I am trying to set up a sampling plan shown below. I wonder if I can statistically show with confidence that this is a good plan. The purpose of this plan is to eliminate inspection if there is no issue found over time.
Parts are received as one part from the inventory when customer order is entered. On recieving the parts, do the following:
100 % inspections of first 50 orders (parts) before re-boxing using X-ray and record the results.
Reduce inspection to 50% if no issue (missing component is not found). i.e. 50% inspection of next 50 alternate orders and record the results.
Reduce inspection to 25% if no issue (missing component is not found). i.e 25% inspections of next 50 (every 4rth) order and record the results.
If issue (missing screw) is found during any of these inspections, go back to 100% X-ray inspection until standard line corrective action is implemented.
@mikeruss – the only way to truly eliminate sampling (inspection) is to prevent the defect from occuring in the first place, or getting the defect rate to be less than what is acceptable to the customer.
While your plan is one commonly used, it is not based on statistics. In order to identify a rational sampling plan based on statistics, you must know the current defect rate, and the population acceptance defect rate (customer acceptable defect rate).
Thank you for your suggestion. If you notice, I mentioned in my note that this sampling plan is till corrective action is implemented. However, as interim I don’t want to continue with 100% inspection and stop it if no issue found. If this cannot be statistically justified, than lets assume if the current defect rate is 2%, and customer acceptable defect rate is 0% (no defect), what statistical approach I can use. Please describe or show example if you can.
@mikeruss – here’s where you get into trouble. If the customer acceptable defect rate is 0%, then you must inspect 100%. No customer “wants” a defect, but what you need to determine is the trade-off in costs for reduced defects.
Let’s say that that point is at 1/10 of your current defect rate, so customer acceptable defect rate is 0.2%. You mention a lot size of 50, but that is too small to do anything other than 100% sampling. So, I chose a lot of 500 and get the following graphs (see attached). Read the left graph as the probability of accepting if the actual defect rate is as shown on the x-axis at the sampling plan rate shown at the bottom. The right graph shows what the customer observable defect rate is at those defect rates and sampling plan. (in this case, with a sampling plan of 149, you would be allowed 1 defect and still accept the lot). There are various different items to consider, including producer vs. consumer risk which would need to be evaluated as well.
Here is the info from Minitab help –
Stat > Quality Tools > Acceptance Sampling by Attributes
Allows you to create an attribute acceptance sampling plan or compare various sampling plans that you specify.
· Create a sampling plan to determine a sample size and make a decision whether to accept or reject an entire lot (batch) of product, based on the number of defectives or defects found in that sample.
· Compare multiple sampling plans to determine the effects of varying sample size or acceptance number.
Dialog box items
Create a sampling plan: Choose to determine a sample size and the criteria for accepting or rejecting an entire lot.
Compare user defined sampling plans: Choose to see how effective your current sampling plan is and to compare various competing plans.
Measurement type: Choose Go/no go (defectives) if you inspect units and record whether the product is defective or not. Choose Number of defects if you inspect units and count and record the number of defects per unit.
Units for quality levels: Choose the units based on your measurement type.
If you specified Go/no go (defectives), then choose either Percent defective (0-100), Proportion defective (0-1), or Defectives per million to represent the level of defectives in the process.
If you specified Number of defects, then choose either Defects per unit, Defects per hundred, or Defects per million to represent the level of defects in your process.
Acceptable quality level (AQL): Enter a number to represent the largest number of defectives or defects in a process that will still be considered acceptable. Typically, a sampling plan is designed to give a high probability of acceptance at the AQL.
You must specify the AQL when you create a sampling plan, but it is not required for comparing sampling plans. The AQL must be consistent with measurement units. For example, with percent defectives 0<AQL<100; with proportion defective 0<AQL<1; and with defectives per million 0<AQL<1,000,000.
Rejectable quality level (RQL or LTPD): Enter a number to represent the number of defectives or defects in an individual lot that you are willing to tolerate. Typically, a sampling plan is designed to give a low probability of acceptance at the RQL.
You must specify the RQL when you create a sampling plan, but it is not required for comparing sampling plans. The RQL must be entered consistently with measurement units and must be larger than the AQL. For example, with percent defectives AQL<RQL<100; with proportion defective AQL<RQL<1; and with defectives per million AQL<RQL<1,000,000.
Lot size: Enter a number to represent the lot size or batch size of the entire shipment that you will accept or reject based on sampling results. You don't need to specify a lot size if you specify the AQL, RQL, and alpha and beta risks; however, Minitab requires the lot size to calculate the AOQ curve and the ATI curve.
For Creating Sampling Plans
Producer's risk (Alpha): Enter a value between 0 and 1 to represent a. 1- a represents the desired probability of accepting a lot at the AQL, which is necessary for creating the sampling plan.
Consumer's risk (Beta): Enter a value between 0 and 1- a to represent b. b represents the desired probability of accepting a lot at the RQL, which is necessary for creating the sampling plan.
@mikeruss I think to answer the question you are trying to answer you should look into the statistical tool known as acceptance sampling. Instead of arbitrary inspection rates like 50% and 25%, it will more accurately determine the appropriate sample size.
That said, as @MBBinWI indicated, the only way 0% defects can be ensured is 100% inspection. That said, there are plans where you reject the entire lot if a single defect is found, and you can still calculate appropriate sample sizes for that test.
If customer excpectations are 0defect then 100% inspection is only way. But i want to ask, whats the actual defect rate of process. Because if it is too high like 25% or even 15%, then the best approach is to launch a rigourus defect elimination drive and fool-proofing of process so that 0% defect level can be achieved. And once defect rate is reduced to below 2% then go for a statistical sampling plan with highest Alpha risk. Becuase keeping high Alpha risk will result in low Beta risk & thus reducing risk at your customer end.