BA 301 Spring 2003 Managing Quality and Statistical Process Control:

BA 301 Spring 2003

Managing Quality

and

Statistical Process Control:

Great Ideas in Quality Management – The Contributors: Genechi Taguchi

– The Quality-Loss Function and Target Oriented Quality Walter Shewhart

– Statistical Quality/Process Control– Process Capability

W. Edwards Deming– Total Quality Management

Shigeo Shingo & Taiichi Ohno– Toyota Production System (aka “Just-in-Time”)

The Great Ideas in Quality Management – Two Stories:

Jon Ozmun’s 1965 Ford “Fairlane 500”– How to keep dust out of a new car.

Watching Monday Night Football in the late 1980s:– San Francisco 49ers vs Detroit Lions – “A tale of two kicks”

Great Contributors: Genechi Taguchi Taguchi Techniques

Experimental methods (Called “Design of Experiments”) to improve product & process design– Identify key component & process variables

affecting product variation

Taguchi Concepts– Quality robustness– Quality loss function– Target specifications

so that it can be produced to specifications under “adverse” manufacturing conditions.”

so that it can perform under conditions more severe than it is expected to encounter.” – Coolant pump failure

on 1983 Honda Accord

© 1984-1994 T/Maker Co.

© 1995 Corel Corp.

Quality Robustness: Tacuchi – “Design the product

Shows social cost ($) of deviation from target value Assumptions

– Most measurable quality characteristics (e.g., length, weight) have a target value

– Deviations from target value are undesirable Equation: L = D2C

– L = Loss ($); D = Deviation; C = Cost

Quality Loss Function

Loss

XTarget USLLSL

Loss

XTarget USLLSL

Loss = (Actual X - Target)2 • (Cost of Deviation)

Lower (upper) specification limit

Measurement

Greater deviation, more people are dissatisfied, higher cost

Quality Loss Function Graph

Freq.

XTarget USLLSL

A study found U.S. consumers preferred Sony TV’s made in Japan to those made in the U.S. Both factories used the same designs & specifications. The difference in quality goals made the difference in consumer preferences.

Japanese factory (Target-oriented)

U.S. factory (Conformance-oriented)

Target Specification Example

Quality Loss Function; Distribution of Products Produced

Low loss

High loss

Frequency

Lower Target UpperSpecification

Loss (to producing organization, customer, and society)

Quality Loss Function (a)Unacceptable

Poor

Fair

Good

Best

Target-oriented quality yields more product in the “best” category

Target-oriented quality brings products toward the target value

Conformance-oriented quality keeps product within three standard deviations

Distribution of specifications for product produced (b)

Japanese “Target-Oriented Quality” -Does it really matter?

In 1983, the Ozmun’s bought a new Honda Accord. Based on their experience, they bought a new 1987 Accord.

The Ozmun’s have purchased five new and four used vehicles since 1983. All have been either Honda/Acura or Toyota products.

Their children and grandchildren have purchased one new Toyota and four used Hondas.

Great Contributors: Walter Shewhart Statistical Quality Control

In the early 1920s, the inspection group at Western Electric (a part of the Bell System) was given the task of developing new theories and methods of inspection for improving and maintaining product quality.

Members of this group were W. Edwards Deming and Walter Shewhart.

Shewhart is credited with the developing Statistical Quality Control (SQC).

An earlier technique, called “Acceptance Sampling” had been the primary tool for quality control.

A form of quality testing used for incoming materials or finished goods– e.g., purchased material & components

The Procedure– Take one or more samples at random from a lot

(shipment) of items– Inspect each of the items in the sample– Decide whether to accept or reject the whole lot

based on the inspection results This amounted to “inspecting defects out” after the

product was made rather than “building quality in” while the product was being made.

SPC was the foundation needed for building quality into the product.

What is/was Acceptance Sampling?

Shewhart determined that all processes are subject to variability. He separated the observed variability into “common cause” and “special cause”.

Today, these are also called:– Natural causes: Random variations– Assignable causes: Correctable problems

Shewhart recognized that it was of utmost importance for management to know which type of variation was present in the process.

If only natural cause variation was present, the process should be left alone.

But, if assignable cause variation was present, it should be found and corrected.

Statistical Quality Control (aka “Statistical Process Control” - SPC)

Shewhart developed SPC to determine when a process is in control, or is out of control.

A process is in statistical control when the only source of variation is common (natural) cause.

SPC is grounded in statistical theory and involves collecting, organizing, & interpreting data.

The objective of SPC is to provide a statistical signal when assignable causes of variation are present.

Today, SPC is used to control processes as products and services are created – to insure that quality is “built into the product”.

“Statistical Process Control” (SPC) continued:

Variation in Processes Natural Variation – the variation that is found

in every process to some degree and is to be expected and tolerated– Natural variations behave like a constant system

of chance causes. – Although the individual values are all different, as

a group they form a pattern that can be described as a distribution.

Assignable Variation – the variation that can be traced to a specific reason and can therefore be corrected, e.g. machine wear, misadjusted equipment, fatigued or untrained workers, or new batches of raw or semi-finished goods materials

Control Charts – The heart of SPC

The only way to know with 100% certainty what a process is doing is by 100% inspection. But this is usually too expensive.

Control Charts provide us with a much less expensive way to know about a process.

Control Charts do not provide 100% certainty. They provide a level of confidence that is dependent upon the way they are constructed.

Different Control Charts for Different Situations

Variable Measurement (Characteristics that have continuous dimensions, e.g. weight, volume, thickness, conductivity, etc…)

Control Charts for “Variables” are the X-bar chart (central tendency)R-chart (range or dispersion)

Attribute Measurement (characteristics that have only two values, e.g. “defective vs non-defective”, “on-time vs late”, etc…)

Control Charts for “Attributes” are thep-chart (proportion defectives) c-chart (number defective)

X

As sample size gets large enough, the

sampling distribution becomes almost normal regardless of population distribution.

Central Limit Theorem

XX

Theoretical Basis of Control Charts

X

Mean

Central Limit Theorem

x

x

n

xx

nX X

Standard deviation

X X

Theoretical Basis of Control Charts

Sampling Distribution of Means, and Process Distribution

Sampling distribution of the means

Process distribution of the sample

)mean(

mx

Process Control & Process Capability

The “ideal” situation is that a process is both in control and capable of meeting the customer’s requirements.

Other situations are:Process is in control but incapable.Process is out of control but capable.Process is both out of control and incapable.

We can determine which of these situations exists through the use information derived from control charts.

Process Capability Cpk

population process theof deviation standard

mean process x where

Limition SpecificatLower x

or , x Limit ion SpecificatUpper

of minimum

pkC

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

Constructing & Using X-bar and R Control Charts

Collect 20-25 samples of n = 4 or 5 from a stable process and compute the mean and range of each.

Compute the overall means (x double bar and R bar) and set appropriate control limits (usually 3 sigma each side).

Graph the sample means and ranges on their respective control charts to determine whether they fall outside the acceptable limits.

If the process is deemed to be “in statistical control”, then continue to take periodic random samples to insure that the process stays in control.

If the process is deemed to be out of control, then determine the source of the “assignable cause” variation and correct it.

If the process is “in control”, can it meet the customers specifications?

To meet the customer’s specifications, the process variability cannot exceed the customer’s upper or lower specification limits.

We determine the process variability from the variability of the sampling distribution.– We have to convert standard deviation information from the

sampling distribution to standard deviation information for the process.

With this information, we determine the Process Capability Index (Cpk).

Converting “Sampling Distribution” information to “Process Distribution” information

For the “Sampling Distribution”:

One standard deviation (“sigma”) is = (A2R-bar)/3

The “Process Distribution” standard deviation is calculated from the “Sampling Distribution”:

Sigma (process) = Sigma(sample) X (sq.rt.n)

Process Control & Process Capability A Sample Problem

Rocky’s Peanut Butter Company and Safeway Stores of Arizona

Rocky’s wants to determine if they can meet Safeway’s quality standards and become a supplier to Safeway.

Rocky’s can learn if their process is “capable” by developing a SPC system.

Go to “Rocky’s Peanut Butter” handout.

Rocky’s Peanut Butter

X double bar = 12.00; R bar = 0.24 Sample Size = n = 4

UCLX bar = X double bar + A2 R bar = 12.175 LCLX bar = X double bar – A2 R bar = 11.825

UCLR = D4 R bar = 2.282 (0.24) = 0.548 LCLR = D3 R bar = 0 (0.24) = 0

Rocky’s Peanut Butter

Plot the ten (10) individual sample means and range values in the control charts.

Is there evidence of assignable cause variation? (Do any of the sample data fall outside the control limits?)

Rocky’s Peanut Butter Can Rocky’s meet Safeway’s Specifications? We need to estimate three standard deviations

of the filling process at Rocky’s: We will use what we know to get the estimate of

the standard deviation of the filling process.– Three standard deviations for the sample

distribution is equal to A2 R bar.– Three standard deviations for the filling process

= (3 std dev of the sample distribution)X(sq rt n) = A2 R bar X sq rt 4 = 0.175 X 2 = 0.35

So we know that 99.7% of Rocky’s jars weigh between 11.65 and 12.35 ounces.

Rocky’s “Process Capability”

CPK = (USL – X bar) / 3 sigma

= (12.25 – 12.00) / 0.35

= 0.25 / 0.35 = 0.71 When the Cpk is less than 1.0, this means

that Rocky’s process is incapable of meeting Safeway’s quality specifications.

What options are open to Rocky’s?