Quality Control

Chapter 6

Transformation Process

Transformation Process

Inputs• Facilities• Equipment• Materials• Energy

OutputsGoods &Services

•Variation in inputs create variation in outputs• Variations in the transformation process create variation in outputs

Variation

All processes have variation. Common cause variation is random

variation that is always present in a process.

Assignable cause variation results from changes in the inputs or the process. The cause can and should be identified.

A process is in control if it has no assignable cause variation. The process is consistent

Statistical Process Control (SPC)

Distinguishes between common cause and assignable cause variation

Measure characteristics of goods or services that are important to customers

Make a control chart for each characteristic The chart is used to determine whether the

process is in control

Capability and Conformance Quality (1)

A process is capable if It is in control and It consistently produces outputs that meet

specifications. A capable process produces outputs that

have conformance quality (outputs that meet specifications).

Capable Transformation Process

Capable Transformation

Process

Inputs• Facilities• Equipment• Materials• Energy

OutputsGoods &Servicesthat meet

specifications

Capability and Conformance Quality (2)

If the process is capable and the product specification is based on current customer requirements, outputs will meet customer expectations.

Customer Satisfaction

Capable Transformation

Process+

Product specification that meets

current customer

requirements

= Customer satisfaction

Objectives of SPC

To determine if the process is in control(predictable)

To determine if the process is capable (in control and meets specifications)

Variable Measures

Continuous random variables Measure does not have to be a whole

number. Examples: time, weight, miles per

gallon, length, diameter

Attribute Measures

Discrete random variables – finite number of possibilities Also called categorical variables

Different types of control charts are used for variable and attribute measures

Examples of Attribute Measures

Good/bad evaluations Good or defective Correct or incorrect

Number of defects per unit Number of scratches on a table

Opinion surveys of quality Customer satisfaction surveys Teacher evaluations

Descriptive StatisticsDescribe Results from a Random Sample

The Mean- measure of central tendency

The Range- difference between largest/smallest observations in a set of data

Standard Deviation measures the amount of data dispersion around mean

n

xx

n

1ii

1n

Xxσ

n

1i

2

i

Important Figures and Charts

Figures 6.1, 6.2, and 6.3, page 176 Figure 6.4 page 177 Control charts, pages 180 and 183 Figure 6.6, page 184

• Random samples are taken from process output• A process characteristic is measured• Sample means are plotted• Control limits are based on a confidence interval for the mean• CL = center line (mean line)• LCL = lower control limit UCL = upper control limit

Control chart forthe mean of a productcharacteristic

Percentage of values under normal curve

= population mean = population standard

deviation 95.4% of the population

is within 2 of the mean 99.74% of the population

is within 3 of the mean 99.74% of the population

is within the interval from

3 to 3 We will compute 3

confidence intervals for sample means

Specification Limits

The target is the ideal value Example: if the amount of beverage in a bottle

should be 16 ounces, the target is 16 ounces Specification limits are the acceptable range of values

for a variable Example: the amount of beverage in a bottle must be at

least 15.8 ounces and no more than 16.2 ounces. Range is 15.8 – 16.2 ounces. Lower specification limit = 15.8 ounces or LSPEC = 15.8

ounces Upper specification limit = 16.2 ounces or USPEC = 16.2

ounces

Test for Process Capability(with respect to x )

The process is in control with respect to x

AND The control limits (LCL and UCL) for x

are within the specification limits

Capability index, Cpk is used to determine whether a process is capable

Process is Capable

UCL

LCL

X

Lower specification limit

Upper specification limit

Process is Not Capable

UCL

LCL

X

Lower specification limit

Upper specification limit

UCL outside specification limits not capable

Cpk Index

= process mean (or estimated mean) LSPEC = lower specification limit USPEC = upper specification limit

Cpk = Smaller {(USPEC- )/3 – LSPEC)/ 3} If Cpk >= 1, process meets customer

requirements 99.74% of the time. To allow for changes in the mean, many firms

set a requirement that Cpk >= 1.33.

3-Sigma Quality

Uses 3 control limits for x Corresponds to 3 defects per 1,000 units. If a product has 250 parts and each has 3 control limits, P[at least 1 bad part] = 0.528

6-Sigma Quality

Use 6- control limits for x. Control limits are (X- 2A2R, X + 2A2R). Corresponds to 3.4 defects per million If a product has 250 parts and each has

6 control limits, P[at least 1 bad part]

<0.001