BUs HEC Ranking

Acceptance Sampling1MEC-7Why Acceptance Sampling?Acceptance Sampling refers to the process of randomly inspecting or testing a certain number of items from a Lot or Batch in order to decide whether to accept or reject the entire Lot or BatchAcceptance Sampling done because:Inspection/Testing of entire Lot time-consuming, overly expensive and even, at times, impracticableSome testing, if not most, is destructive2Agile, Waterfall2Sampling PlanSampling is done to a plan, called the Acceptance Sampling PlanA Sampling Plan precisely specifies the parameters of the sampling process and the acceptance/rejection criteria, in terms of:Size of the Lot (N)Size of the Sample picked randomly from the lot (n)The number of defectives in the Sample above which the Lot will be rejected (c)The number of sample that will be drawnTypes:SingleDoubleMultiple/SequentialAcceptance is at the confluence of Quality Management, Risk Management and Monitoring & Control

3Agile, Waterfall3Representative SampleSampling assumes a Representative Sample i.e. the proportion of defectives in the Lot is reflected in the Sample. If the Lot has d% defects, the Sample is also expected to have d% defectsUnrepresentative Sample has following implications:If Sample has less than d% defects, MORE the chances of its acceptance (disadvantage to the Customer)If Sample has more than d% defects, LESS the chances of its acceptance (disadvantage to the Supplier)

4Agile, Waterfall4Understanding the ConceptA consignment of 10,000 bricks is ready at the brick kiln for transportation to the project site. The scope called for the bricks to clear 1,500 psi breaking strength. The sample acceptance plan calls for subjecting a random single 100 brick sample to breaking test. The entire lot will be accepted if 5 or less bricks fail the test. The entire lot will be rejected if more than 5 bricks fail the test. In this case:N = 10,000 n = 100c = 5Assume there were actually 90 defective bricks in the entire lot. Customer obviously does not know about them. Most likely, the supplier would not know it eitherWhat if the sample is NOT representative of the lot?If all the 90 defective bricks fall into the sample, the entire lot will be rejected. Will it be fair to the supplier? If none of the 90 defective bricks fall into the sample, the lot will be accepted. Does it give the customer a fair assessment of the quality of the entire lot? This brings in the RISK factor and gives rise to the concepts of AQL, LTPD, -risk, -risk and the OC curve

5Agile, Waterfall5AQL & LTPDAcceptable Quality Level (AQL). The small percentage of defects a Consumer is willing to accept in a lot. Generally, 1-2%. For example, in this case, the Customer may be willing to accept 1%, i.e. 100 defective bricks. This will be AQL. Lot Tolerance Percent Defective (LTPD). A percentage of defective items, above the AQL, up to which a customer will accept the lot for certain reasons, like trading quality for time. For example, the Customer may be willing to accept 5% defective bricks, i.e. 500 on the structural engineers advice that 500 weaker bricks in 10,000 will have negligible effect on the structure. So, 5% will be the LTPD6Agile, Waterfall6-Risk, -RiskAdequate safeguards need to be incorporated in Acceptance Sampling to safeguard the interests of the Customer and the Supper, against the risk of the Unrepresentative Sample. This is done through -Risk and -Risk, both expressed as a probability or percentage-Risk (Suppliers Risk/Type-I Error) is the risk that the Customer will REJECT a lot with the number of defects LESS than the AQL. -Risk is usually taken as 5% (same is being considered for this example)-Risk (Customers Risk/Type-I Error) is the risk that the Customer will ACCEPT a lot with the number of defects MORE than the LTPD. -Risk is usually taken as 10% (same is being considered for this example)7Agile, Waterfall7OC CurveThe Operating Characteristic (OC) Curve links all the parameters of the Acceptance Sampling Plan: N, n, c, AQL and LTPD, to determine the -Risk and -RiskThe curve helps manipulate the sample size (n) and the acceptance figure (c) to help bring the -Risk and -Risk within acceptable limitsMore the defective items, greater the chance of their appearing in the Acceptance Sample and, therefore, less the chance of their acceptance by the CustomerThe curve is constructed using probabilities. Well use the probabilities from the Poisson TablesPoisson gives the chance (probability) of acceptance of the lot by the Customer, using n, Percent Defects (d) in the Lot and the Acceptance Level (c)Poisson gives acceptance probability figures for the product np under various values of c. The product np is also called the Poisson Mean ()8Agile, Waterfall8Complete Acceptance Sampling Plan & OC CurveAn order for supply of 2,000 electrical fans has been placed on a Supplier. The agreed acceptance sampling plan calls for a random sample of 120 fans with an acceptance level of 3. AQL has been settled at 2% defectives. The Project Manager is willing to accept up to 6% defectives in the lot.

How much is the risk/chance that a GOOD LOT of fans supplied by the Supplier will be REJECTED by the Project Manager, and a BAD LOT supplied by the Supplier will be ACCEPTED by the Project Manager?

If the Supplier is not willing to take more than 5% risk that his supplied GOOD LOT will be REJECTED by the Project Manager, and the Project Manager is not willing to take more than 10% risk that he will ACCEPT a BAD LOT landed by the Supplier, does the given plan meet the Suppliers and Project Managers risk limits?9N=2,000n=120c=3-Risk = 5% = 0.05AQL = 2% = 0.02-Risk = 10% = 0.10LTPD =6% = 0.06Agile, Waterfall9Complete Acceptance Sampling Plan & OC Curve10Proportion Defective (p)npProbability of c or less defectsRemarks0.010.02 (AQL)0.030.040.050.06 (LTPD)0.070.080.090.101.22.43.64.86.07.28.49.610.812.00.9660.7790.5150.2940.1510.0720.0320.0140.0060.0021-; = 1-0.779 = 0.221

N=2,000n=120c=3-Risk = 5% = 0.05AQL = 2% = 0.02-Risk = 10% = 0.10LTPD = 6% = 0.06Agile, Waterfall10Complete Acceptance Sampling Plan & OC Curve11Agile, Waterfall11Complete Acceptance Sampling Plan & OC Curve12 = 1-0.779 = 0.221 = 0.072At 22.1%, -Risk is well outside the Supplier limit of 5%At 7.2 %, -Risk is well inside the Consumer limit of 10%Adjust n & c to bring the and risks within the limitsAgile, Waterfall12Complete Acceptance Sampling Plan & OC Curve13Proportion Defective (p)n = 120, c = 3npProbability of c or less defectsRemarks0.010.02 (AQL)0.030.040.050.06 (LTPD)0.070.080.090.101.22.43.64.86.07.28.49.610.812.00.9660.7790.5150.2940.1510.0720.0320.0140.0060.002 = 0.221

N=2,000n=120 200c=3 7-Risk = 5% = 0.05AQL = 2% = 0.02-Risk = 10% = 0.10LTPD = 6% = 0.06n = 200, c = 7npProbability of c or less defectsRemarks2.04.06.08.010.012.014.016.018.020.00.9990.9490.7440.4530.2200.0900.0320.0100.0030.001 = 0.051

Agile, Waterfall13Complete Acceptance Sampling Plan & OC Curve14The Suppliers Risk (-Risk) has reduced to 5.1% from the previous 22.1%The Consumers Risk ( -Risk) has increased to 9.0% from the previous 7.2%, but still within limitsBy adjusting the Sample Size (n) and the Acceptance Level (c), the Suppliers and Consumers risk have modified as follows:n=120, c=3n=200, c=7By fine-tuning the curve, the risks cannot be brought down into exact limits. In this case, n=196 and c=7 will return an -Risk of 4.6% and -Risk of 9.9%, both of which are within limits and offer a perfect combinationAgile, Waterfall14Effect of Changing n and c on Acceptance SamplingA project manager has received a shipment of 1,000 items for the project. The sampling plan for inspecting these items calls for a sample size n=60 and an acceptance number c=1. The contract with the supplier calls for an AQL of 1 defective item per 100 and an LTPD of 6 defective items per 100. Construct the OC curve for this plan, and determine the suppliers and the consumers risk for the plan

15N=1,000n=60c=1AQL = 1% = 0.01LTPD = 6% = 0.06Agile, Waterfall15Effect of Changing n and c on Acceptance Sampling16Proportion Defective (p)npProbability of c or less defectsRemarks0.01 (AQL)0.020.030.040.050.06 (LTPD)0.070.080.090.100.61.21.82.43.03.64.24.85.46.00.8780.6630.4630.3080.1990.1260.0780.0480.0290.0171-; = 1-0.779 = 0.221

N=1,000n=60c=1AQL = 1% = 0.01LTPD = 6% = 0.06Agile, Waterfall16What is Monitoring & Controlling Risks?17c n 1600.1220.126Agile, Waterfall17Effect of Changing n and c on Acceptance Sampling18pn = 60n = 80n = 100n = 120npProbnpProbnpProbnpProb0.01 (AQL)0.020.030.040.050.06 (LTPD)0.070.080.090.100.61.21.82.43.03.64.24.85.46.00.8780.6630.4630.3080.1990.1260.0780.0480.0290.0170.81.62.43.24.04.85.66.47.28.00.8090.5250.3080.1710.0920.0480.0240.0120.0060.0031.02.03.04.05.06.07.08.09.010.00.7360.4060.1990.0920.0400.0170.0070.0030.0010.0001.22.43.64.86.07.28.49.610.812.00.6630.3080.1260.0480.0170.0060.0020.0010.0000.000N=1,000n=60, 80, 100, 120c=1AQL = 1% = 0.01LTPD = 6% = 0.06Increasing the Sample Size increases the Suppliers Risk and reduces the Customers RiskAgile, Waterfall18Acceptance Number Same - Effect of Increasing Sample Size19n=60, c=1n=80, c=1n=100, c=1n=120, c=1c n 1600.1220.1261800.1910.04811000.2640.01711200.3320.006Increasing the Sample Size increases the Suppliers Risk and reduces the Customers RiskAgile, Waterfall19Effect of Changing n and c on Acceptance Sampling20pc = 1c = 2c = 3c = 4npProbProbProbProb0.01 (AQL)0.020.030.040.050.06 (LTPD)0.070.080.090.100.61.21.82.43.03.64.24.85.46.00.8780.6630.4630.3080.1990.1260.0780.0480.0290.0170.9770.8790.7310.5700.4230.3030.2100.1430.0950.0620.9970.9660.8910.7790.6470.5150.3950.2940.2130.1511.0000.9920.9640.9040.8150.7060.5900.4760.3730.285N=1,000n=60c=1, 2, 3, 4AQL = 1% = 0.01LTPD = 6% = 0.06Increasing the Acceptance Level reduces the Suppliers Risk and increases the Customers RiskAgile, Waterfall20Sample Size Same - Effect of Increasing Acceptance Number21n=60, c=1n=60, c=2n=60, c=3n=60, c=4cn 1600.1220.1262600.0230.3033600.0030.5154600.0000.706Increasing the Acceptance Level reduces the Suppliers Risk and increases the Customers RiskAgile, Waterfall21Finding n & c by Trial & ErrorA project manager is negotiating sampling plan for procurement of 1,000 items for the project. An AQL of 30 defectives in the entire lot has already been settled. The Project Management will be willing to accept up to 80 defectives in the lot. Assuming that the vendor will not accept a 5% risk that the Project Management will REJECT his good lot (defectives in the lot less than AQL), and the Project Manager will not take more than 10% risk that he will ACCEPT a bad lot (defectives in the lot more than the LTPD), give at least two combination figures for Sample Size and Sample Acceptance Level

22N=1,000n=?c=?AQL = 30/1,000 = 3% = 0.03-Risk = 5%

LTPD = 8/1,000 = 8% = 0.08-Risk = 10%Agile, Waterfall22Finding n & c by Trial & Error23-Risk-Risk0.9500.010Agile, Waterfall23Finding n & c by Trial & Error24-Risk-Risk0.9500.010n=100n=200n=180n=220n=160n=240c=7c=10c=9c=11c=9c=12Agile, Waterfall24Finding n & c by Trial & ErrorA project manager is planning sampling for a certain bulk procurement item. The Supplier has been communicated that the lot should have an accepted quality level of 1%. However, the Project Manager will tolerate up to 4% defectives in the lot.

If the Suppliers risk is to be no more than 5% and the Project Managers no more than 10%, suggest at least two combinations of sample size and acceptance level

25n=?c=?AQL = 1% = 0.01-Risk = 5%LTPD = 4% = 0.04-Risk = 10%Agile, Waterfall25Finding n & c by Trial & Error26-Risk-Risk0.9500.005Agile, Waterfall26Finding n & c by Trial & Error27-Risk-Risk0.9500.005n=100n=200n=400n=300n=280n=340c=3c=5c=8c=6c=6c=7Agile, Waterfall27Ques 4 in own MEC Final Exam28Agile, Waterfall28