Statistical Process Control: Understanding Control Charts for Quality Assurance - Prof. Ro, Study notes of Production and Operations Management

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Chapter 3Chapter 3

Statistical Process

Control

Statistical ProcessStatistical Process

Control Control

• (^) Take periodic samples fromTake periodic samples from

process process

• (^) Plot sample points on aPlot sample points on a

control chart control chart

• (^) Determine if processDetermine if process

is within limits is within limits

• (^) Correct process beforeCorrect process before

defects are produced defects are produced

UCLUCL LCL LCL

VariationVariation

Common Causes Common Causes

Variation inherent in a process Can be eliminated only through improvements in the system

Special Causes Special Causes

Variation due to identifiable factors Can be modified through operator or management action

Types of DataTypes of Data

Attribute data Attribute data

Product characteristic evaluated with a discrete choice Good/bad, yes/no

Variable data Variable data

Product characteristic that can be measured Length, size, weight, height, time, velocity

p-Chartp-Chart

UCL = UCL = pp ++ zz  pp LCL = LCL = pp - - zz  pp where where z z == the number of standardthe number of standard deviations from the process average deviations from the process average p p == the sample percentthe sample percent defective; an estimate of the process defective; an estimate of the process average average  pp ==^ the standard deviation ofthe standard deviation of the sample proportion the sample proportion  pp == pp (1 -(1 - pp )) nn

p-Chart Examplep-Chart Example

20 samples of 20 samples of 100100 pairs of jeanspairs of jeans

NUMBER OF NUMBER OF PROPORTIONPROPORTION

SAMPLESAMPLE DEFECTIVESDEFECTIVES DEFECTIVEDEFECTIVE

11 66 6/6/ (^100100) = .06=. 22 00 .00. 33 44 .04. : : :: :: : : :: :: 2020 1818 .18. Total 200 Total 200 Avg .10Avg.

0.020. 0.040. 0.060. 0.080. 0.100. 0.120. 0.140. 0.160. 0.180. 0.200. Proportion defectiveProportion defective Sample numberSample number 22 44 66 88 1010 1212 1414 1616 1818 2020 UCL = 0. LCL = 0. p = 0. Is the process in control? No! Pts are outside the limits.

c-Chartc-Chart

UCL = UCL = cc ++ zz  cc LCL = LCL = cc - - zz  cc where c = number of defects per sample   cc == cc

c-Chartc-Chart

33 66 99 1212 (^1515) 1818 2121 (^2424) Number of defectsNumber of defects Sample number Sample number 22 44 66 88 1010 1212 1414 1616 UCL = 23. LCL = 1. c = 12. Is this process in control? Yes

Control ChartsControl Charts

for Variables for Variables

 Mean chart ( X-bar Chart )

 (^) uses average of a sample

 Range chart ( R Chart )

 (^) uses amount of dispersion in a sample

X-bar Chart ExampleX-bar Chart Example

OBSERVATIONS (SLIP- RING DIAMETER, CM)

SAMPLE k 1 2 3 4 5 x- bar R

Total 50.09 1.

X-bar is the average of each row.

R is the range, i.e., the difference between the largest and smallest value in a row.

UCL = x + A 2 R = 5.01 + (0.58)(0.115) = 5. LCL = x - A 2 R = 5.01 - (0.58)(0.115) = 4. = = x = = = 5.01 cm =  x k

10 X- bar Chart X- bar Chart Calculations Calculations Lookup A 2 from the table (on next slide) by sample size Look back at the data (on previous slide). There are 10 samples. The size of each sample is 5. X-bar-bar is the average of the x’s

X- barX- bar Chart Chart

UCL = 5.

LCL = 4.

Mean Sample number

x = 5.

Is this process in control? Yes, pt 9 is on the line, not over it.

R- ChartR- Chart

UCL = UCL = DD

(^44)

RR LCL =LCL = DD

(^33)

RR

R R ==

RR

k k

where where R R = range of each sample= range of each sample k k = number of samples= number of samples D D (^33) , D, D 44 = values from table= values from table