chapter 13 statistical quality control method. statistical quality control methods statistical...

Chapter 13 Statistical Quality Control Method

Statistical Quality Control Methods

Statistical QualityControl Methods

Acceptance SamplingStatistical Process

Control

Attributes Variables Attributes Variables

Type of Data

Statistical Quality Control Methods

Attribute Data: data which count items, such as the number of defective items on a sample

Variable Data: data which measure a particular product characteristic such as length or weight

Statistical Quality Control Methods

Sampling Error

Sample results are not representative of the actualpopulation or process

In agreement

The populationor process is actually

Good or in control Bad or out of control

In agreement

or Type II error

or Type I error

Good orin control

Bad or out of control

The samplesays that thepopulation orprocess is

Prducer’s risk

Customer’srisk

Acceptance Sampling

Designing a Sampling Plan for Attribute

Costs to justify inspection

Full or 100% inspection or not?

Cost to InspectCost incurred by passing a reject

Acceptance Sampling

Purpose of Sampling Plan

•Find its quality

•Ensure that the quality is what it is supposed to be

Acceptance Sampling

n: Number of units in the sample depended on the lot size

c: the acceptance number

Designing a Sampling Plan for Attribute

AQL (acceptable quality level): maximum percentage of defects that a company is willing to accept

LTPD (lot tolerance percent defective): minimum percentage of defects that a company is willing to reject

: producer’s risk

: consumer’s risk

Acceptance Sampling

Designing a Sampling Plan for Attribute

c LTPD/AQL nAQL

0 44.890 0.0521 10.946 0.3552 6.509 0.8183 4.890 1.3664 4.057 1.9705 3.549 2.6136 3.206 3.2867 2.957 3.9818 2.768 4.6959 2.618 5.426

=0.05=0.10

MIL-STD-105E

Operating Characteristic Curve

Operating Characteristic Curve

!

)()(

r

nperP

rnp

p np P(r c)

1% 0.99 0.97

2% 1.98 0.95

…

Acceptance Sampling

Determine a Sampling Plan for Variables

Control Limit: Points on an acceptance sampling chart that distinguish the accept and reject regions. Also, points on a process control chart that distinguish between a process being in and out of control.

nzCL

2

Acceptance Sampling

Determine a Sampling Plan for Variables

Acceptance Sampling

LCL

Statistical Process Control

Statistical process control (SPC)

Statistical method for determining whether a particularprocess is in or out of control.

Central Limit Theorem

Statistical Process Control

Statistical Process Control

Statistical Process Control

SPC Using Attribute Measurement

Attribute data are data that are counted, such as good or badunits produced by a machine.

Samples

defects

Sample size=6defects=2

Statistical Process Control

SPC Using Attribute Measurement

Center line = p = Long-run average percent defective

Standard deviation of sample = n

ppS p

)1(

n

ppzpCL

)1(2

Note: X~Bernoulli distribution E(x)=p V(x)=p(1-p)

32Z

Statistical Process Control

Variable Measurements Using X and R Charts

An X chart tracks the changes in the means of samples by plottingthe means that were taken from a process.

An R chart tracks the changes in the variability by plotting the range within each sample.

Statistical Process Control

Variable Measurements Using X and R Charts

Setup Control Chart:

1. At least 25 samples2. Setup control limits

RAXX 2Control limits for

RDR 4RDR 3

Upper control limit for

Lower control limit for

Statistical Process Control

n A2 D3 D4

2 1.88 0 3.273 1.02 0 2.574 0.73 0 2.285 0.58 0 2.116 0.48 0 2.007 0.42 0.08 1.928 0.37 0.14 1.869 0.34 0.18 1.8210 0.31 0.22 1.7811 0.29 0.26 1.7412 0.27 0.28 1.7213 0.25 0.31 1.69

n A2 D3 D4

14 0.24 0.33 1.6715 0.22 0.35 1.6516 0.21 0.36 1.6417 0.20 0.38 1.6218 0.19 0.39 1.6119 0.19 0.40 1.6020 0.18 0.41 1.59

Statistical Process Control

Process Capability

Process Capability

Process Capability Ratio

sC p 6

limit ranceLower tole -limit ranceUpper tole

The larger the ratio, the greater the potential for producingparts within tolerance from the specified process.

Process Capability

Capability Index

s

XUSL

s

LSLXC pk 3

,3

min

To determine whether the process mean is closer to theupper specification limit, or the lower specification limit.

Six Sigma

Quality improvement program developed by Motorola to reduceprocess variation to 50% of design tolerance

Cp=1; defect rate = 2700 per million parts Cp=2; defect rate = 3.4 per million parts