Statistical Quality Control/Statistical Process Control Acceptance Sampling Operating Characteristic Curve Process Control Procedures Variable data Attribute or Characteristic data Process Capability 2 2

Basic Forms of Statistical Sampling for Quality Control Sampling to accept or reject the immediate lot of product at hand (Acceptance Sampling). Sampling to determine if the process is within acceptable limits (Statistical Process Control) 3 3

Acceptance Sampling Purposes Advantages Determine quality level Ensure quality is within predetermined level Advantages Economy Less handling damage Fewer inspectors Upgrading of the inspection job Applicability to destructive testing Entire lot rejection (motivation for improvement) 4 4

Acceptance Sampling Disadvantages Risks of accepting “bad” lots and rejecting “good” lots Added planning and documentation Sample provides less information than 100-percent inspection 5 5

Statistical Sampling--Data Attribute (Go no-go information) Defectives--refers to the acceptability of product across a range of characteristics. Defects--refers to the number of unacceptable conditions per unit--may be higher than the number of defectives. Variable (Continuous) Usually measured by the mean and the standard deviation. 6 6

Acceptance Sampling--Single Sampling Plan A simple goal Determine (1) how many units, n, to sample from a lot, and (2) the maximum number of defective items, c, that can be found in the sample before the lot is rejected. 7 7

Risk Acceptable Quality Level (AQL) (Producer’s risk) Max. acceptable percentage of defectives defined by producer. (Producer’s risk) The probability of rejecting a good lot. Lot Tolerance Percent Defective (LTPD) Percentage of defectives that defines consumer’s rejection point.  (Consumer’s risk) The probability of accepting a bad lot. 8 8

Example: Acceptance Sampling Zypercom, a manufacturer of video interfaces, purchases printed wiring boards from an outside vender, Procard. Procard has set an acceptable quality level of 1% and accepts a 5% risk of rejecting lots at or below this level. Zypercom considers lots with 3% defectives to be unacceptable and will assume a 10% risk of accepting a defective lot. Develop a sampling plan for Zypercom and determine a rule to be followed by the receiving inspection personnel. 10 10

Sorting It Out For this example, how do we determine AQL? ? LTPD? ? 11 11

Example: Continued n (AQL) = 3.286 How can we determine the value of n? What is our sampling procedure? c LTPD/AQL n AQL 44.890 0.052 5 3.549 2.613 1 10.946 0.355 6 3.206 3.286 2 6.509 0.818 7 2.957 3.981 3 4.890 1.366 8 2.768 4.695 4 4.057 1.970 9 2.618 5.426 Exhibit TN 7.10 12 12

Example: Continued c = 6, from Table; c is also called acceptance number n (AQL) = 3.286, from Table AQL = .01, given in problem n(AQL/AQL) = 3.286/.01 = 328.6, or 329 (always round up) Sampling Procedure: Take a random sample of 329 units from a lot. Reject the lot if more than 6 units are defective. 13 13

Operating Characteristic Curve AQL LTPD 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2 3 4 5 6 7 8 9 10 11 12 Percent defective Probability of acceptance =.10 (consumer’s risk) = .05 (producer’s risk) 9 9

Chance Versus Assignable Variation Chance variation is variability built into the system. Assignable variation occurs because some element of the system or some operating conditions are out of control. Quality control seeks to identify when assignable variation is present so that corrective action can be taken.

Control Based on Attributes and Variables Inspection for Variables: measuring a variable that can be scaled such as weight, length, temperature, and diameter. Inspection of Attributes: determining the existence of a characteristic such as acceptable-defective, timely-late, and right-wrong.

Control Charts: Assumptions Developed in 1920s to distinguish between chance variation in a system and variation caused by the system’s being out of control - assignable variation.

Control Charts - Assumptions continued Repetitive operation will not produce exactly the same outputs. Pattern of variability often described by normal distribution. Random samples that fully represent the population being checked are taken. Sample data plotted on control charts to determine if the process is still under control.

Control Chart with Limits Set at Three Standard Deviations

Control Limits If we establish control limits at +/- 3 standard deviations, then we would expect 99.7% of our observations to fall within these limits x LCL UCL 15 15

Statistical Process Control The McGraw-Hill Companies, Inc., 1998 What other evidence(s) might prompt investigation? 16

Attribute Data: Constructing a p-Chart 17 17

Statistical Process Control--Attribute Measurements (P-Charts) (Std Deviation) 18 18

1. Calculate the sample proportion, p, for each sample. 19 Irwin/McGraw-Hill The McGraw-Hill Companies, Inc., 1998 19

2. Calculate the average of the sample proportions. 3. Calculate the standard deviation of the sample proportion 20 Irwin/McGraw-Hill The McGraw-Hill Companies, Inc., 1998 20

UCL = 0.1014 LCL = -0.0214 (or 0) 4. Calculate the control limits. Irwin/McGraw-Hill The McGraw-Hill Companies, Inc., 1998 21

p-Chart (Continued) 5. Plot the individual sample proportions, the average of the proportions, and the control limits UCL LCL 22 22

Variable Data Example: x-Bar and R Charts 23 23

Calculate sample means, sample ranges, mean of means, and mean of ranges. 24 24

Control Limit Formulas & Factor Table Exhibit TN 7.7 25 25

x-Bar Chart UCL LCL 26 26

R-Chart UCL LCL 27 27

Process Capability Process limits - determined from manufacturing process data. Tolerance limits - specified in engineering design drawing How do the limits relate to one another? 28 28

Process Capability TQM’s emphasis on “making it right the first time” has resulted in organizations emphasizing the ability of a production system to meet design specifications rather than evaluating the quality of outputs after the fact with acceptance sampling. Process Capability measures the extent to which an organization’s production system can meet design specifications.

Engineering Tolerance Versus Process Capability

Process Capability Depends On: Location of the process mean. Natural variability inherent in the process. Stability of the process. Product’s design requirements.

Natural Variation Versus Product Design Specifications (Look for more economical means of production) (Mean out of sync.)

Process Capability Ratio (Text calls it Index) Cp < 1: process not capable of meeting design specs Cp > 1: process capable of meeting design specs As rule of thumb, many organizations desire a Cp ratio of at least 1.5. Six sigma quality (fewer than 3.4 defective parts per million) corresponds to a Cp (index/ratio) of 2.

Effect of Production System Variability on Cp

Process Capability Index, Cpk Shifts in Process Mean 29 29

Taguchi’s View of Variation Incremental Cost of Variability High Zero Lower Spec Target Upper Traditional View Incremental Cost of Variability High Zero Lower Spec Target Upper Taguchi’s View 30 30