when 25 samples of 400 calls were inspection. Construct the np-chart, showing the control limits and average number of call not responded.

(15 marks)

b) Does the process appear to be in control? What can the operations manager do to improve the situation?

(5 marks)

 

3.
You are requested by customer to demonstrate your production plant’s ability by providing statistical process control charts from a pre-production trial. The following measurements are readings of cylinder diameter manufactured by your plant. The specification is 250 mm ± 5 mm. Five pieces in a row were measured every 30 minutes.

Below are 10 samples taken at 30-minute intervals. Each sample contains five observations.

Sample Number
1 2 3 4 5 6 7 8 9 10
1 243 252 250 252 248 255 243 244 255 251
2 252 249 250 250 252 248 251 251 258 252
3 255 252 249 253 251 253 253 253 268 255
4 250 249 250 258 243 256 250 253 256 253
5 253 250 253 250 250 251 249 254 255 243
a) Construct the mean ( ) and range (R) charts and comment on the state of control of the process.

UCL = + A2 UCL R = D4
LCL = – A2 LCL R = D3

When sample size (n) 2 3 4 5
A2 1.880 1.023 0.729 0.577
D2 1.128 1.693 2.059 2.326
D3 0 0 0 0
D4 3.268 2.574 2.282 2.114

(15 marks)
b) Calculate and comment on the process capability indices Cp and Cpk. What actions do you think you need to take before full production starts?
(10 marks)
4.

a) Describe how JIT/Lean reduces each of the seven wastes for a manufacturing organization.
(15 marks)
b) Explain the role of Total Productive Maintenance (TPM) in JIT/Lean manufacturing.
(5 marks)
c) Identify and discuss the six big losses that TPM aims to eliminate.
(5 marks)
d) A production plant has recorded the following performance rates for the first 3 weeks. The plant operates 40 hours a week and the cycle time for each product is 3 minutes.

Using the worksheet supplied, calculate:

(i) the average Overall Equipment Efficiency (OEE) for the production plant for the three-week period; and
(ii) the expected increase in sales revenue during these three weeks if the principles of “Best of the Best” is achieved.

Assume the sales value of a finished product to be $100 per unit.

Week No. Downtime (minutes) Output (units) Scrap (units)
1 300 550 20
2 200 600 50
3 250 680 60

(10 marks)

Question 4: TPM Worksheet

 

WEEK AVAILABILITY PERFORMANCE QUALITY OEE GOOD UNITS Revenue /week

 

 

 

Average
Best of Best

Gain

 

Total expected increase in sales revenue in the three-week period =
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