Statistical Process Control

Chapters 20

1 2 3 4 5 6 7 8

A

B

C

D

E

F

G

H

Some Common Problems in Planning

We plan in terms of actions (tasks) rather than objectives

Responsibilities are not clearWe plan in silos, out of contextWe underestimate the time and effort

required to implementWe don’t make reviews part of the plan.

Six-Step Problem-Solving Process

Step 1: Identify and Select the problemStep 2: Analyze the problemStep 3: Generate Potential SolutionsStep 4: Select and Plan the SolutionStep 5: Implement the SolutionStep 6: Evaluate the Solution

StatisticalQuality Control

ProcessControl

AcceptanceSampling

VariablesCharts

AttributesCharts

Variables Attributes

Types of Statistical Quality Control

Measures performance of a processUses mathematics (i.e., statistics)Involves collecting, organizing, &

interpreting data Objective: Regulate qualityUsed to

Control the process as products are produced or service is performed

Statistical Quality Control (SPC) key tool for 6 Sigma

ControlCharts

RChart

VariablesCharts

AttributesCharts

XChart

PChart

CChart

Continuous Numerical Data

Categorical or Discrete Numerical Data

Control Chart Types

Characteristics for which you focus on defects

Classify products as either ‘good’ or ‘bad’, or count # defects e.g., radio works or not

Categorical or discrete random variables

AttributesAttributesVariablesVariables

Quality Characteristics

¨ Characteristics that you measure, e.g., weight, length

¨ May be in whole or in fractional numbers

¨ Continuous random variables

Statistical Process Control

VariationsCommon cause: due

to process itselfSpecial cause

2 ways of investigating variationPlot data using

histogram, looking for a normal distribution.

Standard Deviation

1 σ away from mean in either direction accounts for approx. 68% of readings in the group (red area)

2 σ away from mean in either direction accounts for approx. 95% of readings in the group (red and green area)

3 σ away from mean in either direction accounts for approx. 99% of readings in the group (red, green, and blue areas)

Process Control Charts

Plot of Sample Data Over Time

010203040506070

1 5 9 13 17 21

Time

Sam

ple

Va

lue

SampleValueUCL

Average

LCL

Show changes in data patterne.g., trends

Make corrections before process is out of control

Show causes of changes in dataAssignable causes

Data outside control limits or trend in data

Natural causesRandom variations around average

Control Chart Purposes

Type of variables control chart Interval or ratio scaled numerical data

Shows sample means over timeMonitors process averageExample: Weigh samples of coffee &

compute means of samples; Plot

X Chart

Type of variables control chart Interval or ratio scaled numerical data

Shows sample ranges over timeDifference between smallest & largest values

in inspection sample

Monitors variability in processExample: Weigh samples of coffee &

compute ranges of samples; Plot

R Chart

Formulas

Type of attributes control chartNominally scaled categorical data

e.g., good-bad

Shows % of nonconforming itemsExample: Count # defective chairs &

divide by total chairs inspected; PlotChair is either defective or not defective

p Chart

# Defective Items in Sample i

Size of sample i

z = 2 for 95.5% limits; z = 3 for 99.7% limits

p Chart Control Limits

i

k

1i

i

k

1ii

k

i

p

p

n

xp and

k

nn

n)p(p

zpLCL

n)p(p

zpUCL

Statistical Process Control Chart

Using SPC to Address On-Time Medication Delivery

Type of attributes control chartDiscrete quantitative data

Shows number of nonconformities (defects) in a unit Unit may be chair, steel sheet, car etc.Size of unit must be constant

Example: Count # defects (scratches, chips etc.) in each chair of a sample of 100 chairs; Plot

c Chart

# Defects in Unit i

# Units Sampled

Use 3 for 99.7% limits

c Chart Control Limits

k

c c

ccLCL

ccUCL

i

k

1i

c

c

Process Capability Cpk

population process theof deviation standard

mean process x where

LimitionSpecificat Lower x ,

x Limit ionSpecificatUpper of minimumCpk

Assumes that the process is:•under control•normally distributed

Form of quality testing used for incoming materials or finished goodse.g., purchased material & components

ProcedureTake one or more samples at random from a lot

(shipment) of items Inspect each of the items in the sampleDecide whether to reject the whole lot based on

the inspection results

What Is Acceptance Sampling?

Set of procedures for inspecting incoming materials or finished goods

IdentifiesType of sampleSample size (n)Criteria (c) used to reject or accept a lot

Producer (supplier) & consumer (buyer) must negotiate

What Is an Acceptance Plan?

Producer's risk ()Probability of rejecting a good lot Type 1 error – results in over adjustment

Consumer's risk (ß)Probability of accepting a bad lot Type II error – results in under adjustment

Producer’s & Consumer’s Risk

ANY QUESTIONS?