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QUALITY CONTROL Chapter 10 MIS 373: Basic Operations Management

Additional content from Jeff Heyl

LEARNING OBJECTIVES • After this lecture, students will be able to 1. 2. 3. 4.

Explain the need for quality control. List and briefly explain the elements of the control process. Explain Type I and Type II errors Explain how control charts are used to monitor a process and the concepts that underlie their use.

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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

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

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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 often 3. 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

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HOW MUCH TO INSPECT

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HOW MUCH TO INSPECT 1 defect in Trying to catch: 1 thousand unites

MIS 373: Basic Operations Management

1 defect in 1 million unites

1 defect in 1 billion unites

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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

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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

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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

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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

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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

MIS 373: Basic Operations Management

• 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

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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

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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

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DEMO • Use simulation to test the Central Limit Theorem

THE NORMAL DISTRIBUTION

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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

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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

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CONTROL CHART EXAMPLE Variation due to assignable causes

Out of control UCL

Variation due to natural causes

Mean LCL | | | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 12

Sample number

Out of control

Variation due to assignable causes

• Each point on the control chart represents a sample of n observations MIS 373: Basic Operations Management

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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.

Process In-Control Process Out-of-Control

Alarm

No Alarm

Type I

no-error

no-error

Type II

• Consumer’s Risk

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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

CONTROL CHARTS Out of Control

In Control

Improved

UCL  LCL • 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 MIS 373: Basic Operations Management

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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

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X-BAR (SAMPLE AVERAGE) CHART CONTROL LIMITS 𝑥 ) 𝑘

𝑥 = 𝑥𝑥 = 𝜇𝑥 (= k = number of samples 𝜎𝑥 𝜎𝑥 = 𝑛 n = sample size 𝑈𝐶𝐿𝑥 = 𝑥 + 𝑧𝜎𝑥 = 𝜇𝑥 + 𝑧 𝜎𝑛𝑥 𝐿𝐶𝐿𝑥 = 𝑥 − 𝑧𝜎𝑥 = 𝜇𝑥 + 𝑧 𝜎𝑛𝑥

commonly: z = 3 𝑈𝐶𝐿𝑥 = 𝑥 + 3𝜎𝑥 = 𝜇𝑥 + 3 𝜎𝑛𝑥 𝐿𝐶𝐿𝑥 = 𝑥 − 3𝜎𝑥 = 𝜇𝑥 + 3 𝜎𝑛𝑥 MIS 373: Basic Operations Management

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X-BAR CHART • Mean = 5.5. • STD = 0.4 ft

6.5

• 99.74% within ± 3 STD

4.3

• 𝑥 ∓ 3𝜎 = 5.5 ∓ 3 ∗ 0.4 = [4.3,6.7]

5.1

5.5

5.9

6.7

5.5

•

(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 𝜎 = 𝑛

5.5 + 3

.4 =5.9 9

•

UCL= 𝑥 + 3

•

GROUP above “normal” (outside control limits)

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ft.

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R-CHART: CONTROL LIMITS • Range charts or R-charts are used to monitor process dispersion

R Chart Control Limits UCLR  D4 R LCLR  D3 R where D3  a control chart factor based on sample size, n D4  a control chart factor based on sample size, n MIS 373: Basic Operations Management

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MEAN AND RANGE CHARTS (a) These sampling distributions result in the charts below

(Sampling mean is shifting upward but range is consistent)

UCL

x-chart LCL UCL

R-chart LCL MIS 373: Basic Operations Management

(x-chart detects shift in central tendency)

(R-chart does not detect change in mean)

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MEAN AND RANGE CHARTS (b) These sampling distributions result in the charts below

(Sampling mean is constant but dispersion is increasing) UCL

x-chart LCL UCL

R-chart LCL MIS 373: Basic Operations Management

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

(R-chart detects increase in dispersion)

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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

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RUN TESTS A: Above B: Below

U: Upward D: Downward MIS 373: Basic Operations Management

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PATTERNS IN CONTROL CHARTS UCL

UCL

Target

Target

LCL

LCL

Normal behavior. Process is “in control.”

UCL

Target LCL Two plots very near lower (or upper) control. MIS 373: Basic Operations Management

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

UCL

Target LCL Trends in either direction, 5 plots. Progressive change.

UCL

UCL

Target

Target

LCL Run of 5 above (or below) central line.

LCL Erratic behavior. 32

DEMO • ASQ Control chart template • http://asq.org/learn-about-quality/data-collection-analysistools/overview/asq-control-chart.xls

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.

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