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QUALITY CONTROLChapter 10

MIS 373: Basic Operations Management

Additional content from Jeff Heyl

MIS 373: Basic Operations Management 2

LEARNING OBJECTIVES

• After this lecture, students will be able to 1. Explain the need for quality control.2. List and briefly explain the elements of the control process.3. Explain Type I and Type II errors4. Explain how control charts are used to monitor a process and the

concepts that underlie their use.

BACKGROUND KNOWLEDGE• How many of you have had at least one statistics course?

• Normal distribution?

• Standard deviation?

• Z score?

MOTIVATIONS• Making Beer Better With Quality and Statistics

• http://videos.asq.org/making-beer-better-with-quality-and-statistics

• Quality for Life: Psychic Pizza • http://videos.asq.org/quality-for-life-psychic-pizza

MIS 373: Basic Operations Management 5

WHAT IS QUALITY CONTROL?

• Quality Control• A process that evaluates output relative to a standard and takes

corrective action when output doesn’t meet standards• If results are acceptable no further action is required• Unacceptable results call for correction action

• Phases of Quality Assurance

MIS 373: Basic Operations Management 6

INSPECTION

• Inspection• An appraisal activity that compares goods or services to a standard• Inspection issues:

1. What to inspect• Count number of times defect occurs• Measure the value of a characteristic

2. How much to inspect and how often3. At what points in the process to inspect

• Raw materials and purchased parts• Finished products• Before a costly operation• Before an irreversible process

• Costly, possibly destructive, and disruptive – non value-adding• Full inspection vs. Sampling

MIS 373: Basic Operations Management 7

HOW MUCH TO INSPECT

MIS 373: Basic Operations Management 8

HOW MUCH TO INSPECT1 defect in 1 thousand

unites

1 defect in 1 million unites

1 defect in 1 billion unites

Trying to catch:

MIS 373: Basic Operations Management 9

CENTRALIZED VS. ON-SITE INSPECTION

• Effects on cost and level of disruption are a major issue in selecting centralized vs. on-site inspection

• Centralized• Specialized tests that may best be completed in a lab

• More specialized testing equipment• More favorable testing environment

• On-Site• Quicker decisions are rendered• Avoid introduction of extraneous factors• Quality at the source

MIS 373: Basic Operations Management 10

STATISTICAL PROCESS CONTROL (SPC)

• Quality control seeks• Quality of Conformance

• A product or service conforms to specifications

• A tool used to help in this process:• SPC

• Statistical evaluation of the output of a process• Helps us to decide if a process is “in control” or if corrective action

is needed

• “In control” means that the variation in the provided products/services is tolerable

MIS 373: Basic Operations Management 11

PROCESS VARIABILITY

• Two basic questions: concerning variability:1. Issue of Process Control

• Are the variations random? If nonrandom variation is present, the process is said to be unstable.

Variations randomly distributed within control limits

2. Issue of Process Capability• Given a stable process, is the inherent variability of the process

within a range that conforms to performance criteria? The control limits satisfy the design specification

MIS 373: Basic Operations Management 12

VARIATION

• Variation• Random (common cause) variation:

• Natural variation in the output of a process, created by countless minor factors

• Assignable (special cause) variation: • A variation whose cause can be identified. • A nonrandom variation

• Illustration: M&M’s• Size• Color

MIS 373: Basic Operations Management 13

VARIATION• Common cause

• Inappropriate procedures• Poor design• Poor maintenance of machines• Lack of clearly defined

standard operating procedures• Poor working conditions, e.g.

lighting, noise, dirt, temperature, ventilation

• Substandard raw materials• Measurement error• Quality control error• Vibration in industrial processes• Ambient temperature and

humidity• Normal wear and tear• Variability in settings

• Special cause• Poor adjustment of equipment• Operator falls asleep• Faulty controllers• Machine malfunction• Fall of ground• Computer crash• Poor batch of raw material• Power surges• High healthcare demand from elderly

people• Broken part• Abnormal traffic (click fraud) on web

ads• Extremely long lab testing turnover

time due to switching to a new computer system

• Operator absent

MIS 373: Basic Operations Management 14

SAMPLING AND SAMPLE DISTRIBUTION

• SPC involves periodically taking samples of process output and computing sample statistics:

• Sample means• The number of occurrences of some outcome

• Sample statistics are used to judge the randomness of process variation

MIS 373: Basic Operations Management 15

SAMPLING AND SAMPLE DISTRIBUTION

• Sampling Distribution• A theoretical distribution that describes the random

variability of sample statistics• The normal distribution is commonly used for this purpose

• Central Limit Theorem• The distribution of sample averages tends to be normal

regardless of the shape of the underlying process distribution

DEMO

• Use simulation to test the Central Limit Theorem

MIS 373: Basic Operations Management 17

THE NORMAL DISTRIBUTION

MIS 373: Basic Operations Management 18

CONTROL PROCESS

• Sampling and corrective action are only a part of the control process

• Steps required for effective control:• Define: What is to be controlled?• Measure: How will measurement be accomplished?• Compare: There must be a standard of comparison• Evaluate: Establish a definition of out of control• Correct: Uncover the cause of nonrandom variability and fix it• Monitor results: Verify that the problem has been eliminated

MIS 373: Basic Operations Management 19

CONTROL CHARTS: THE VOICE OF THE PROCESS

• Control Chart• A time ordered plot of representative sample statistics obtained from

an ongoing process (e.g. sample means), used to distinguish between random and nonrandom variability

• Control limits• The dividing lines between random and nonrandom deviations from the

mean of the distribution• Upper and lower control limits define the range of acceptable variation

• Upper control limit = UCL = mean + zσ• Lower control limit = LCL = mean + zσ

MIS 373: Basic Operations Management 20

UCL

LCL

Mean

CONTROL CHART EXAMPLE

• Each point on the control chart represents a sample of n observations

Sample number

| | | | | | | | | | | |1 2 3 4 5 6 7 8 9 101112

Variation due to

assignable causes

Variation due to

assignable causes

Variation due to natural

causes

Out of control

Out of control

MIS 373: Basic Operations Management 21

ERRORS

• Type I error• Narrow control limits• Concluding a process is not in

control when it actually is.• Manufacturer’s Risk

• Type II error• Wide control limits• Concluding a process is in

control when it is not.• Consumer’s Risk

Alarm No Alarm

ProcessIn-Control

ProcessOut-of-Control

Type I

Type II

no-error

no-error

ERRORS ILLUSTRATION• Q: I always get confused about Type I and II errors. Can you

show me something to help me remember the difference?

Source: Effect Size FAQs by Paul Ellis

MIS 373: Basic Operations Management 23

CONTROL CHARTS

• Every process displays variation in performance: normal or abnormal• Control charts monitor process to identify abnormal variation • Do not tamper with a process that is “in control” with normal variation • Correct an “out of control” process with abnormal variation• Control charts may cause false alarms – too narrow - (or missed signals –

too wide) by mistaking normal (abnormal) variation for abnormal (normal) variation

Out of Control In ControlImproved

LCL

UCL

MIS 373: Basic Operations Management 24

CONTROL CHARTS

• Data that are measured• “x-bar” charts (Mean)

• Used to monitor the central tendency of a process.

• R charts (Range)• Used to monitor the process dispersion

MIS 373: Basic Operations Management 25

X-BAR (SAMPLE AVERAGE) CHART CONTROL LIMITS

)k = number of samples

n = sample size

commonly: z = 3

MIS 373: Basic Operations Management 26

X-BAR CHART

• Mean = 5.5.• STD = 0.4 ft • 99.74% within ± 3 STD• (random) 9 students {6.5, 6.4, 6.6, 6.3, 6.7, 6.5, 6.6, 6.4, 6.5} each

within “normal” average = 6.5 ft• Sample control limits tighter than population• UCL= = =5.9 ft.• GROUP above “normal” (outside control limits)

5.5 6.74.3 5.1 5.95.5

6.5

MIS 373: Basic Operations Management 27

R-CHART: CONTROL LIMITS

• Range charts or R-charts are used to monitor process dispersion

nDnD

RDLCL

RDUCL

R

R

size, sampleon basedfactor chart control a size, sampleon basedfactor chart control a

where

Limits ControlChart R

4

3

3

4

MIS 373: Basic Operations Management 28

MEAN AND RANGE CHARTS

(a)These sampling distributions result in the charts below

(Sampling mean is shifting upward but range is consistent)

R-chart(R-chart does not detect change in mean)

UCL

LCL

x-chart(x-chart detects shift in central tendency)

UCL

LCL

MIS 373: Basic Operations Management 29

MEAN AND RANGE CHARTS

R-chart(R-chart detects increase in dispersion)

UCL

LCL

(b)These sampling distributions result in the charts below

(Sampling mean is constant but dispersion is increasing)

x-chart(x-chart does not detect the increase in dispersion)

UCL

LCL

MIS 373: Basic Operations Management 30

RUN TESTS

• Even if a process appears to be in control, the data may still not reflect a random process

• Analysts often supplement control charts with a run test

• Run test• A test for patterns in a sequence

• Run• Sequence of observations with a certain characteristic

MIS 373: Basic Operations Management 31

RUN TESTS

A: AboveB: Below

U: UpwardD: Downward

MIS 373: Basic Operations Management 32

PATTERNS IN CONTROL CHARTS

UCL

Target

LCL

Erratic behavior.

UCL

Target

LCLRun of 5 above (or below) central line.

UCL

Target

LCLTwo plots very near lower (or upper) control.

Normal behavior. Process is “in control.”

UCL

Target

LCL

UCL

Target

LCLOne plot out above (or below). Process is “out of control.”

UCL

Target

LCLTrends in either direction, 5 plots. Progressive change.

DEMO• ASQ Control chart template

• http://asq.org/learn-about-quality/data-collection-analysis-tools/overview/asq-control-chart.xls

MIS 373: Basic Operations Management 34

KEY POINTS

• All processes exhibit random variation. Quality control's purpose is to identify a process that also exhibits nonrandom (correctable) variation on the basis of sample statistics (e.g., sample means) obtained from the process.

• Control charts and run tests can be used to detect nonrandom variation in sample statistics. It is also advisable to plot the data to visually check for patterns.