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Session 13

Vinay Kumar Kalakbandi

Assistant Professor

Operations & Systems Area

2/27/2016 Vinay Kalakbandi 1

Operations Management - II Post Graduate Program 2015-17

Agenda

• Recap

• Statistical Quality Control

– Control charts

– Process capability

– Six sigma


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Key terms

• Quality metric

• User specifications

• Process parameters


Starbucks

• Coffee is best served at 140+/-15 degrees

• What is the metric of quality?


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PVC pipes

• PVC pipes come in different

diameters

• What is the metric of

quality?


Printed Circuit boards

• Three main causes of defects

in PCBs are

– Opens, Solder bridges,

Component shift

• Can happen anywhere on the

board!

• Will need rework!


quality?


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30 minute pizza delivery!


quality?


Metric of quality

• The nature of the quality dimension with the

context

– Continuous data: PVC, Starbucks

– Count data: PCB

– Proportion data: Dominos


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Quality metric examples

Sl. No. Type of Applications Quality metric

1 Component Manufacturing Conformance of physical measurements of components

and sub-assemblies to specifications

Conformance to operating characteristics of machines and

other resources involved in the process

2 Final Assembly Number of defects in the product

Conformance to test specifications

Number of missing elements

3 Process Industries Temperature, Pressure and Heat specifications

Conformance to product specifications

Conformance to equipment specifications

Vibrations and other variations in equipments and sub-

systems

Conformance to specifications of the automation &

control system

4 Service Systems Number of defects in various business processes

Errors in processing documents

Conformance to waiting time/lead time related

specifications

User specifications

• Starbucks

• Pizza delivery:

• PVC pipes:

• PCB manufacturing

• 140+/- 15

• 30 minutes or free

• +/-0.01mm

• upto 3 defects


Determined by industry standards

Determined by the consumer

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Process parameters

• The process parameters impact the quality metric

• The quality metric varies due to

– Natural causes: Non-controllable; inherent variability in the system, noise, usually minor

– Assignable causes: Controllable, bring about a fundamental change on the nature of the process, causes considerable impact on quality

• The aggregate impact of process parameters is captured by the mean and the standard deviation of the quality metric


What are the process parameters?

• Starbucks

• PCBs

• PVC pipes

• Pizza delivery


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Key terms

• Quality metric

• User specifications

• Process parameters

• Which comes first?

• How are they related?


Funnel and Pencil Systems

Always on the dot!


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Our orders

• Raw material: paper with circle

• Customer 1

– Produce 10 dots per paper within the circle

• Will reject if any dots are outside circle

• Customer 2

– Produce dots 3 cm away from the centre of circle

• We have a tolerance of +/- 3 mm

• Customer 3

– Produce 10 dots per paper

• We will tolerate at most 3 dots inside circle.


Objective of Process control

• To constantly monitor the quality metric


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Run charts

• Run charts plot the quality metric over time.

• Monitor every occurrence of the quality metric

• Downsides of run charts

– Might be difficult to monitor every item coming out of the line

– Not sure if variation is due to change in process parameters

– Not clear when to adjust input parameters

• We might be overreacting to random variation




• Ensure that the quality metric has no

assignable cause of variation


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Process control charts

• Information: Monitor process variability over

time

• Control limits: Average + z * standard deviation

– Usually z = 3. Why?

• Decision Rule: Ignore variation outside

“abnormal”

• Are control limits related to user specifications?


Types of Data

• Depending on quality metric

• Continuous data

– X-bar and R charts

• Count data

– c-charts

• Proportion data

– P-charts


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Constructing a control chart

• Determine the quality metric

– Choose appropriate measurement method

• Collect sample data using a sampling procedure

• Choose appropriate control chart

– Calculate and plot control limits on the control chart

• Control limits are + or – 3*sigma

• Determine if data is in control

• If non-random variation is present, fix the problem and recalculate control limits.


Standard deviation?


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Coefficients for computing LCL and

UCL in X-bar and R charts*

Sample size (n) A2 D3 D4

2 1.880 0 3.268

3 1.023 0 2.574

4 0.729 0 2.282

5 0.577 0 2.114

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

Source: Juran, J.M. and F.M. Gryna, (1995), “Quality Planning and Analysis”, Tata McGraw-Hill, 3rd Edition, New Delhi, pp 385.


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Utility of X-bar and R chart


Utility of X-bar and R chart


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Other charts

• P-charts

– Calculate percentage defectives in a sample

– an item is either good or bad

– Based on binomial distribution


Other charts

• c Charts

– Count number of defects in an item

– Based on poisson distribution


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• Detect and remove assignable cause of

variation


Output


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Performance variation patterns



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• Detect and remove assignable cause of

variation

• Adjust process parameters such that the

quality metric falls within user specifications


From Control to improvement


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Process capability


Process Capability

• Process Capability is defined by the spread of the process

• Potential capability (Cp) is defined as the ratio of the difference in specification limits to the process spread

Cp =

• Actual capability (Cpk) takes into consideration the extent to which the process has deviated from the desired target

Cpk =

6

)(

Pr

LSLUSL

Capabilityocess

RangeionSpecificat

3

Pr,

3

Pr CentreocessUSLLSLCentreocessMin

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Impact of 99% defectives!


99.9% is already VERY GOOD

But what could happen at a quality level of 99.9% (i.e., 1000 ppm),

in our everyday lives (about 4.6)?

• More than 3000 newborns accidentally falling

from the hands of nurses or doctors each year

• 4000 wrong medical prescriptions each year

• 400 letters per hour which never arrive at their destination

• Two long or short landings at American airports each day

How good is good enough?

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Process Capability & Defects

Process Capability Index (Cpk)

Total Products outside two-sided specification limits

0.25 453,255 ppm

0.50 133,614 ppm

0.60 71,861 ppm

0.80 16,395 ppm

1.00 2,700 ppm

1.20 318 ppm

1.50 7 ppm

1.70 0.34 ppm

2.00 0.0018 ppm

Source: Quality Planning & Analysis, Juran & Gryna, Chapter 17, 3e

Sigma statistics


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Six sigma quality

612)(26

)(

ofspreadALSLUSL

LSLUSLCp

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