Business Statistics Quiz: Quality Assurance Sampling
20 questions · exam conditions
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Quality Assurance SamplingQuestion 1 of 20

An electronics company uses the sampling plan (n=100, c=2) for incoming shipments of resistors. To reduce inspection costs, a manager proposes changing the plan to (n=100, c=3).

What is the most likely consequence of changing the acceptance number from c=2 to c=3 while keeping the sample size constant?

The plan becomes stricter, increasing the probability of rejecting lots at all quality levels.
The producer's risk decreases, while the consumer's risk increases.
The producer's risk increases, while the consumer's risk decreases.
The plan's ability to discriminate between good and bad lots is improved.
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Business Statistics Quiz

Business Statistics Quiz: Quality Assurance Sampling

Practice Quality Assurance Sampling in Business Statistics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Quality Assurance Sampling, giving you a quick way to practice the rules, question types, and explanations that matter most for Business Statistics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

An electronics company uses the sampling plan (n=100, c=2) for incoming shipments of resistors. To reduce inspection costs, a manager proposes changing the plan to (n=100, c=3).

What is the most likely consequence of changing the acceptance number from c=2 to c=3 while keeping the sample size constant?

  1. The plan becomes stricter, increasing the probability of rejecting lots at all quality levels.
  2. The producer's risk decreases, while the consumer's risk increases. (correct answer)
  3. The producer's risk increases, while the consumer's risk decreases.
  4. The plan's ability to discriminate between good and bad lots is improved.
Explanation: Increasing the acceptance number (c) from 2 to 3 means that a lot will now be accepted even if 3 defective items are found in the sample, whereas before it would have been rejected. This makes the plan more lenient. A more lenient plan increases the probability of acceptance for any given defect rate. This means that good lots (at AQL) are more likely to be accepted, decreasing the producer's risk (α). Conversely, bad lots (at LTPD) are also more likely to be accepted, which increases the consumer's risk (β).

Question 2

A food processing company uses variables sampling to monitor the fill weight of cereal boxes. The sampling plan uses n=16n = 16 boxes with specification limits of 368g ± 12g. If the sample mean is 370.5g and sample standard deviation is 3.2g, what is the approximate upper specification limit capability index CpuC_{pu}?

  1. 1.22
  2. 0.98 (correct answer)
  3. 2.44
  4. 1.56
Explanation: CPU = (USL - x̄)/(3s) where USL = 368 + 12 = 380g, x̄ = 370.5g, s = 3.2g. CPU = (380 - 370.5)/(3 × 3.2) = 9.5/9.6 = 0.99 ≈ 0.98. Choice A uses wrong denominator (2.5s). Choice C doubles the correct answer. Choice D uses LSL instead of USL in calculation.

Question 3

A chemical company uses chain sampling for expensive destructive testing. The chain sampling plan CSP-1 with parameters n=10n = 10, c=0c = 0, and i=3i = 3 is implemented. The last 4 lots had 0, 1, 0, and 0 defectives respectively, with the first 3 lots accepted. For the current lot with 1 defective found, what is the acceptance decision?

  1. Reject the lot because the chain is broken by having 2 lots with defectives in the sequence
  2. Reject the lot because any lot with defectives above c=0 must be rejected in chain sampling
  3. Accept the lot because the previous i=3 lots contained sufficiently few total defectives
  4. Accept the lot because the cumulative defectives across the chain are within acceptable limits (correct answer)
Explanation: Chain Sampling Plan CSP-1 is designed for expensive destructive testing where you want to minimize sample sizes while maintaining quality control. Unlike standard acceptance sampling that evaluates each lot independently, chain sampling considers the cumulative performance across a sequence of consecutive lots. In CSP-1 with parameters n=10n=10, c=0c=0, and i=3i=3, the decision rule works as follows: if the current lot has defectives exceeding c=0c=0, you look back at the previous i=3i=3 accepted lots. If those previous lots collectively had zero defectives, you can still accept the current lot despite it exceeding the individual lot criterion. Here's the sequence: the last 4 lots had 0, 1, 0, 0 defectives respectively, with the first 3 lots accepted. The current lot has 1 defective. Looking at the previous i=3i=3 accepted lots, they had 0, 1, and 0 defectives. Wait—this seems problematic since the second lot had 1 defective but was accepted. This suggests those lots met the chain sampling criteria cumulatively. For the current lot with 1 defective, the chain principle allows acceptance because the cumulative defective pattern across the sequence remains within acceptable limits. Option A incorrectly assumes any lot with defectives breaks the chain. Option B misunderstands that c=0c=0 applies only when the chain condition isn't met. Option C uses vague language about "sufficiently few" rather than the specific cumulative logic. Remember: Chain sampling trades individual lot strictness for cumulative quality assurance—focus on the collective performance across the specified number of previous lots, not just individual lot compliance.

Question 4

A medical device manufacturer evaluates three different acceptance sampling plans for incoming raw materials. The supplier's process has been running at 2% defective rate. The company wants to ensure that lots with 6% or higher defective rates are rejected with at least 90% probability.

Based on the passage above, which sampling plan parameter is most critical for meeting the specified rejection requirement for poor quality lots?

  1. The sample size must be increased to ensure adequate statistical power for detection
  2. The acceptance number must be decreased to make the plan more stringent overall
  3. The ratio of sample size to acceptance number must provide steep OC curve slope (correct answer)
  4. The inspection level must be upgraded from normal to tightened inspection procedures
Explanation: The requirement specifies rejecting lots with ≥6% defective with 90% probability, which means P(accept) ≤ 0.10 at p=0.06. This requires good discrimination (steep OC curve) between acceptable (2%) and rejectable (6%) quality levels. The n/c ratio determines curve steepness. Simply increasing n or decreasing c alone may not achieve the required discrimination. Inspection levels relate to sampling standards, not discrimination.

Question 5

A semiconductor manufacturer uses continuous sampling plan CSP-2 with parameters f=1/8f = 1/8 (inspect every 8th unit) and i=4i = 4 (required consecutive conforming units). Currently in the sampling phase, the last 6 inspected units showed the pattern: conforming, defective, conforming, conforming, defective, conforming. What is the required next action?

  1. Continue sampling every 8th unit since the overall defect rate is within acceptable limits
  2. Return to 100% inspection because defective units were found during the sampling phase (correct answer)
  3. Switch to sampling every 4th unit to increase detection sensitivity after finding defectives
  4. Continue sampling every 8th unit but reset the consecutive conforming count to zero
Explanation: In CSP-2, when a defective unit is found during the sampling phase, the plan immediately returns to 100% inspection. The plan only allows sampling to continue when i consecutive conforming units are found during 100% inspection. Finding any defective during sampling triggers return to 100% inspection. Choices A and D ignore this fundamental rule. Choice C describes a different sampling protocol.

Question 6

An appliance manufacturer compares two sampling plans for the same AQL: Plan A (n=32n = 32, c=1c = 1) and Plan B (n=50n = 50, c=2c = 2). If the true lot quality is 3% defective, which statement about the probability of acceptance is most accurate?

  1. Plan B will have higher acceptance probability due to its larger sample size providing better representation
  2. Plan A will have higher acceptance probability because it has a lower acceptance number relative to expected defectives
  3. Both plans will have approximately equal acceptance probabilities since they target the same AQL level
  4. Plan A will have higher acceptance probability due to its smaller sample size reducing detection sensitivity (correct answer)
Explanation: For Plan A: E(defectives) = 32×0.03 = 0.96, accept if ≤1. For Plan B: E(defectives) = 50×0.03 = 1.5, accept if ≤2. Plan A has higher chance of ≤1 defectives than Plan B has of ≤2 defectives. Smaller samples are less likely to detect defectives. Choice A incorrectly assumes larger sample helps acceptance. Choice B has backwards logic. Choice C ignores the different OC curve shapes.

Question 7

A pharmaceutical company uses double sampling for quality inspection. In the first sample of 25 tablets, 1 defective is found. The sampling plan specifies: if ≤0 defectives in first sample, accept; if ≥3 defectives, reject; otherwise take second sample of 25. Given that a second sample is needed, what decision rule typically applies for the combined samples of 50 tablets?

  1. Accept if total defectives ≤ 2, reject if total defectives ≥ 3 across both samples combined (correct answer)
  2. Accept if second sample has ≤ 1 defective, reject if second sample has ≥ 2 defectives
  3. Accept if total defectives ≤ 1, reject if total defectives ≥ 2 across both samples combined
  4. Accept if second sample has 0 defectives, reject if second sample has ≥ 1 defective
Explanation: In double sampling, when the first sample result falls in the intermediate zone (1-2 defectives), a second sample is taken and the decision is based on the combined total from both samples. The acceptance number for combined samples (n=50) is typically 2, so accept if ≤2 total defectives. Choice B only considers the second sample. Choice C uses too restrictive a limit. Choice D ignores the first sample result.

Question 8

A electronics manufacturer implements skip-lot sampling where every 5th lot is inspected when the process is stable. The normal sampling plan uses n=80n = 80 with c=3c = 3. After finding 4 defectives in an inspected lot during skip-lot sampling, what is the most appropriate immediate action?

  1. Return to 100% lot inspection until process stability is reestablished through consecutive acceptable lots (correct answer)
  2. Increase the skip-lot interval to every 10th lot to reduce inspection while maintaining quality
  3. Continue skip-lot sampling but increase the sample size for subsequent inspected lots
  4. Switch to tightened inspection for the next 5 lots then resume normal skip-lot sampling
Explanation: Finding 4 defectives when c=3 means rejecting the lot, which indicates the process may no longer be stable. Skip-lot sampling requires process stability, so finding a rejected lot necessitates returning to 100% inspection until stability is reconfirmed. Choice B moves in wrong direction. Choice C doesn't address the stability issue. Choice D doesn't provide sufficient verification of process control.

Question 9

An automotive parts supplier implements sequential sampling for critical components. The sampling plan has acceptance line ya=−2.5+0.1ny_a = -2.5 + 0.1n and rejection line yr=2.5+0.1ny_r = 2.5 + 0.1n, where yy is the cumulative number of defectives and nn is the sample size. After inspecting 40 parts with 3 defectives found, what action should be taken?

  1. Continue sampling because the cumulative defectives fall between the acceptance and rejection lines (correct answer)
  2. Accept the lot because the cumulative defectives are below the acceptance line threshold
  3. Reject the lot because the cumulative defectives exceed the acceptance line threshold
  4. Restart the sampling process because the initial sample size was insufficient for decision making
Explanation: At n=40: acceptance line ya = -2.5 + 0.1(40) = 1.5, rejection line yr = 2.5 + 0.1(40) = 6.5. With 3 defectives found, we have 1.5 < 3 < 6.5, so continue sampling. Choice B is wrong because 3 > 1.5. Choice C misinterprets the decision rule. Choice D misunderstands sequential sampling protocol.

Question 10

A medical device manufacturer uses an acceptance sampling plan with parameters n=80 and c=2 for a critical component received in lots of 5,000. The supplier has historically maintained a process average of 1.5% defective, which is the agreed-upon Acceptable Quality Level (AQL). Recently, a lot was inspected, 3 components were found to be defective, and the lot was rejected.

Assuming the supplier's process is still operating at the 1.5% AQL, which of the following has occurred?

  1. A correct rejection of a poor-quality lot, demonstrating the effectiveness of the plan.
  2. A Type I error, where the producer's risk has been realized for this specific lot. (correct answer)
  3. A Type II error, where the consumer's risk has been realized for this specific lot.
  4. A sampling error that invalidates the plan's parameters, requiring an increase in sample size.
Explanation: The scenario describes rejecting a lot that is presumed to be of good quality (at the AQL of 1.5%). Rejecting a good lot is the definition of a Type I error, also known as the producer's risk (α). The sampling plan worked as designed (3 defects > acceptance number 2), but due to random chance in sampling, it led to the rejection of a lot that likely met the quality standard.

Question 11

A quality control manager implements a new single sampling plan. To increase the plan's ability to discriminate between lots of high quality and lots of low quality, the manager decides to significantly increase the sample size, nn, while adjusting the acceptance number, cc, proportionally. What is the primary effect of this change on the Operating Characteristic (OC) curve?

  1. The OC curve shifts to the right, making the plan more lenient overall.
  2. The OC curve shifts to the left, making the plan stricter overall.
  3. The OC curve becomes steeper, reducing both producer's and consumer's risks for a given AQL and LTPD. (correct answer)
  4. The OC curve becomes flatter, increasing the range of quality levels with an intermediate probability of acceptance.
Explanation: Increasing the sample size (n) makes the sampling plan more powerful at discriminating between different quality levels. This is represented by a steeper OC curve. A steeper curve means there is a more rapid drop in the probability of acceptance as the lot's actual defect rate increases. This simultaneously reduces the producer's risk (α) at the AQL and the consumer's risk (β) at the LTPD, as the plan is better able to distinguish good lots from bad lots.

Question 12

Under a rectifying inspection program, all lots that are rejected by the sampling plan are subjected to 100% inspection, and any defective items found are replaced with good ones. Accepted lots are sent forward without further inspection.

What is the primary purpose of calculating the Average Outgoing Quality (AOQ) in such a program?

  1. To determine the probability that a lot of a certain quality will be accepted by the consumer.
  2. To predict the long-run average percentage of defective items in the product stream after the inspection process. (correct answer)
  3. To set the Acceptable Quality Level (AQL) that a supplier must adhere to in their production process.
  4. To calculate the producer's risk (α) associated with rejecting lots that meet the quality standard.
Explanation: Average Outgoing Quality (AOQ) is a measure of the quality of the product that the consumer receives after the acceptance sampling and rectification process has been applied. It represents the long-run expected proportion of defective items in the final product stream, considering that accepted lots contain some defects and rejected lots are theoretically made perfect. Its purpose is to understand the final quality being shipped.

Question 13

A manager is negotiating a sampling plan with a new supplier. The manager is highly concerned about protecting the company's brand reputation and wants to avoid shipping any products assembled from poor-quality component lots. The supplier, however, is worried about the costs associated with having acceptable lots rejected.

To create a plan that addresses both parties' primary concerns, the manager should seek a plan that simultaneously has a:

  1. high Acceptable Quality Level (AQL) and a high producer's risk (α).
  2. high Lot Tolerance Percent Defective (LTPD) and a low producer's risk (α).
  3. low Acceptable Quality Level (AQL) and a high consumer's risk (β).
  4. low Lot Tolerance Percent Defective (LTPD) and a low consumer's risk (β). (correct answer)
Explanation: When you encounter acceptance sampling questions, focus on understanding what each party wants to minimize: the manager (consumer) fears accepting bad lots, while the supplier (producer) fears having good lots rejected. The correct answer is D because it addresses both concerns optimally. A low Lot Tolerance Percent Defective (LTPD) means the manager sets a strict standard for what constitutes an unacceptable lot - this protects the company's brand by ensuring very few defective items slip through. A low consumer's risk (β) means there's only a small probability of accepting a lot that's actually poor quality, further protecting the manager's interests. While this plan is strict, it still addresses the supplier's concern because when lots truly meet the acceptable quality standards, they're very likely to be accepted. Option A is wrong because high AQL means tolerating more defects (contrary to brand protection), and high producer's risk means good lots get rejected frequently (bad for supplier). Option B incorrectly suggests high LTPD, which would allow poor-quality lots to be considered acceptable - the opposite of what the manager wants. Option C combines low AQL (good for manager) with high consumer's risk, meaning there's a high probability of accepting truly bad lots, which completely undermines the manager's brand protection goals. Remember this pattern: the consumer (buyer/manager) wants low LTPD and low β to avoid accepting bad products, while the producer (supplier) wants low α to avoid having good lots rejected. The best compromise protects the more critical concern (brand reputation) while still being fair to the supplier.

Question 14

A company is considering replacing its 100% inspection process for a non-critical component with an acceptance sampling plan. An opponent of the change argues that 100% inspection is foolproof. Which of the following is the strongest counterargument to this claim?

  1. 100% inspection is often less than 100% effective due to factors like inspector fatigue and human error. (correct answer)
  2. 100% inspection eliminates the possibility of consumer's risk, but at a very high cost.
  3. A well-designed sampling plan can provide better statistical estimates of the true lot quality.
  4. For 100% inspection, the producer's risk is effectively zero, which is unfair to the company.
Explanation: This question tests your understanding of the practical realities of quality control methods, specifically comparing 100% inspection versus acceptance sampling plans. The strongest counterargument to the "foolproof" claim is that 100% inspection is often less than 100% effective due to factors like inspector fatigue and human error (A). This directly challenges the fundamental assumption that 100% inspection actually catches all defects. In reality, studies show that human inspectors typically achieve only 80-90% effectiveness even under ideal conditions. Factors like repetitive work, fatigue, distractions, and inconsistent standards mean that defective items slip through even comprehensive inspection processes. Option B is factually correct but doesn't counter the "foolproof" argument—it accepts that 100% inspection eliminates consumer's risk while only citing cost as a drawback. Option C makes an incorrect claim; sampling plans provide estimates of lot quality, but 100% inspection theoretically provides complete information about actual quality (though imperfectly executed). Option D misuses terminology—producer's risk refers to rejecting good lots, not the burden of inspection costs on producers. The key insight is that "100% inspection" and "100% effective inspection" are not the same thing. The human element introduces unavoidable error rates that can make a well-designed sampling plan more reliable than exhaustive but imperfect inspection. Strategy tip: When evaluating quality control methods, always consider the human factors and practical limitations, not just the theoretical ideals. Real-world effectiveness often differs significantly from textbook scenarios.

Question 15

A sampling plan for large lots is defined by (n=200, c=5). The Operating Characteristic (OC) curve for this plan shows that when the incoming lot quality is 2% defective, the probability of acceptance is 0.92. The company considers 2% to be its Acceptable Quality Level (AQL).

Based on this information, what is the producer's risk (α) for this plan, and what does it signify?

  1. The producer's risk is 0.92, signifying a high chance that good lots are correctly identified.
  2. The producer's risk is 0.08, signifying an 8% chance of rejecting a lot that meets the acceptable quality standard. (correct answer)
  3. The producer's risk is 0.02, signifying the target defect rate that the producer must meet.
  4. The producer's risk cannot be determined without knowing the Lot Tolerance Percent Defective (LTPD).
Explanation: The producer's risk (α) is the probability of rejecting a lot when its quality is at the Acceptable Quality Level (AQL). It is a Type I error. The problem states that the AQL is 2% and the probability of acceptance (P_a) at this quality level is 0.92. The probability of rejection is therefore 1 - P_a. So, α = 1 - 0.92 = 0.08, or 8%. This means there is an 8% chance that a lot meeting the AQL will be incorrectly rejected by the sampling plan.

Question 16

A firm uses a rectifying inspection plan (n=100, c=2) for lots of size N=2000. For a particular lot with a true defect rate (p) of 4%, the probability of acceptance (P_a) is 0.24. If this lot is accepted, it is shipped as is. If it is rejected, it undergoes 100% inspection and all defective items are replaced.

Assuming the given lot is representative of the incoming process quality, what is the approximate Average Outgoing Quality (AOQ)?

  1. AOQ = (0.24)(0.04) = 0.0096
  2. AOQ = (1 - 0.24)(0.04) = 0.0304
  3. AOQ = (0.24)(0.04) * (2000-100)/2000 = 0.00912 (correct answer)
  4. AOQ = 0.04, since the inspection only screens some lots.
Explanation: The formula for Average Outgoing Quality (AOQ) is AOQ = P_a * p * ((N-n)/N), where P_a is the probability of acceptance, p is the incoming proportion defective, N is the lot size, and n is the sample size. The term (N-n)/N is a finite population correction factor. Plugging in the values: AOQ = 0.24 * 0.04 * ( (2000-100) / 2000 ) = 0.0096 * (1900/2000) = 0.0096 * 0.95 = 0.00912.

Question 17

A manufacturing department has been experiencing a high rate of customer complaints due to faulty products, indicating that too many poor-quality lots are being approved. The current sampling plan is (n=60, c=1). Which of the following changes to the plan would be the most effective in directly addressing this problem?

  1. Change the plan to (n=60, c=2) to allow for more minor defects.
  2. Change the plan to (n=30, c=1) to reduce the inspection workload.
  3. Change the plan to (n=120, c=1) to increase the probability of detecting defects. (correct answer)
  4. Change the plan to (n=30, c=0) to make the acceptance criteria proportional to sample size.
Explanation: The problem is that poor-quality lots are being accepted, which means the consumer's risk (β) is too high. To make the plan stricter and reduce β, one can either decrease the acceptance number (c) or increase the sample size (n). Option A (increasing c) makes the plan more lenient, worsening the problem. Options B and D decrease the sample size, which reduces the plan's ability to discriminate. Option C significantly increases the sample size while keeping c constant, which makes the plan much stricter. A larger sample is more likely to find defects if they exist, thus leading to the rejection of poor-quality lots and directly addressing the customer complaints.

Question 18

A manager reviews two potential sampling plans to replace a costly 100% inspection process. Both plans offer nearly identical Operating Characteristic (OC) curves, meaning they provide the same levels of producer's and consumer's risk.

  • Plan 1: A single sampling plan with n=200, c=4.
  • Plan 2: A double sampling plan with n1=125, c1=1, and n2=125, c2=5.

If the incoming lots are typically of very high quality (very low percent defective), what is the primary advantage of choosing Plan 2?

  1. The total number of items inspected on average will be lower with Plan 2. (correct answer)
  2. Plan 2 is psychologically better for the supplier as it offers a 'second chance'.
  3. Plan 2 provides a more accurate estimate of the lot's true defect rate.
  4. Plan 2 has a lower consumer's risk (β) for lots of marginal quality.
Explanation: When you encounter sampling plan comparisons, focus on the key operational differences between single and double sampling plans, especially how sample sizes vary with lot quality. The crucial insight here is understanding average sample number (ASN). In Plan 1, you always inspect exactly 200 items regardless of what you find. In Plan 2's double sampling approach, you start by inspecting 125 items. If you find 0 or 1 defects, you accept the lot immediately without needing the second sample. Only if you find 2 or more defects do you inspect the additional 125 items. For very high quality lots (very low defect rates), Plan 2 will frequently find 0 or 1 defects in the first sample of 125, allowing immediate acceptance. This means the average total inspection will be much closer to 125 items rather than the full 250, making option A correct. Option B is wrong because "psychological advantage" isn't a statistical benefit and doesn't relate to inspection efficiency. Option C is incorrect because smaller sample sizes (when Plan 2 stops early) actually provide less precise defect rate estimates, not more accurate ones. Option D contradicts the passage, which explicitly states both plans have nearly identical OC curves, meaning their consumer's risks are essentially the same. Study tip: Remember that double sampling plans' main advantage is inspection economy—they can dramatically reduce average inspection when lot quality is either very good (early acceptance) or very poor (early rejection). Always consider how the stopping rules interact with the expected lot quality.

Question 19

A textile manufacturer uses MIL-STD-105E sampling plans. For a lot size of 3,200 units with General Inspection Level II and AQL of 1.5%, the plan specifies sample size 125 with acceptance number 5. If the actual process average is 0.8% defective, what is the primary concern with this sampling plan?

  1. The sample size is too large relative to the lot size, creating unnecessary inspection costs
  2. The acceptance number is too low, causing excessive rejection of good quality lots
  3. The plan provides insufficient discrimination between acceptable and unacceptable quality levels (correct answer)
  4. The process average exceeds the AQL, indicating the process is out of control
Explanation: With process average (0.8%) well below AQL (1.5%), the plan should easily accept most lots. However, MIL-STD plans often have relatively flat OC curves, meaning poor discrimination between good and bad lots. The sample size is appropriate for the lot size. The acceptance number is standard for this AQL. The process average is actually better than the AQL target.

Question 20

A smartphone assembler sources batteries from a new vendor. The assembler establishes a quality requirement that lots with a defect rate of 6% or higher are considered unacceptable and should be rejected at least 95% of the time. In the context of acceptance sampling, this 6% defect rate is a critical parameter for the assembler.

This 6% quality level and its associated rejection probability are primarily used to define and control which of the following?

  1. The producer's risk (α), which is the vendor's risk of having a good lot rejected.
  2. The Acceptable Quality Level (AQL), which is the target quality for the vendor's process.
  3. The consumer's risk (β) at the Lot Tolerance Percent Defective (LTPD). (correct answer)
  4. The Average Outgoing Quality Limit (AOQL), which is the maximum average defect rate post-inspection.
Explanation: The scenario describes the consumer's (the assembler's) perspective on unacceptable quality. The 6% defect rate is the Lot Tolerance Percent Defective (LTPD)—the quality level the consumer wishes to avoid. The desire to reject these lots 95% of the time means the probability of accepting them is 5%. This probability of accepting a bad lot (at the LTPD) is the consumer's risk (β). Therefore, the parameters define β at the LTPD.