Quality control

Slide 1

Quality Control By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

Shakeel NoumanM.Phil Statistics

Quality Control

Slide 2

• Using Statistics• W. Edwards Deming Instructs• Statistics and Quality• The x-bar Chart• The R Chart and the s Chart• The p Chart• The c Chart• The x Chart• Summary and Review of Terms

Quality Control 13


Slide 3

A control chart is a time plot of a statistic, such as a sample mean, range, standard deviation, or proportion, with a center line and upper and lower

control limits. The limits give the desired range of values for the statistic. When the statistic is outside the bounds, or when its time plot reveals certain

patterns, the process may be out of control.

A process is considered in statistical control if it has no assignable causes, only natural variation.

UCL

LCL

CenterLine

Time

ValueThis point is out of the control limits

3

3

13-3 Statistics and Quality


Slide 4

Value

Time

Value

Time

Process is in control

Process mean varies over time: process is

out of control

Control Charts


Slide 5

Time

Value

Process variance changes over time:

process is out of control.

Time

ValueProcess mean and variance change

over time: process is out of control.

Control Charts (Continued)


Slide 6

A Pareto diagram is a bar chart of the various problems in production and their percentages, which must add to 100%.

Pareto Diagrams – Using the Template

A Pareto chart helps to identify the most significant problems

and thus one can concentrate on their solutions rather than

waste time and resources on

unimportant causes.


Slide 7

Elements of a control chart for the process mean:

Center line:

LCL: UCL: where: k = number of samples, each of size n = Sample mean for sample i Ri Range of sample i

R =Rii=1

k

kIf the sample size in each group is more than 10:

LCL = x - 3s / c4

n UCL = x + 3

s / c4n

where s is the average of the standard deviations of all groups.

xxii

k

kx A R x A R

xi

1

2 2

n A2 c4

2 1.880 0.7979 3 1.023 0.8862 4 0.729 0.9213 5 0.577 0.9400 6 0.483 0.9515 7 0.419 0.9594 8 0.373 0.9650 9 0.337 0.969310 0.308 0.972715 0.223 0.982320 0.180 0.986925 0.153 0.9896

13-4 The Chart: A Control Chart for the Process Mean X


Slide 8

• Tests for assignable causes:One point beyond 3 (3s)Nine points in a row on one side of the center lineSix points in a row steadily increasing or decreasingFourteen points in a row alternating up and downTwo out of three points in a row beyond 2 (2s)Four out of five points in a row beyond 1 (1s)Fifteen points in a row within 1 (1s) of the center lineEight points in a row on both sides of the center line, all

beyond 1 (1s)

The Chart: A Control Chart for the Process Mean (Continued)

X


Slide 9

Time

Value

112

2

3

3

Test 1: One value beyond

3 (3s)

Time

Value

112

2

3

3

Test 2: Nine points in a row on one side

of the center line.

Tests for Assignable Causes


Slide 10

Time

Value

112

2

3

3

Test 3: Six points in arow steadilyincreasing ordecreasing.

Time

Value

112

2

3

3

Test 4: Fourteen points in

a row alternating

up and down.

Tests for Assignable Causes (Continued)


Slide 11

Time

Value

112

2

3

3

Test 5: Two out of three points in a rowbeyond 2 (2s)

Time

Value

112

2

3

3

Test 6: Four out of fivepoints in a rowbeyond 1 (1s)



Slide 12

Time

Value

112

2

3

3

Test 7: Fifteen points in arow within 1

(1s) of the center

line.

Time

Value

112

2

3

3

Test 8: Eight points in arow on both

sidesof the center

line,all beyond 1 (1s)



Slide 13X-bar Chart: Example 13-1 –

Using the Template


Slide 14

X-bar Chart: Example 13-1(continued) – Using the

Template

Note: The X-bar chart cannot be interpreted unless the R or s chart has been examined and is in control.


Slide 15

n D3 D4 B3

B4

2 0 3.267 0 3.267 3 0 2.575 0 2.568 4 0 2.282 0 2.266 5 0 2.115 0 2.089 6 0 2.004 0.030 1.970 7 0.076 1.924 0.118 1.882 8 0.136 1.864 0.185 1.815 9 0.184 1.816 0.239 1.76110 0.223 1.777 0.284 1.71615 0.348 1.652 0.428 1.57220 0.414 1.586 0.510 1.49025 0.459 1.541 0.565 1.435

Elements of a control chart for the process range:Center line: RLCL: UCL:

where: R =Rii=1

k

k

D R D R3 4

Elements of a control chart for the process standarddeviation:Center line: sLCL: UCL:

where: s =sii=1

k

k

B s B s3 4

13-5 The R Chart and s Chart


Slide 16R Chart: Example 13-1 using the

Template

The process range seems to be in control.


Slide 17s Chart: Example 13-1 using the

Template

The process standard deviation seems to be in control.


Slide 18Example 13-2 using the

Template


Slide 19Example 13-2 using the Template - Continued


Slide 20Example 13-2 using the Template - Continued

Based on the x-bar, R, and s charts, the process seems to be in control.


Slide 21

Elements of a control chart for the process proportion:Center line: p

LCL: - 3p(1 - p)

n UCL: + 3

p(1 - p)n

where: n is the number of elements in each sample p is the proportion of defectives in the combined, overall sample

p p

13-6 The p Chart: Proportion of Defective Items


Slide 2213-6 The p Chart: Proportion of Defective Items – Using the Template for Example 13-3


Slide 23

Elements of a control chart for the number of imperfections per item, c:Center line: cLCL: - 3 c UCL: + 3 c where: c is the average number of defects or imperfections per item (or area, volume, etc. )

c c

13-7 The c Chart: (Defects Per Item)


Slide 24The c Chart: Example 13-4 using

the Template

Observe that one observation is outside the upper control limit, indicating that the process may be out of control. The general

downward trend should be investigated.


Slide 2513-8 The x Chart

Sometimes we are interested in controlling the process mean, but our observations come so slowly from the production process that we cannot aggregate them into groups. In such case we may consider an x chart. An x-chart is a chart for the raw values of the variable in question.

The chart is effective if the variable has an approximate normal distribution. The bounds are 3 standard deviations from the mean of the process.


Slide 26

M.Phil (Statistics)

GC University, . (Degree awarded by GC University)

M.Sc (Statistics) GC University, . (Degree awarded by GC University)

Statitical Officer(BS-17)(Economics & Marketing Division)

Livestock Production Research Institute Bahadurnagar (Okara), Livestock & Dairy Development

Department, Govt. of Punjab

Name Shakeel NoumanReligion ChristianDomicile Punjab (Lahore)Contact # 0332-4462527. 0321-9898767E.Mail [email protected] [email protected]


mailto:[email protected]

mailto:[email protected]

Date post:	11-Feb-2017
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Quality control

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