Posted: December 7th, 2015

Statistics

Statistics

OPERATING CHARACTERISTICS CURVES COST ANALYSIS

PRODUCER SCENARIO

1)  Assume you are the producer.  You send a truckload of 10,000 cans to company X with proportion defective p=0.05.  Each can sold yields a profit of $0.50 to your company.   The process of sending a truckload to company X is the following.  Loading wages are $10/hr.  It takes 6 Loaders  1.5 hours to unload a full truck  Inspector wages are $12/hr.  It takes 2 inspectors 5 hours to inspect 100% a full truck if a truck is returned.  The driver wages are $20/hr whether he/she is driving or not.  The driver starts working from the time the truck starts loading and returns empty handed if the truck is accepted or he/she starts driving from the time the truck starts loading until the truck gets fully unloaded if the truck is rejected.

If the truck is accepted:

If the truck is rejected:

If Company X has a policy that says:  If in a sample size of 20, there are 3 or less defective, accept the truck.  If there are more than 3 defective, reject the truck.  Using the binomial distribution, construct the operating characteristic curve for this scenario.   Construct a plot that shows the expected (gain or loss) incurred by the supplier as a function of the proportion defective.

Expected gain =p(acceptance)*Expected Profit –p(rejected)*Expected Cost

The Acceptable Quality Level (AQL)= 0.5% and the Lot Tolerance Percentage Defective = 7.5%.   Determine  the producer risk.  Determine the cost/profit associated with the producer risk.

CONSUMER SCENARIO:

2)   Assume you are the consumer (or Company X) . Company X has a policy that says:  If in a sample size of 20, there are 3 or less defective, accept the truck.  If there are more than 3 defective, reject the truck.   The cans bought will be used in the manufacturing operating.  The handling of these cans is as follows:

If truckload is accepted.

If truckload is rejected

1)   Construct the operating characteristic curve for the final product sampling by the consumer.  Show how this is related to the supplier operating characteristic curve.    Also, construct a plot that shows the expected (gain or loss) incurred by the consumer as a function of the proportion defective from the supplier.   Include in the assessment of costs , the opportunity costs.  Opportunity costs  is the potential profit that could have been made if the cans had been produced and sold.

Knowing the Acceptable Quality Level (AQL)= 0.5% and the Lot Tolerance Percentage Defective = 7.5%.   Determine the consumer risk.  Determine the cost/profit associated with the consumer risk.

CHANGING SAMPLING PLANS

Company X is trying to minimize the costs of processing 10,000 cans in an 8 hour shift.  The company believes that a better sampling can achieve this for them.  The company comes up with a more stringent sampling plan to receive the supplies.   If in a sample size of 20, there are 2 or less defective, accept the truck.  If there are more than 2 defective, reject the truck. Because now, the plan is more stringent, the supplier now takes additional measures to comply with new quality policy.  This causes the cost to produce a can to increase from $1.25/can to $1.35 for the producer.   This also impacts Company X.  Now that it takes longer for the supplier to deliver product, this causes the manufacturing operation of company X to stop for 6 hours instead of 5 hours if a truck load is rejected.      Repeat the analysis for the supplier and for the consumer.  Determine the impact on both the supplier and the consumer based on changing the quality policy.

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