Quality Control

Ross L. Fink

Quality Control

Quality control involves controlling the delivery processes to adhere to the specifications (or product design).

Quality Control Approaches

100 % Inspection Acceptance Sampling Statistical Process Control (SPC) or

Control-Chart Method

Acceptance Sampling

Production Lot or Batch

Sample

Accept or Reject Entire Lot Based Upon Quality of Sample

Statistical Process Control

Basic Approach– Take one sample of size 5 each hour– Measure quality characteristic– Plot measurement over time (sample number)

Run Chart

Distribution of Measurement on Control Chart Since we are taking a mean, the Central

Limit Theorem of the Sample Mean applies Therefore, mean follows a normal

distribution. Three Sigma Limits

Plot of Mean

Theory of Control Charts

Purpose of control charts is to separate natural variability (common cause) from nonrandom variability (assignable cause).

In-control (common cause) versus out-of-control (assignable cause).

Types of Variability

X-bar Chart

Control Chart Rules

Simple Rules– One point above UCL– One point below LCL

Most organizations use more complex rules– e.g., seven consecutive points increasing

Constructing a Control Chart Obs. 1 2 3 4 5 Sample 1 11.63 14.44 14.52 17.58 12.71 2 13.30 16.21 15.04 16.09 14.19 3 12.60 11.49 14.73 15.58 17.41 4 13.68 13.49 13.24 16.98 16.23 5 15.12 15.21 11.69 14.91 16.36 6 15.70 16.09 16.78 15.48 14.56 7 13.46 14.28 17.09 13.84 15.85 8 14.22 13.90 14.47 15.18 19.31 9 12.44 15.12 16.00 14.62 16.05 10 14.04 14.88 19.26 14.37 16.35 11 12.42 13.25 15.56 15.18 14.13 12 15.65 12.94 16.16 15.98 18.67 13 15.71 13.78 14.19 16.02 13.78 14 14.80 12.17 16.00 12.93 12.34 15 15.63 12.14 14.98 16.61 14.21 16 10.13 15.43 17.09 17.72 18.72 17 13.73 15.26 13.53 14.43 15.22 18 11.44 17.00 13.72 13.11 13.80 19 10.72 10.12 15.80 19.72 11.72 20 15.43 15.00 15.58 14.99 15.40

Find Sample Means and Ranges Obs. 1 2 3 4 5 Mean Range Sample 1 11.63 14.44 14.52 17.58 12.71 14.18 5.95 2 13.30 16.21 15.04 16.09 14.19 14.96 2.93 3 12.60 11.49 14.73 15.58 17.41 14.36 5.92 4 13.68 13.49 13.24 16.98 16.23 14.72 3.75 5 15.12 15.21 11.69 14.91 16.36 14.66 4.67 6 15.70 16.09 16.78 15.48 14.56 15.72 2.22 7 13.46 14.28 17.09 13.84 15.85 14.90 3.63 8 14.22 13.90 14.47 15.18 19.31 15.42 5.39 9 12.44 15.12 16.00 14.62 16.05 14.85 3.62 10 14.04 14.88 19.26 14.37 16.35 15.78 5.22 11 12.42 13.25 15.56 15.18 14.13 14.11 3.14 12 15.65 12.94 16.16 15.98 18.67 15.88 5.72 13 15.71 13.78 14.19 16.02 13.78 14.70 2.23 14 14.80 12.17 16.00 12.93 12.34 13.65 3.83 15 15.63 12.14 14.98 16.61 14.21 14.71 4.47 16 10.13 15.43 17.09 17.72 18.72 15.82 8.59 17 13.73 15.26 13.53 14.43 15.22 14.43 1.73 18 11.44 17.00 13.72 13.11 13.80 13.81 5.56 19 10.72 10.12 15.80 19.72 11.72 13.61 9.60 20 15.43 15.00 15.58 14.99 15.40 15.28 0.59

Calculate Grand Mean and Grand Range

44.4

78.14

R

X

Control Limits

RDLCL

RDUCL

RLCLUCLR

RAXXLCLUCLX

R

R

RRR

XXX

3

4

2

3,:

3,:

Table

Factors for Computing Control Chart Limits Sample Size Mean Factor Upper Range Lower Range

– N A2 D4 D3– 2 1.880 3.268 0– 3 1.023 2.574 0– 4 .729 2.282 0– 5 .577 2.115 0– 6 .483 2.004 0– 7 .419 1.924 0.076– 8 .373 1.864 0.136– 9 .337 1.816 0.184– 10 .308 1.777 0.223

Control Limits

00.0)44.4(0

39.9)44.4(115.2

22.12,34.17

)44.4(577.78.14,

R

R

XX

LCL

UCL

LCLUCL

X-bar Chart

R Chart

In-Control v. Out-Of-Control

What are the implications of being in-control?

What are the implications of being out-of-control?