1 / 60

Ch5 Control Charts for Variables

- Variablenumerical measurement
- A single measurable quality

characteristic, such as a - dimension, weight, or volume, is called a

variable.

- Process mean?Process variability????control.
- (a) Mean and standard deviation at nomial levels.

(No Transcript)

Statistical Basis of the Charts

?X ??Normal,?n ???,???C.L.?????

relative range.

App. VI)

?n?????

??exhibit in control.

C.C. for process mean

C.C. for process mean

R chart???

App. VI)

Example 1

25?samples,??n5(???)

(???)

(???)

Estimating Process Capability

?????????Capability(??)

- ??????specification limits?74 0.05mm,
- ??????????????????

- PCR(process capability ratio)?????capability???

????????natural tolerance limits????? USL?LSL???

- PCR gt 1

(No Transcript)

Revision of Control Limits and Center Lines

(?????C.L.?Center Lines)

?????????25?50?100????

- ?R chart??in control?process mean?????variable??,?

??center line??target value,??process

mean??????variables???,????????? - ?R chart??out of control,?eliminate????????center

line?control limit?

- ???????

- ?????tolerance chart(??tier diagram)?

- ?n?7 or 8?,????Box plot.

- CL ?SL?NTL CL ?SL??????????????

- CL??process?natural variability(?NTL)????

- SP???management?engineer?customers??
- (??????????)?

- Control chart??CL?

- Tolerance chart??specification limits?

2. ?R chart?? ? ??process variability within

sample

??variability within samples???chance ?random

causes

??C.C.???

- CC?????

- ?????cost of sampling, costs of investigating

- and possibly correcting the process in

response to out - of control signals, costs associated with

producing a - product that does not meet specifications.

- small n ???shift?????sample???

- ????small, frequent or larger samples less

frequently, - ?????????small, frequent?????

- ??????rate of production???

(No Transcript)

(No Transcript)

(No Transcript)

Example 2??????

??process exhibits good control

(???)

(???)

(?????Type I level????control limitUK?????)

(No Transcript)

- ??????,???out of control???!

Case 1 Cycles

Case 2 Mixture pattern

???? ?????overlapping ??????????

??,overlap??,? ????????????overcontrol????

Case 3 Shift in process level

???? ?????????? ??????????

???????,?? skill????????motivations?

Case 4 Trend

???? tool?????,operator

fatigue?presence of supervisor(????

critical process component)?????????????

??????????(??????)?

Case 5 Stratification (?????????? ???,lack of

natural variability!)

- ???????underlying????????????
- ????,???????probability limit,????
- CC,????????,underlying???????,
- ??????CC?normality???robustness???

(No Transcript)

The Operating-Characteristic Function

(???)

(??k?sample(after the shift)?detect?shift???)

(???????????)

R chart?O.C. curve

(???)

??O.C. curve????????,?????2025 subgroups???C.C. ?

(???)

Average Time to Signal ATSARL.k

Expected number of individual units

sampled InARL (???)

?

2. The sample size n is variable.

(No Transcript)

(No Transcript)

(No Transcript)

Example 3

???????(???)

(No Transcript)

(No Transcript)

Example 4

??????n3n5(???)

????sample,n5?C.L.

(??????)

(No Transcript)

(recommended by some practitioners)

Control Limits Base on a Small Number of

Samples (Short Production Runs)

Control Charts for Individual Measurements

- ?n1???
- 1. ??????????
- 2. ??????,???ngt1?
- 3. ?????????????????????,
- (e.g. ????),???????????
- 4. ????????????,???????,
- ?????????,????std. dev.?????

- ??detect?shift???,????Ch 7?cumulative
- sum?exponential weighted moving-average

C.C. ?

Example 5

- ????????
- ????????
- ????????
- ??batch???,
- ????????
- ???batch?

Control chart for the moving range

In control

Control chart for individual observations

- ???,???????1630 batches?

??Moving range C.C.????moving ranges???,

??,???Moving range C.C.??pattern?,?

???????????moving range chart,?

???????center line??,?????out of

control,???x chart?,??????? out of

control !

- ???individual?moving range C.C.?3-sigma limit
- ???narrow???detect small process shift???,
- ?????????cumulative sum C.C.?
- exponentially weighted moving-average C.C. ?

- ?individual C.C.??,?????normality???,?
- 1. ??percentiles of underlying

distribution???control - limits?
- 2. ?transfer variable??????Normal???,??
- ?C.C.?

Applications of Variable Control Charts

Example 7

Supplier A

Center??,?variability??(??SPC??)?

Supplier B

Center??,?variability??(????,?? ????NC?????center?

?????)?

Example 8

- Job-shop???????????short production runs?

- ???? process characteristic.

- ?????????part?,?????????,
- ???????????,????????????
- ???????correct diameter,????????
- deviation of the actual hole diameter from

the nominal - diameter, ??????????????

Example 9

- ??????,??????specification limits,?
- process capability?????!

Example 10

- ????????????????,???????
- ????????????(???)?

- ??????

1. ??????????5?????(vane), ??????(i.e. n5)?

4. ??????,????part??5????,? ??????rational

subgroup?

- ?????five vanes???????individual
- measurement,??moving-range chart?monitor
- between sample?variability?

- ??S chart Moving range chart tolerance

chart - ????????

- ???quality characteristic?casting??opening

diameter? - ?????????,???opening???24?(??
- ??????)(i.e. n24)

- S chart??????????part?roundness,??out
- of control????,??????????(???) ?

Back

Back

Back

Back

Inside diameter measurements(mm) on forged piston

rings

Back

R chart for Example 1

Back

Back

Back

Continuation of the R chart for Example 1

Back

Tolerance chart for Example 1

Back

Recalculated control limits for the piston- ring

data to reflect changing the sample size form

n5 to n3.

Back

Back

O.C. curve for the R chart with 3-sigma limits

Back

Back

Back

Computation of control limits for Example 4

Back

Back

Control chart for individual observations

Control chart for the moving range

Back

Actions taken to improve a process

Is the process capable?

Yes

No

Yes

Is the process in control?

No

Back

Control chart for S and tolerance chart for vane

height data, Example 10

?S chart???within part ?variation??????

?

Back

S chart for diameter, Example 10. This is

essentially a control chart for roundness

??wax pattern??,????wooden cooling

fixture???pattern?????

Back

An aerospace casting

Back