TM 720: Statistical Process Control Acceptance Sampling Plans TM 720 - Lecture 11 Acceptance Sampling Plans 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Assignment: Reading: Finish Chapter 14 Sections 14.1 – 14.2 Sections 14.4 Start Chapter 12 Assignment: Download and complete Assign 08: Acceptance Sampling Requires MS Word for Nomograph Requires MS Excel for AOQ Solutions for 8 will post on Thursday 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Acceptance Sampling 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

Three Important Aspects of Acceptance Sampling TM 720: Statistical Process Control Three Important Aspects of Acceptance Sampling Purpose is to sentence lots, not to estimate lot quality Acceptance sampling does not provide any direct form of quality control. It simply rejects or accepts lots. Process controls are used to control and systematically improve quality, but acceptance sampling is not. Most effective use of acceptance sampling is not to “inspect quality into the product,” but rather as audit tool to insure that output of process conforms to requirements. 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

Three Approaches to Lot Sentencing TM 720: Statistical Process Control Three Approaches to Lot Sentencing Accept with no inspection 100% inspection – inspect every item in the lot, remove all defectives Defectives – returned to vendor, reworked, replaced or discarded Acceptance sampling – sample is taken from lot, a quality characteristic is inspected; then on the basis of information in sample, a decision is made regarding lot disposition. 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

Acceptance Sampling Used When: TM 720: Statistical Process Control Acceptance Sampling Used When: Testing is destructive 100% inspection is not technologically feasible 100% inspection error rate results in higher percentage of defectives being passed than is inherent to product Cost of 100% inspection extremely high Vender has excellent quality history so reduction from 100% is desired but not high enough to eliminate inspection altogether Potential for serious product liability risks; program for continuously monitoring product required 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

Advantages of Acceptance Sampling over 100% Inspection TM 720: Statistical Process Control Advantages of Acceptance Sampling over 100% Inspection Less expensive because there is less sampling Less handling of product hence reduced damage Applicable to destructive testing Fewer personnel are involved in inspection activities Greatly reduces amount of inspection error Rejection of entire lots as opposed to return of defectives provides stronger motivation to vendor for quality improvements 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

Disadvantages of Acceptance Sampling (vs 100% Inspection) TM 720: Statistical Process Control Disadvantages of Acceptance Sampling (vs 100% Inspection) Always a risk of accepting “bad” lots and rejecting “good” lots Producer’s Risk: chance of rejecting a “good” lot –  Consumer’s Risk: chance of accepting a “bad” lot –  Less information is generated about the product or the process that manufactured the product Requires planning and documentation of the procedure – 100% inspection does not 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Lot Formation Lots should be homogeneous Units in a lot should be produced by the same: machines, operators, from common raw materials, approximately same time If lots are not homogeneous – acceptance-sampling scheme may not function effectively and make it difficult to eliminate the source of defective products. Larger lots preferred to smaller ones – more economically efficient Lots should conform to the materials-handling systems in both the vendor and consumer facilities Lots should be packaged to minimized shipping risks and make selection of sample units easy 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Random Sampling IMPORTANT: Units selected for inspection from lot must be chosen at random Should be representative of all units in a lot Watch for Salting: Vendor may put “good” units on top layer of lot knowing a lax inspector might only sample from the top layer Suggested technique: Assign a number to each unit, or use location of unit in lot Generate/pick a random number for each unit/location in lot Sort on the random number – reordering the lot/location pairs Select first (or last) n items to make sample 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

Single Sampling Plans for Attributes TM 720: Statistical Process Control Single Sampling Plans for Attributes Quality characteristic is an attribute, i.e., conforming or nonconforming N - Lot size n - sample size c - acceptance number Ex. Consider N = 10,000 with sampling plan n = 89 and c = 2 From lot of size N = 10,000 Draw sample of size n = 89 If # of defectives  c = 2 Accept lot If # of defectives > c = 2 Reject lot 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

How to Compute the OC Curve Probabilities TM 720: Statistical Process Control How to Compute the OC Curve Probabilities Assume that the lot size N is large (infinite) d - # defectives ~ Binomial() where p - fraction defective items in lot n - sample size Probability of acceptance: 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Example Lot fraction defective is p = 0.01, n = 89 and c = 2. Find probability of accepting lot. 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control OC Curve Performance measure of acceptance-sampling plan displays discriminatory power of sampling plan Plot of: Pa vs. p Pa = P[Accepting Lot] p = lot fraction defective p = fraction defective in lot Pa = P[Accepting Lot] 0.005 0.9897 0.010 0.9397 0.015 0.8502 0.020 0.7366 0.025 0.6153 0.030 0.4985 0.035 0.3936 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control OC Curve OC curve displays the probability that a lot submitted with a certain fraction defective will be either accepted or rejected given the current sampling plan 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Ideal OC Curve Suppose the lot quality is considered bad if p = 0.01 or more A sampling plan that discriminated perfectly between good and bad lots would have an OC curve like: 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Ideal OC Curve In theory it is obtainable by 100% inspection IF inspection were error free. Obviously, ideal OC curve is unobtainable in practice But, ideal OC curve can be approached by increasing sample size, n. 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Effect of n on OC Curve The precision with which a sampling plan differentiates between good and bad lots increases as the sample size increases 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Effect of c on OC Curve Changing acceptance number, c, does not dramatically change slope of OC curve. Plans with smaller values of c provide discrimination at lower levels of lot fraction defective 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

Producer and Consumer Risks in Acceptance Sampling TM 720: Statistical Process Control Producer and Consumer Risks in Acceptance Sampling Because we take only a sub-sample from a lot, there is a risk that: a good lot will be rejected (Producer’s Risk – a ) and a bad lot will be accepted (Consumer’s Risk – b ) 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Producer’s Risk - a Producer wants as many lots accepted by consumer as possible so Producer “makes sure” the process produces a level of fraction defective equal to or less than: p1 = AQL = Acceptable Quality Level a is the probability that a good lot will be rejected by the consumer even though the lot really has a fraction defective  p1 That is, 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Consumer’s Risk - b Consumer wants to make sure that no bad lots are accepted Consumer says, “I will not accept a lot if percent defective is greater than or equal to p2” p2 = LPTD = Lot Tolerance Percent Defective b probability bad lot is accepted by the consumer when lot really has a fraction defective  p2 That is,   4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

Designing a Single-Sampling Plan with a Specified OC Curve TM 720: Statistical Process Control Designing a Single-Sampling Plan with a Specified OC Curve Use a chart called a Binomial Nomograph to design plan Specify: p1 = AQL (Acceptable Quality Level) p2 = LTPD (Lot Tolerance Percent Defective) 1 – a = P[Lot is accepted | p = AQL] β = P[Lot is accepted | p = LTPD] 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

Use a Binomial Nomograph to Find Sampling Plan (Figure 14-9, p. 658) TM 720: Statistical Process Control Use a Binomial Nomograph to Find Sampling Plan (Figure 14-9, p. 658) Draw two lines on nomograph Line 1 connects p1 = AQL to (1- a) Line 2 connects p2 = LTPD to b Pick n and c from intersection of lines Example: Suppose p1 = 0.01, α = 0.05, p2 = 0.06, β = 0.10. Find the acceptance sampling plan. 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

Rectifying Inspection Programs TM 720: Statistical Process Control Rectifying Inspection Programs Acceptance sampling programs usually require corrective action when lots are rejected, that is, Screening rejected lots Screening means doing 100% inspection on lot In screening, defective items are Removed or Reworked or Returned to vendor or Replaced with known good items 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

Rectifying Inspection Programs TM 720: Statistical Process Control Rectifying Inspection Programs 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

Where to Use Rectifying Inspection TM 720: Statistical Process Control Where to Use Rectifying Inspection Used when manufacturer wishes to know average level of quality that is likely to result at given stage of manufacturing Example stages: Receiving inspection In-process inspection of semi-finished goods Final inspection of finished goods Objective: give assurance regarding average quality of material used in next stage of manufacturing operations 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

Average Outgoing Quality: AOQ TM 720: Statistical Process Control Average Outgoing Quality: AOQ Quality that results from application of rectifying inspection Average value obtained over long sequence of lots from process with fraction defective p N - Lot size, n = # units in sample Assumes all known defective units replaced with good ones, that is, If lot rejected, replace all bad units in lot If lot accepted, just replace the bad units in sample 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Development of AOQ If lot accepted: Number defective units in lot: Expected number of defective units: Average fraction defective, Average Outgoing Quality, AOQ: 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Example for AOQ Suppose N = 10,000, n = 89, c = 2, and incoming lot quality is p = 0.01. Find the average outgoing lot quality. 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

Military Standard 105E (MIL STD 105E) (ANSI/ASQC Z1.4, ISO 2859) TM 720: Statistical Process Control Military Standard 105E (MIL STD 105E) (ANSI/ASQC Z1.4, ISO 2859) Most widely used acceptance sampling system for attributes MIL STD 105E is Acceptance Sampling System collection of sampling schemes Can be used with single, double or multiple sampling plans We will consider single sampling plans for this course 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Inspection Types Normal Inspection Used at start of inspection activity Tightened Inspection Instituted when vendor’s recent quality history has deteriorated Acceptance requirements for lots are more stringent Reduced Inspection Instituted when vendor’s recent quality history has been exceptionally good Sample size is usually smaller than under normal inspection 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Switching Rules 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Procedure for MIL STD 105E STEP 1: Choose AQL MIL STD 105E designed around Acceptable Quality Level, AQL Recall that the Acceptable Quality Level, AQL, is producer's largest acceptable fraction defective in process Typical AQL range: 0.01%  AQL  10% Specified by contract or authority responsible for sampling 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Procedure for MIL STD 105E STEP 2: Choose inspection level Level II Designated as normal Level I Requires about one-half the amount of inspection as Level II Use when less discrimination needed Level III Requires about twice as much Use when more discrimination needed Four special inspection levels used if very small samples necessary S-1, S-2, S-3, S-4 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Procedure for MIL STD 105E STEP 3–Determine lot size, N Lot size most likely dictated by vendor STEP 4: Find sample size code letter From Table 14-4, p 675 Given lot size, N, and Inspection Level, use table to determine sample size code letters STEP 5: Determine appropriate type sampling plan Decide if Single, Double or Multiple sampling plan is to be used 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Procedure for MIL STD 105E STEP 6: Find Sample Size, n, and Acceptance Level, c Given sample size letter code, use Master Tables: 14-5, 14-6, and 14-7 on pp.676-678 Find n and c for all three inspection types: Normal Inspection Tightened Inspection Reduced Inspection 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Example Suppose product comes from vendor in lots of size 2000 units. The acceptable quality level is 0.65%. Determine the MIL STD 105E acceptance-sampling system. 4/17/2017 TM 720: Statistical Process Control (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Questions & Issues 4/17/2017 TM 720: Statistical Process Control