Introduction to Operations Management 1

Quality Assurance

(Quality Control)

Introduction to Operations Management 2

Phases of Quality Assurance

Acceptancesampling

Processcontrol

Continuousimprovement

Inspectionbefore/afterproduction

Correctiveaction duringproduction

Quality builtinto theprocess

The leastprogressive

The mostprogressive

Introduction to Operations Management 3

Inspection

How Much/How OftenWhere/When Centralized vs. On-site

Inputs Transformation Outputs

Acceptancesampling

Processcontrol

Acceptancesampling

Introduction to Operations Management 4

Inspection Costs

Optimal

Cos

t

Amount of Inspection

Cost of inspection

Cost of passingdefectives

Total Cost

Introduction to Operations Management 5

Where to Inspect in the Process

Raw materials and purchased partsFinished productsBefore a costly operationBefore an irreversible processBefore a covering process

Introduction to Operations Management 6

Examples of Inspection PointsT y p e o fb u s i n e s s

I n s p e c t i o np o i n t s

C h a r a c t e r i s t i c s

F a s t F o o d C a s h i e rC o u n t e r a r e aE a t i n g a r e aB u i l d i n gK i t c h e n

A c c u r a c yA p p e a r a n c e , p r o d u c t i v i t yC l e a n l i n e s sA p p e a r a n c eH e a l t h r e g u l a t i o n s

H o t e l / m o t e l P a r k i n g l o tA c c o u n t i n gB u i l d i n gM a i n d e s k

S a f e , w e l l l i g h t e dA c c u r a c y , t i m e l i n e s sA p p e a r a n c e , s a f e t yW a i t i n g t i m e s

S u p e r m a r k e t C a s h i e r sD e l i v e r i e s

A c c u r a c y , c o u r t e s yQ u a l i t y , q u a n t i t y

Introduction to Operations Management 7

Statistical Process Control

The Control Process Define Measure Compare to a standard Evaluate Take corrective action Evaluate corrective action

Introduction to Operations Management 8

Statistical Process Control

Variations and Control Random variation: Natural variations in the out

put of process, created by countless minor factors

Assignable variation: A variation whose source can be identified

Introduction to Operations Management 9

Sampling Distribution

Samplingdistribution

Processdistribution

Mean

Introduction to Operations Management 10

Normal Distribution

Mean3 2 2 3

95.5%

99.7%

Standard deviation

Introduction to Operations Management 11

Control Limits (Type I Error)

Mean

LCL UCL

/2 /2

Probabilityof Type I error

Introduction to Operations Management 12

Control LimitsSamplingdistribution

Processdistribution

Mean

Lowercontrol

limit

Uppercontrol

limit

Introduction to Operations Management 13

Mean Charts

Two approaches: If the process standard deviation is

available (x If the process standard deviation is not

available (use sample range to approximate the process variability)

Introduction to Operations Management 14

Mean charts (SD of process available)

Upper control limit (UCL) = average sample mean + z (S.D. of sample mean)

Lower control limit (LCL) = average sample mean - z (S.D. of sample mean)

Introduction to Operations Management 15

Mean charts (SD of process not

available)

UCL = average of sample mean + A2 (average of sample range)

LCL = average of sample mean - A2 (average of sample range)

A2 is a parameter depending on the sample size and is obtainable from table.

Introduction to Operations Management 16

Example

Means of sample taken from a process for making aluminum rods is 2 cm and the SD of the process is 0.1cm (assuming a normal distribution). Find the 3-sigma (99.7%) control limits assuming sample size of 16 are taken.

Introduction to Operations Management 17

Example (solution)

x = SD of sample mean distribution = SD of process / (sample size) = 0.1 / (16) = 0.025

z = 3UCL = 2 + 3(0.025) = 2.075LCL = 2 - 0.075 = 1.925

Introduction to Operations Management 18

Example(p.427)

Twenty samples of size 8 have been taken from a process. The average sample range of the 20 samples is 0.016cm and the average mean is 3cm. Determine the 3-sigma control limits.

Introduction to Operations Management 19

Example

Average sample mean = 3cmAverage sample range = 0.016cmSample size = 8A2 = 0.37 (From Table 9-2)

UCL = 3 + 0.37(0.016) = 3.006LCL = 3 + 0.37(0.016) = 2.994

Introduction to Operations Management 20

Control Chart

970

980

990

1000

1010

1020

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

UCL

LCL

Sample number

Mean

Out ofcontrol

Normal variationdue to chance

Abnormal variationdue to assignable sources

Abnormal variationdue to assignable sources

Introduction to Operations Management 21

Observations from Sample Distribution

Sample number

UCL

LCL

1 2 3 4

Introduction to Operations Management 22

Mean and Range Charts

UCL

LCLUCL

LCL

R-chart

x-Chart Detects shift

Does notdetect shift

Introduction to Operations Management 23

Mean and Range ChartsUCL

LCL

UCL

LCL

x-Chart

UCL

LCL

R-chart Detects shift

Does notdetect shift

Introduction to Operations Management 24

Control Chart for Attributes

p-Chart - Control chart used to monitor the proportion of defectives in a process

c-Chart - Control chart used to monitor the number of defects per unit

Introduction to Operations Management 25

Use of p-ChartsWhen observations can be placed into two

categories. Good or bad Pass or fail Operate or do not operate

When the data consists of multiple samples of several observations each

Introduction to Operations Management 26

p-chart

The center line is the average fraction (defective) p in the population if p is known, or it can be estimated from samples is it is unknown.

p = SD of sample distribution = {p(1-p)/n}

UCLp = p + zp LCLp = p - zp

Introduction to Operations Management 27

Example (p.431)

The following table indicates the defective items in 20 samples, each of size 100. Construct a control chart that will describe 95.5% of the chance variations of the process

Introduction to Operations Management 28

Example

The following table indicates the defective items in 20 samples, each of size 100. Construct a control chart that will describe 95.5% of the chance variations of the process

No. of defective items

14 11 8 1010 10 12 812 12 9 1213 13 10 10 9 10 11 16

11

Introduction to Operations Management 29

Example (solution)Population mean not available, to be estimated

from sample meanTotal No. of defective items = 220Estimate sample mean = 220/{20(100)}=.11SD of sample = {.11(1-.11)/100}= 0.03z = 2 (2-sigma)UCLp = .11 + 2(.03) = 0.17

LCLp = .11 - 2(.03) = 0.05

Thus a control chart can be plotted (p.431)

Introduction to Operations Management 30

Use of c-ChartsUse only when the number of occurrences per

unit of measure can be counted; nonoccurrences cannot be counted. Scratches, chips, dents, or errors per item Cracks or faults per unit of distance Calls, complaints, failures per unit of time

Introduction to Operations Management 31

Process CapabilityLowerSpecification

UpperSpecification

Process variabilitymatches specifications

LowerSpecification

UpperSpecification

Process variabilitywell within specifications

LowerSpecification

UpperSpecification

Process variabilityexceeds specifications