13573_Extra Numericals of Control Charts

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HOW TO DEVELOP AND USE X BAR AND R CONTROL CHARTS?

AN EXAMPLE

Example: Control Charts for Variable DataSample 1 2 3 4 5 6 7 8 9 10 Slip Ring Diameter (cm) 1 2 3 4 5 5.02 5.01 4.94 4.99 4.96 5.01 5.03 5.07 4.95 4.96 4.99 5.00 4.93 4.92 4.99 5.03 4.91 5.01 4.98 4.89 4.95 4.92 5.03 5.05 5.01 4.97 5.06 5.06 4.96 5.03 5.05 5.01 5.10 4.96 4.99 5.09 5.10 5.00 4.99 5.08 5.14 5.10 4.99 5.08 5.09 5.01 4.98 5.08 5.07 4.99 X 4.98 5.00 4.97 4.96 4.99 5.01 5.02 5.05 5.08 5.03 50.09 R 0.08 0.12 0.08 0.14 0.13 0.10 0.14 0.11 0.15 0.10 1.15

DETERMINE CENTERLINE The centerline should be the population mean, Since it is unknown, we use X Double bar, or the grand average of the subgroup averages.

X =

m

X m

i

i=1

DETERMINE CONTROL LIMITS

Xbar chart The normal curve displays the distribution of the sample averages. A control chart is a time-dependent pictorial representation of a normal curve. Processes that are considered under control will have 99.73% of their graphed averages fall within 6.

UCL & LCL calculation

UCL = X + 3 LCL = X 3 = standard deviation

DETERMINING THE VALUES OF THE CONTROL LIMITS USING RANGE

R

=

m

R m

i=1

i

UCL

= X + A

2

R

LCL

= X A

2

R

3-Sigma Control Chart FactorsSample size n 2 3 4 5 6 7 8 X-chart A2 1.88 1.02 0.73 0.58 0.48 0.42 0.37 R-chart D3 0 0 0 0 0 0.08 0.14 D4 3.27 2.57 2.28 2.11 2.00 1.92 1.86

DETERMINE CONTROL LIMITS

R chart The range chart shows the spread or dispersion of the individual samples within the subgroup. If the product shows a wide spread, then the individuals within the subgroup are not similar to each other. Equal averages can be deceiving.

Calculated similar to x-bar charts; Use D3 and D4

CalculationFrom Table above: Sigma X-bar = 50.09 Sigma R = 1.15 m = 10 Thus; X-Double bar = 50.09/10 = 5.009 cm R-bar = 1.15/10 = 0.115 cmNote: The control limits are only preliminary with 10 samples. It is desirable to have at least 25 samples.

CONTROL LIMITS UCLx-bar = X-D bar + A2 R-bar = 5.009 + (0.577)(0.115) = 5.075 cm LCLx-bar = X-D bar - A2 R-bar = 5.009 (0.577)(0.115) = 4.943 cm UCLR = D4R-bar = (2.114)(0.115) = 0.243 cm LCLR = D3R-bar = (0)(0.115) = 0 cm n=5 For A2, D3, D4: see Table

X-bar Chart5.10 5.08 5.06UCL

X bar

5.04 5.02 5.00 4.98 4.96 4.94 0 1 2 3 4 5 6 7 8 9 10 11LCL CL

Subgroup

R Chart0.25 0.20UCL

Range

0.15 0.10 0.05

CL

LCL

0.00 0 1 2 3 4 5 6 7 8 9 10 11

Subgroup

WHAT DO YOU DO NOW ? Revise Control Limits ? The concept of Trial Control Limits

HOW TO REVISE CONTROL LIMITS ? One or two points outside ? Quite a few points outside ?

THREE CATEGORIES OF VARIATION Within-piece variation One portion of surface is rougher than another portion.

Piece-to-piece variation Variation among pieces produced at the same time.

Time-to-time variation Service given early would be different from that given later in the day.

SOURCES OF VARIATION Equipment Tool wear, machine vibration,

Material Raw material quality

Environment Temperature, pressure, humadity

Operator Operator performs- physical & emotional

CONTROL CHART VIEWPOINT Variation due to Common or chance causes Assignable causes

Control chart may be used to discover assignable causes

TYPICAL OUT-OF-CONTROL PATTERNS Point outside control limits Sudden shift in process average Cycles Trends Hugging the center line Hugging the control limits Instability20

Shift in Process Average

Identifying Potential Shifts

Cycles

8-3 Introduction to Control Charts8-3.4 Analysis of Patterns on Control Charts

8-3 Introduction to Control Charts8-3.4 Analysis of Patterns on Control Charts

Trend

Process in Control When a process is in control, there occurs a natural pattern of variation. Natural pattern has: About 34% of the plotted point in an imaginary band between 1 on both side CL. About 13.5% in an imaginary band between 1 and 2 on each side of CL. About 2.5% of the plotted point in an imaginary band between 2 and 3 on both side CL.

The Normal Distribution = Standard deviation Mean -3 -2 -1 +1 +2 +3 68.26% 95.44% USL 99.74%

LSL

-3

CL

+3

Control Chart Design Issues Basis for sampling Sample size Frequency of sampling Location of control limits

29

Setting Control Limits

Pre-ControlLTL Red Zone UTL Red Zone

Green Zone

nominal value

Yellow Zones

31