More Variable Control Charts

A. A. Elimam

What about the Short Run?

X-bar and R charts track process with long production runs or repeated services

No. of sample measurements : Insufficient to create either chart

Would SPC ideas apply to new processes or short runs?

What happens when only one sample is taken from a process?

Situations when the traditional X-bar, R and S charts cannot be used.

Individual & Moving Range Charts

When ? data is collected once per period single value measurement few units of each product individual Values Chart• Plot Individual measurements, XPlot Individual measurements, Xii

• X-bar is the average of all XX-bar is the average of all Xii

Individual & Moving Range Charts

Moving Range Chart• Value-to-value difference of Value-to-value difference of

individual data, Rindividual data, Rii

• R-bar is the average of all RR-bar is the average of all Rii

• (m-1) ranges(m-1) ranges

• Plot Individual measurements, RPlot Individual measurements, Ri i

starting on the second observationstarting on the second observation

Individual & Moving Range Charts Control Limits

Individual Charts

UCL x x = X + = X + 2.66 R R

LCL x x = X - = X - 2.66 R R

Moving Range Charts

UCL R R = = 3.27 R R

LCL R R = = 0

At least 80 samples Interpret similar to traditional charts

Moving-Average & Moving-Range Charts

Combine n individual values to form a group

Create average & range per group Moving: new value in- oldest one out Find UCL, LCL & Process

Capability using the same methods for traditional control charts (TCC)

Moving-Average Charts

Moving Average smoothes out short term variation

User Concentrate on trends Mostly used for seasonal products Always lag behind changes in

process Best when process changes slowly

A Chart Plotting Individual Values

Explains concept of variation

compared to the average

Picture worth 1000 words

Useful in training staff on

interpreting R or S charts

Median and Range Charts

Study process variation Steps:• record subgroup measurements• rank in decreasing order• find median & range in each subgroup• Median Chart Center = all medians AVG• Range Chart Center = all ranges AVG• Determine UCL & LCL for the Median &

Range Charts

Median and Range Charts

Median Charts:

UCL Md Md = = XMdMd + + A6 6 RMdMd

LCL Md Md = = XMdMd - - A6 6 RMdMd

Range Charts

UCL R R = = D4 4 RMdMd

LCL R R = = D3 3 RMdMd

Record Median & Range on chart Interpret Charts similar to TCC

Run Charts Monitor changes in a particular

characteristic over time Can be used for Variable or Attribute Data: measurements, counts,

subgroup averages Easily spot trends, runs and other

patterns

Run Charts: Steps Identify time increments to study process Scale the Y axis to reflect values Collect data Record data on chart Interpret the chart (limited to looking for

data patterns) No out of control points

Variable Subgroup Size Charts

Subgroup size, n, Varies

Re-compute Control Limits (CL) for

each n

As n increases - CLs closer to center

Too many calculations

Limit the useful of this chart

Precontrol Charts Compare product made against tolerance

limits

Assumes process is capable of meeting

specifications

Uses specifications for limits

More false alarms or missed signals

Simple to setup

Precontrol Charts Useful for setup operations or short

production runs

Less powerful than TCC

Provide little about actual process

performance

Cannot be used in problem solving or

calculating process capability

Precontrol Charts

Use Portion of Tolerance Spread (PTS) to account for difference in spread for individuals and averages

Desired Process Capability (PC) dictates this portion:

PC index PTS

1.2 (100/1.2) = 83 %

1.1 (100/1.1) = 90 %

Precontrol Charts: Steps Create the zones for the used PTS

• Place USL, LSL and center (SC) on chart

• Divide (USL-SC) in 2 equal zones: green- yellow

• Divide (SC-LSL) in 2 equal zones: green- yellow

• Green zones (GO SECTION) are next to center

• Yellow zones (CAUTION) are next to the limits

• Zones above or below yellow area are colored

in RED (UNDESIRABLE)

Precontrol Charts: Steps Take measurements & apply setup rules Record and plot measurement If measured piece is • in green zone-continue running• inside limits but outside green zone-check next piece• second piece is also outside green zone-reset process• in red zone, stop, make corrections & reset process

If 2 successive pieces fall outside green zone, one high and the other low, reduce variability

Whenever process is reset, need 5 successive pieces inside the green zone before sampling

Precontrol Charts: Steps Apply the precontrol sampling plan If 5 pieces in a row fall in the the green zonegreen zone--

begin running the jobbegin running the job Use the run rules, randomly sampling 2 Use the run rules, randomly sampling 2

pieces at intervals to monitor processpieces at intervals to monitor process For example: Sampling Two PARTS every For example: Sampling Two PARTS every

15 minutes.15 minutes. Suggest Sampling >= 25 pairs after setupsSuggest Sampling >= 25 pairs after setups Repeat whenever the process is resetRepeat whenever the process is reset

Short-Run Charts

TCC : effective in long continuous operations

Real life: need to switch products (FMS) Use Short-Run charts Different Methods:• First and last pieces• 100 % inspection (costly, maybe inaccurate)• TCC for each part # & each different run of

each part # (many charts- little information)

Nominal X-bar and R Charts

Uses coded measurements based on nominal dimension. For example “Print Dimension” of 3.75 (+ or -) 0.005 = 3.75

Shows process centering and spread Assumes similar variations for each of

the part numbers If variation of a part > 1.3 R-bar, then it

must be plotted on a separate graph

Nominal X-bar and R ChartsSteps

Identify parts monitored using same chart (same operator, machine , material, ...)

Find nominal spec. for each part Collect data using same subgroup size for

all parts

Coded Xi= measured value-nominal value

Calculate X-bar for each subgroup

Nominal X-bar and R ChartsSteps

Plot all X-bars on the chart Continue the above for the entire run of

this particular part number Repeat the above for another part

number If the number of subgroups (from any

combination of parts) >= 20, calculate the control limits

Nominal X-bar and R ChartsSteps

Centerline = Average of all coded X-bars Control limits: Nominal X-bar Chart

UCL x x = = Centerline + + A2 2 R

LCL x x = = Centerline - - A2 2 R Control limits: Nominal range Charts

UCL R R = = D4 4 R

LCL R R = = D3 3 R Draw center and CL on the chart Interpret the chart

Nominal X-bar and R Charts Most useful when FOR ALL PARTS• Subgroup size, n, is the same• Nominal is the most appropriate target value

Control charts should be selected based on:

• What aspect of process need to be monitored.• Identifying the chart that best meet such

need.