Statistical Process Control SCM Pearson Education, Inc. publishing as Prentice Hall

Transcription

1 S6 Statistical Process Control SCM 352

2 Outline Statistical Quality Control Common causes vs. assignable causes Different types of data attributes and variables Central limit theorem SPC charts Control charts for variables Control charts for attribute

3 Statistical Process Control (SPC) The objective of a process control system is to provides a statistical signal when assignable causes are present Variability is inherent in every process Natural or common causes Special or assignable causes Detect and eliminate assignable causes of variation

4 Natural Variations Also called common causes Affect virtually all production processes Expected amount of variation Output measures follow a probability distribution For any distribution there is a measure of central tendency and dispersion If the distribution of outputs falls within acceptable limits, the process is said to be in control A process with only natural variations is in statistical control

5 Assignable Variations Also called special causes of variation Generally this is some change in the process Variations that can be traced to a specific reason Operators errors Defective raw materials Improperly adjusted machines The objective is to discover when assignable causes are present Eliminate the bad causes Incorporate the good causes

6 Natural & Assignable Variation

7 Types of Data Variables Characteristics that you measure, e.g., weight, length May be in whole or in fractional numbers Continuous random variables Attributes Characteristics for which you focus on defects Classify products as either good or bad, or count number of defects e.g., radio works or not Categorical or discrete random variables

8 Theoretical Basis of Control Charts Central Limit Theorem As sample size gets large enough, sampling distribution becomes almost normal regardless of population distribution. X X

9 The Normal Distribution σ = Standard deviation Mean -3σ -2σ -1σ +1σ +2σ +3σ 68.26% 95.44% 99.74%

10 Control Charts for Variables For variables that have continuous dimensions Weight, speed, length, etc. x-charts are to control the central tendency of the process R-charts are to control the dispersion of the process These two charts must be used together

11 Setting Chart Limits For x-charts Upper control limit (UCL) = x + A 2 R Lower control limit (LCL) = x - A 2 R where R = average range of the samples A 2 = control chart factor found in Table S6.1 x = mean of the sample means

12 Control Chart Factors Sample Size Mean Factor Upper Range Lower Range n A 2 D 4 D Table S6.1

13 Setting Chart Limits For R-Charts Upper control limit (UCL R ) = D 4 R Lower control limit (LCL R ) = D 3 R where R = average range of the samples D 3 and D 4 = control chart factors from Table S6.1

14 Control Charts for Variables Special Metal Screw Time Sample Taken Range Mean 7 am am am am am Average

15 Control Charts for Variables Special Metal Screw Time Sample Taken Range Mean 7 am am am am am Average

16 Control Charts for Variables Control Charts - Special Metal Screw R - Charts R = UCL R = D 4 R = 2.282(0.0021) = LCL R = D 3 R = 0(0.0021) = 0

17 Control Chart Factors Sample Size Mean Factor Upper Range Lower Range n A 2 D 4 D Table S6.1

18 Range Chart - Special Metal Screw UCL R = Range (in.) LCL R = Sample number R =

19 Control Charts for Variables Control Charts - Special Metal Screw x - Charts R = x = UCL x = x + A 2 R = (0.0021) LCL x = x - A 2 R = (0.0021) UCL = LCL =

20 Control Chart Factors Sample Size Mean Factor Upper Range Lower Range n A 2 D 4 D Table S6.1

21 x Chart - Special Metal Screw Average (in.) UCL x = x = LCL x = Sample number

22 Thank You Questions??