CONTROL CHARTS

CONTROL CHARTS

QUALITY MANAGEMENT

SPRING, 1998

Larry W. Jacobs

Control Charts

Most useful in maintaining process in control after setting process where it meets your capability needs, i.e., X or R is where you want and process variability is acceptable for your needs.
Control charts allow you to separate
Common cause variation
Special cause variation
Two kinds of control charts
-variances X , R: control process maintained in some quantity (variable) such as weight, length, width, color, strength, hardness,
-Attributes: An item is good/bad or sample contains some good or bad items, i.e.,

R-Chart Control s

UCLR = D4R

LCLR = D3R

X-Chart Control m

UCLx = X + A2R

LCLx = X - A2R

Here is a brief description of the 8 tests: Sigma

UCL ------------------+3

Zone A

------------------+2

Zone B

------------------+1

Zone C

Ctr = = = = = = = = 0

Zone C

------------------ -1

Zone B

------------------ -2

Zone A

LCL ------------------ -3

X-BAR TESTS

1. One point beyond zone A.

2. Nine points in a row in zone C or

beyond (on one side of center line ).

3. Six points in a row, all increasing or all decreasing.

4. Fourteen points in a row,alternating up and down.

5. Two out of three points in a row in zone A ot beyond.

6. Four out of five points in a row in zone B or beyond (on one side of center line).

7. Fifteen points in a row in C zones (above and below center line).

8. Eight points in a row beyond C zones (above and below center line).

Here is a brief description of the 4 tests: Sigma

UCL ------------------+3

Zone A

------------------+2

Zone B

------------------+1

Zone C

Ctr = = = = = = = = 0

Zone C

------------------ -1

Zone B

------------------ -2

Zone A

LCL ------------------ -3

P-CHART TESTS

1. One point beyond zone A.

2. Nine points in a row in zone C or beyond (on one side of center line ).

3. Six points in a row, all increasing or all decreasing.

4. Fourteen points in a row,alternating up and down.

What are control charts

P-Chart is P + 3Sp, i.e., 3 sigma control chart on proportion (p) around average proportion ( p )

X, R ?

Example for X

Given: sx = R / d2 (Standard Deviation of Individual X’s)

and

sx = R/ d2 n (Standard Deviation of Average X’s)

Given: A2 = 3 / d2 n

X + A2R is equal to X + 3 ( R / d2 n )

is equal to X + 3 s x ( 3 sigma control limits on Average(X’s) around Grand Average (X)

Note: Similar Analysis for R-Chart is on Page 724

SINCE: sx = R / d2, we can Link control charts and process capability.

Control limits on X-Bar Chart refer to limits on Averages (3sx).

But sx pertains to individual X.

Consider previous example: 27 sample of 5 observation each, X = 40.644 ; R = 8.630

sx = R / d2 = 8.63 / 2.326 = 3.71

Process capability = m + 3 sx or X + 3sx ( 40+11.13)

29.51 51.77

Note UCLx = 45.61 ; LCLx = 35.68

Assume Design Tolerance Is 40.5 + 8

What is Process Capabilty Index ?

Process Is Not Centered 40.5 does not equal 40.644

Therefore, Use Cpk

Cpu = = =.07

Cpl = = =.73

Cpk = Min [Cpu , Cpl] = 0.7