© 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e KR: Chapter 7 Statistical Process Control

Chapter Outline Introduction Process control vs. acceptance sampling

Statistical Quality Control Acceptance sampling Process Control AttributesVariables Statistical Quality Control for Acceptance Sampling and for Process Control. AttributesVariables

Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Quality Control Approaches Statistical process control (SPC) Monitors production process to prevent poor quality Acceptance sampling Inspects random sample of product to determine if a lot is acceptable

Chapter Outline Introduction Process control vs. acceptance sampling Sources of process variations

Types of Variations Common Cause Random Chronic Small System problems Mgt controllable Process improvement Process capability Special Cause Situational Sporadic Large Local problems Locally controllable Process control Process stability

Variation from Common Causes

Variation from Special Causes

Chapter Outline Introduction Process control vs. acceptance sampling Sources of process variation The inspection process Quality measures

Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Types Of Data Attribute data Product characteristic evaluated with a discrete choice Good/bad, yes/no Variable data Product characteristic that can be measured Length, size, weight, height, time, velocity

Chapter Outline Introduction Process control vs. acceptance sampling Sources of process variation The inspection process Quality measures Sampling vs. screening

Sampling vs. Screening Sampling When you inspect a subset of the population Screening When you inspect the whole population The costs consideration

Chapter Outline Introduction Process control vs. acceptance sampling Sources of process variation The inspection process Quality measures Sampling vs. screening Control charts

Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Statistical Process Control Take periodic samples from process Plot sample points on control chart Determine if process is within limits Prevent quality problems

Control Charts Function of control charts Theoretical foundation of control charts Control charts for variables: Mean (x-bar) chart Range (R) chart Control charts for attribute p-chart c-chart

Common Causes Grams (a) Location Average Figure 7.2

Assignable Causes (a) Location Grams Average Figure 7.2

Assignable Causes (b) Spread Grams Average Figure 7.2

The Normal Distribution Mean  = Standard deviation Figure 7.5

The Normal Distribution Mean 68.26% -1  +1   = Standard deviation Figure 7.5

The Normal Distribution -2  -1  +1  +2  Mean 68.26% 95.44%  = Standard deviation Figure 7.5

The Normal Distribution -3  -2  -1  +1  +2  +3  Mean 68.26% 95.44% 99.74%  = Standard deviation Figure 7.5

Control Charts UCL Nominal LCL Samples Figure 7.6

Control Charts UCL Nominal LCL Samples Figure 7.6

Control Charts UCL Nominal LCL Assignable causes likely Samples Figure 7.6

X-R CHART INTERPRETATION “ Out-of-Control” X I.OUTSIDE THE CONTROL LIMITS Rule: The process is “out-of-control” anytime an X is outside the control limits. UCL LCL x UCL x LCL Process “in-control” for averages Process “out-of- control” for averages (a point beyond the control limits)

X-R CHART INTERPRETATION “ Out-of-Control” X II.RUNS Rule: The existence of seven or more consecutive averages (X’s) above the process average (X), or seven or more consecutive averages (X’s) below the process average (X), represents an “out-of-control” condition. UCL LCL x Process not in control for averages (long runs both above and below the average)

X-R CHART INTERPRETATION “ Out-of-Control” X II.RUNS Rule: Seven or more averages (X’s) constantly moving either up or down indicate an “out-of control” situation UCL LCL x Process “out-of-control” for averages (long runs up)

X-R CHART INTERPRETATION “ Out-of-Control” X III.PATTERNS Rule: The pattern of X’s between the control limits should follow a normal distribution If we look at the middle third between our control limits, we should expect to find two-thirds of our X’s to be within this area. UCL LCL x Process “out-of-control” for averages (points too close to the control limits)) Middle third

X-R CHART INTERPRETATION “ Out-of-Control” X III.PATTERNS Rule: The pattern of X’s between the control limits should follow a normal distribution If we look at the middle third between our control limits, we should expect to find two-thirds of our X’s to be within this area. UCL LCL x Process “out-of-control” for averages (points too close to the process average) Middle third

Chapter Outline Introduction Process control vs. acceptance sampling Sources of process variation The inspection process Quality measures Sampling vs. screening Control charts Process capability

Process Control

Process Capability

Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Process Capability Process cannot meet specifications Process can meet specifications Process capability exceeds specifications PROCESS Natural variation limits Natural variation limits Natural variation limits Design specifications Design specifications Design specifications

Process Capability Nominal value Hours Upper specification Lower specification Process distribution (a) Process is capable Figure 7.13

Process Capability Lower specification Mean Upper specification Two sigma Nominal value Figure 7.14

Process Capability Lower specification Mean Upper specification Four sigma Two sigma Nominal value Figure 7.14

Process Capability Lower specification Mean Upper specification Six sigma Four sigma Two sigma Nominal value Figure 7.14

Sample Means and the Process Distribution 425 Grams Mean Process distribution Distribution of sample means Figure 7.4