Operations Management

Transcription

1 10-1 Quality Control Operations Management William J. Stevenson 8 th edition 10-2 Quality Control CHAPTER 10 Quality Control McGraw-Hill/Irwin Operations Management, Eighth Edition, by William J. Stevenson Copyright 2005 by The McGraw-Hill Companies, Inc. All rights reserved Quality Control Phases of Quality Assurance Figure 10.1 Inspection before/after production Acceptance sampling Inspection and corrective action during production Process control Quality built into the process Continuous improvement The least progressive The most progressive

2 10-4 Quality Control Figure 10.2 Inspection How Much/How Often Where/When Centralized vs. On-site Inputs Transformation Outputs Acceptance sampling Process control Acceptance sampling 10-5 Quality Control Figure 10.3 Inspection Costs Cost Total Cost Cost of inspection Optimal Amount of Inspection Cost of passing defectives 10-6 Quality Control Where to Inspect in the Process Raw materials and purchased parts Finished products Before a costly operation Before an irreversible process Before a covering process

3 10-7 Quality Control Examples of Inspection Points Table 10.1 Type of business Fast Food Hotel/motel Inspection points Cashier Counter area Eating area Building Kitchen Parking lot Accounting Building Main desk Supermarket Cashiers Deliveries Characteristics Accuracy Appearance, productivity Cleanliness Appearance Health regulations Safe, well lighted Accuracy, timeliness Appearance, safety Waiting times Accuracy, courtesy Quality, quantity 10-8 Quality Control Statistical Process Control: Statistical evaluation of the output of a process during production Quality of Conformance: A product or service conforms to specifications 10-9 Quality Control Control Chart Control Chart Purpose: to monitor process output to see if it is random A time ordered plot representative sample statistics obtained from an on going process (e.g. sample means) Upper and lower control limits define the range of acceptable variation

4 10-10 Quality Control Figure 10.4 Control Chart Abnormal variation due to assignable sources Out of control UCL Normal variation due to chance Abnormal variation due to assignable sources Mean LCL Sample number Quality Control Statistical Process Control The essence of statistical process control is to assure that the output of a process is random so that future output will be random Quality Control Statistical Process Control The Control Process Define Measure Compare Evaluate Correct Monitor results

5 10-13 Quality Control Statistical Process Control Variations and Control Random variation: Natural variations in the output of a process, created by countless minor factors Assignable variation: A variation whose source can be identified Quality Control Sampling Distribution Figure 10.5 Sampling distribution Process distribution Mean Quality Control Figure 10.6 Normal Distribution σ = Standard deviation 3σ 2σ Mean +2σ +3σ 95.44% 99.74%

6 10-16 Quality Control Figure 10.7 Control Limits Sampling distribution Process distribution Mean Lower control limit Upper control limit Quality Control SPC Errors Type I error Concluding a process is not in control when it actually is. Type II error Concluding a process is in control when it is not Quality Control Figure 10.8 Type I Error α/2 α/2 α = Probability of Type I error LCL Mean UCL

7 10-19 Quality Control Observations from Sample Distribution Figure 10.9 UCL LCL Sample number Quality Control Control Charts for Variables Variables generate data that are measured. Mean control charts Used to monitor the central tendency of a process. X bar charts Range control charts Used to monitor the process dispersion R charts Quality Control Mean and Range Charts Figure 10.10A Sampling Distribution (process mean is shifting upward) UCL x-chart Detects shift LCL R-chart UCL LCL Does not detect shift

8 10-22 Quality Control Figure 10.10B Mean and Range Charts Sampling Distribution (process variability is increasing) x-chart UCL LCL Does not reveal increase UCL R-chart LCL Reveals increase Quality Control Control Chart for Attributes p-chart - Control chart used to monitor the proportion of defectives in a process c-chart - Control chart used to monitor the number of defects per unit Attributes generate data that are counted Quality Control Table 10.3 Use of p-charts When observations can be placed into two categories. Good or bad Pass or fail Operate or don t operate When the data consists of multiple samples of several observations each

9 10-25 Quality Control Table 10.3 Use of c-charts Use only when the number of occurrences per unit of measure can be counted; nonoccurrences cannot be counted. Scratches, chips, dents, or errors per item Cracks or faults per unit of distance Breaks or Tears per unit of area Bacteria or pollutants per unit of volume Calls, complaints, failures per unit of time Quality Control Use of Control Charts At what point in the process to use control charts What size samples to take What type of control chart to use Variables Attributes Quality Control Run Tests Run test a test for randomness Any sort of pattern in the data would suggest a non-random process All points are within the control limits - the process may not be random

10 10-28 Quality Control Nonrandom Patterns in Control charts Figure Trend Cycles Bias Mean shift Too much dispersion Quality Control Counting Runs Figure Counting Above/Below Median Runs (7 runs) B A A B A B B B A A B Figure Counting Up/Down Runs (8 runs) U U D U D U D U U D Quality Control Process Capability Tolerances or specifications Range of acceptable values established by engineering design or customer requirements Process variability Natural variability in a process Process capability Process variability relative to specification

11 10-31 Quality Control Figure Lower Specification Process Capability Upper Specification A. Process variability matches specifications Lower Specification Upper Specification B. Process variability well within specifications Lower Upper Specification Specification C. Process variability exceeds specifications Quality Control Process Capability Ratio Process capability ratio, Cp = specification width process width Cp = Upper specification lower specification 6σ Quality Control 3 Sigma and 6 Sigma Quality Lower specification Upper specification 1350 ppm 1350 ppm 1.7 ppm 1.7 ppm Process mean +/- 3 Sigma +/- 6 Sigma

12 10-34 Quality Control Improving Process Capability Simplify Standardize Mistake-proof Upgrade equipment Automate Quality Control Taguchi Loss Function Figure Cost Traditional cost function Taguchi cost function Lower spec Target Upper spec Quality Control Limitations of Capability Indexes 1. Process may not be stable 2. Process output may not be normally distributed 3. Process not centered but C p is used

13 10-37 Quality Control CHAPTER 10 Additional PowerPoint slides contributed by Geoff Willis, University of Central Oklahoma Quality Control Statistical Process Control (SPC) Invented by Walter Shewhart at Western Electric Distinguishes between common cause variability (random) special cause variability (assignable) Based on repeated samples from a process Quality Control Empirical Rule % 95% 99.7%

14 10-40 Quality Control Control Charts in General Are named according to the statistics being plotted, i.e., X bar, R, p, and c Have a center line that is the overall average Have limits above and below the center line at ± 3 standard deviations (usually) Upper Control Limit (UCL) Center line Lower Control Limit (LCL) Quality Control Variables Data Charts Process Centering X bar chart X bar is a sample mean Process Dispersion (consistency) R chart R is a sample range X n i= = 1 n X R = max( X i ) min( X ) i i Quality Control X bar charts Center line is the grand mean (X double bar) Points are X bars UCL = X + zσ x -OR- σ = σ / x n X LCL = X zσ UCL = X + A2 R LCL = X A2 R x m j= = 1 m X j

15 10-43 Quality Control R Charts Center line is the grand mean (R bar) Points are R D 3 and D 4 values are tabled according to n (sample size) UCL = D4 R LCL = D3 R Quality Control Use of X bar & R charts Charts are always used in tandem Data are collected (20-25 samples) Sample statistics are computed All data are plotted on the 2 charts Charts are examined for randomness If random, then limits are used forever Quality Control Attribute Charts c charts used to count defects in a constant sample size c = n m c i =1 = centerline UCL = c + z LCL = c z c c

16 10-46 Quality Control Attribute Charts p charts used to track a proportion (fraction) defective p n i= i = 1 n x i p = m p j =1 ij = = m x nm centerline UCL = p + z p( 1 p) n LCL = p z p( 1 p) n Quality Control Process Capability The ratio of process variability to design specifications Natural data spread -1σ +2σ -2σ +1σ +3σ -3σ µ The natural spread of the data is 6σ Lower Spec Upper Spec