PROCESS CAPABILITY AND SPC

Chapter 9A

1. Explain what statistical quality control is.

2. Calculate the capability of a process.

3. Understand how processes are monitored with control charts.

OBJECTIVES 9A-2

Types of Situations where SPC can be Applied How many paint defects are there in the

finish of a car? How long does it take to execute market

orders? How well are we able to maintain the

dimensional tolerance on our ball bearing assembly?

How long do customers wait to be served from our drive-through window?

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Basic Forms of Variation

Assignable variation is caused by factors that can be clearly identified and possibly managed

Common variation is inherent in the production process

Example: A poorly trained employee that creates variation in finished product output.

Example: A poorly trained employee that creates variation in finished product output.

Example: A molding process that always leaves “burrs” or flaws on a molded item.

Example: A molding process that always leaves “burrs” or flaws on a molded item.

9A-4

Test

ing

exam

ple

s

Taguchi’s View of Variation

Traditional view is that quality within the range is good and that the cost of quality outside this range is constant

Taguchi views costs as increasing as variability increases, so seek to achieve zero defects and that will truly minimize quality costs

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Process Capability

Taguchi argues that tolerance is not a yes/no decision, but a continuous function

Other experts argue that the process should be so good the probability of generating a defect should be very low

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Types of Statistical Sampling

Attribute (Go or no-go information) Defectives refers to the acceptability

of product across a range of characteristics.

Defects refers to the number of defects per unit which may be higher than the number of defectives.

p-chart application

Variable (Continuous) Usually measured by the mean and

the standard deviation. X-bar and R chart applications

9A-8

Statistical Process Control (SPC) Charts

UCL

LCL

Samples over time

1 2 3 4 5 6

UCL

LCL

Samples over time

1 2 3 4 5 6

UCL

LCL

Samples over time

1 2 3 4 5 6

Normal BehaviorNormal Behavior

Possible problem, investigatePossible problem, investigate

Possible problem, investigatePossible problem, investigate

9A-9

Control Limits are based on the Normal Curve

x

0 1 2 3-3 -2 -1z

Standard deviation units or “z” units.

Standard deviation units or “z” units.

9A-10

Control Limits

We establish the Upper Control Limits (UCL) and the Lower Control Limits (LCL) with plus or minus 3 standard deviations from some x-bar or mean value. Based on this we can expect 99.7% of our sample observations to fall within these limits.

xLCL UCL

99.7%

9A-11

Process Control with Attribute Measurement: Using ρ Charts

Created for good/bad attributes Use simple statistics to create the

control limits

p

p

p

zspLCL

zspUCL

n

pps

p

1

size Sample samples ofNumber

samples all from defects ofnumber Total

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Example of Constructing a p-Chart: Required Data

1 100 42 100 23 100 54 100 35 100 66 100 47 100 38 100 79 100 1

10 100 211 100 312 100 213 100 214 100 815 100 3

Sample

No.

No. of

Samples

Number of defects found in each sample

9A-13

1. Calculate the sample proportions, p (these are what can be plotted on the p-chart) for each sample

1. Calculate the sample proportions, p (these are what can be plotted on the p-chart) for each sample

Sample n Defectives p1 100 4 0.042 100 2 0.023 100 5 0.054 100 3 0.035 100 6 0.066 100 4 0.047 100 3 0.038 100 7 0.079 100 1 0.01

10 100 2 0.0211 100 3 0.0312 100 2 0.0213 100 2 0.0214 100 8 0.0815 100 3 0.03

Example of Constructing a p-chart: Step 1

9A-14

2. Calculate the average of the sample proportions2. Calculate the average of the sample proportions

0.036=1500

55 = p 0.036=1500

55 = p

3. Calculate the standard deviation of the sample proportion 3. Calculate the standard deviation of the sample proportion

.0188= 100

.036)-.036(1=

)p-(1 p = p n

s .0188= 100

.036)-.036(1=

)p-(1 p = p n

s

Example of Constructing a p-chart: Steps 2&3

9A-15

4. Calculate the control limits4. Calculate the control limits

3(.0188) .036 3(.0188) .036

UCL = 0.0924LCL = -0.0204 (or 0)UCL = 0.0924LCL = -0.0204 (or 0)

p

p

z - p = LCL

z + p = UCL

s

s

p

p

z - p = LCL

z + p = UCL

s

s

Example of Constructing a p-chart: Step 4

9A-16

Example of Constructing a p-Chart: Step 5

5. Plot the individual sample proportions, the average of the proportions, and the control limits

5. Plot the individual sample proportions, the average of the proportions, and the control limits

9A-17

How to Construct and R Charts

RD

RD

R

RAX

RAX

X

3R

4R

2X

2X

LCL

UCL

Chart

LCL

UCL

Chart

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Example of x-bar and R Charts: Required Data

Sample Obs 1 Obs 2 Obs 3 Obs 4 Obs 51 10.68 10.689 10.776 10.798 10.7142 10.79 10.86 10.601 10.746 10.7793 10.78 10.667 10.838 10.785 10.7234 10.59 10.727 10.812 10.775 10.735 10.69 10.708 10.79 10.758 10.6716 10.75 10.714 10.738 10.719 10.6067 10.79 10.713 10.689 10.877 10.6038 10.74 10.779 10.11 10.737 10.759 10.77 10.773 10.641 10.644 10.72510 10.72 10.671 10.708 10.85 10.71211 10.79 10.821 10.764 10.658 10.70812 10.62 10.802 10.818 10.872 10.72713 10.66 10.822 10.893 10.544 10.7514 10.81 10.749 10.859 10.801 10.70115 10.66 10.681 10.644 10.747 10.728

9A-19

Example of x-bar and R charts: Step 1. Calculate sample means, sample ranges, mean of means, and mean of ranges.

Sample Obs 1 Obs 2 Obs 3 Obs 4 Obs 5 Avg Range1 10.68 10.689 10.776 10.798 10.714 10.732 0.1162 10.79 10.86 10.601 10.746 10.779 10.755 0.2593 10.78 10.667 10.838 10.785 10.723 10.759 0.1714 10.59 10.727 10.812 10.775 10.73 10.727 0.2215 10.69 10.708 10.79 10.758 10.671 10.724 0.1196 10.75 10.714 10.738 10.719 10.606 10.705 0.1437 10.79 10.713 10.689 10.877 10.603 10.735 0.2748 10.74 10.779 10.11 10.737 10.75 10.624 0.6699 10.77 10.773 10.641 10.644 10.725 10.710 0.13210 10.72 10.671 10.708 10.85 10.712 10.732 0.17911 10.79 10.821 10.764 10.658 10.708 10.748 0.16312 10.62 10.802 10.818 10.872 10.727 10.768 0.25013 10.66 10.822 10.893 10.544 10.75 10.733 0.34914 10.81 10.749 10.859 10.801 10.701 10.783 0.15815 10.66 10.681 10.644 10.747 10.728 10.692 0.103

Averages 10.728 0.220400

9A-20

Example of x-bar and R charts: Step 2. Determine Control Limit Formulas and Necessary Tabled Values

x Chart Control Limits

UCL = x + A R

LCL = x - A R

2

2

x Chart Control Limits

UCL = x + A R

LCL = x - A R

2

2

R Chart Control Limits

UCL = D R

LCL = D R

4

3

R Chart Control Limits

UCL = D R

LCL = D R

4

3

n A2 D3 D42 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 1.82

10 0.31 0.22 1.7811 0.29 0.26 1.74

9A-21

Example of x-bar and R charts: Steps 3&4. Calculate x-bar Chart and Plot Values

10.601

10.856

=).58(0.2204-10.728RA - x = LCL

=).58(0.2204-10.728RA + x = UCL

2

2

10.601

10.856

=).58(0.2204-10.728RA - x = LCL

=).58(0.2204-10.728RA + x = UCL

2

2

9A-22

Then plot both graphs: Means to Then plot both graphs: Means to the Mean chart and Ranges to the the Mean chart and Ranges to the

Range chart.Range chart.

0

0.46504

)2204.0)(0(R D= LCL

)2204.0)(11.2(R D= UCL

3

4

0

0.46504

)2204.0)(0(R D= LCL

)2204.0)(11.2(R D= UCL

3

4

ANY QUESTIONS?

9A-23