Tech 31: Unit 4 Control Charts for Attributes Statistical Process Control (SPC)

Attributes Are: Quality characteristics that conform or do not conform to specifications. Used where measurements are not possible due to nature of quality characteristics, cost, time or need. A nonconformity is a departure of a quality characteristic from its intended level or state...

Nonconformities Vs Quality A nonconformity refers to a quality characteristic. A nonconforming unit refers to the overall product. A unit may have many nonconformities, but the unit itself is either conforming or nonconforming.

Attribute Versus Variable Control Charts Variable type control charts use measured data (time, money, length, width, depth, weight, etc.). Attribute type control charts use counted data (number of defects, mistakes, errors, injuries, etc.)

Examples of Attributes: Poor Paint Jobs

Examples of Attributes: Poor Paint Jobs

Examples of Attributes: Drug Manufacturing

Examples of Attributes: In Products

Examples of Attributes: In Products

Examples of Attributes: In Products

Identifying Attributes: (Check Sheets)

Visual Inspection

Go-No-Go Gauges

Fundamentals of Probability Definition of probability: a) Probability is the measure of how likely an event is. b) The probability of event A is the number of ways event A can occur divided by the total number of possible outcomes. It is expressed as: P(A) =  The Number of Ways Event A Can Occur   The Total Number of Possible Outcomes

Theorems of probability. Theorem 1. Probability is expressed as a number between 1.000 and 0. Theorem 2. If P(A) is the probability that event A will occur, then the probability that A will not occur is 1.000 - P(A). Theorem 3. If A and B are two mutually exclusive events, then the probability that either event A or event B will occur is the sum of their respective probabilities. Theorem 4. If event A and event B are not mutually exclusive events, then the probability of either event A or event B or both is given by: P(A or B or both) = P(A) + P(B) - P(both)

Theorems of probability. Theorem 5. The sum of the probabilities of the events of a situation is equal to 1.000. P(A) + P(B) +...+ P(N) = 1.000 Theorem 6. If A and B are independent events, then the probability of both A and B occurring is the product of their respective probabilities. P(A and b) = P(A) * P(B) Theorem 7. If A and B are dependent events, the probability of both A and B occurring is the product of the probability of A and the probability that if A occurred, then B will occur also. P(A and B) = P(A) * P(B/A)

Examples of probability problems A spinner has 4 equal sectors colored yellow, blue, green and red. After spinning the spinner, what is the probability of landing on each color? A single 6-sided die is rolled. What is the probability of each outcome? What is the probability of rolling an even number? of rolling an odd number? A glass jar contains 6 red, 5 green, 8 blue and 3 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of choosing a red marble? a green marble? a blue marble? a yellow marble?

Control Charts Control charts are tools used to determine whether or not a manufacturing process is in a state of statistical control

Limitations of Variable Control Charts: Not suitable for attributes Too expensive for multiple characteristics

Np Chart The purpose of an np chart is to evaluate process stability when counting the fraction defective Used to report the fraction/percent nonconforming Values greater than 0.10 indicate a problem company Subgroup size must be large to produce meaningful chart

Normality & Control Charts: Principles

Sample Control Chart

Determining the Control Limits The control limit is equal to the grand mean CL = Grand mean or Center Line =

Determining the Control Limits

Objectives of Nonconforming Charts: To determine the average quality level To bring to management’s attention changes in average To improve the product quality To evaluate quality performance of operating and management personnel To suggest places to use x and r charts To determine acceptance criteria of a product before shipment to the customer

Control Chart Techniques Select the quality characteristic Choose the rational subgroup Collect Data Determine the trial central line (CL) and control limits (UCL & LCL) Establish the revised CL, UCL, & LCL Achieve Objectives

Control Charts continued Control Charts for Attributes p & np charts c charts u charts