University:
California State University, Northridge
Course:
SOM 306 | Operations Management
Academic year:

2024
Views:

35

Pages:

18
Author:

Isaac Copeland

Chapter 6 - Part 1 SPC – Attribute Control Charts Types of Control Charts • Attribute charts Monitor fraction of defective units • Monitor number of defects • Difference between “defective unit” and a “defect?” • • • • • A defective unit is a unit that is either defective. A defect is flaw on a given unit of a product. A unit can have many defects. A defective unit may be defined as, for example, a unit that has 3 or more defects. Types of Control Charts • Variables charts Monitors continuous quality characteristics. • Continuous values (variables data) can theoretically assume an infinite number of values in some interval. • • • • • Time Weight Ounces Diameter Types of Control Control Chart Attribute control charts Monitors p chart Process fraction defective c chart number of defects u chart defects per unit Variables control charts X-bar chart Process mean R chart (Range Chart) Process variability Use of p-Charts • When observations can be placed into two categories. • Good or bad • Pass or fail • Operate or doesn’t operate p-chart A company that makes light bulbs wants to monitor the fraction of defective bulbs. • The company decides to select a random sample of 100 bulbs in each day over a 5 day period • Each of the 100 bulbs are tested to determine if they light up. • p-chart If a bulb does not light up, the bulb is defective. • The company wants to • Estimate the percentage of defective bulbs and • Determine if the percentage of defective bulbs is increasing over time. • • A p chart is the appropriate tool for providing the company with this information. Notation • Sample size = n = 100 • Number of samples (subgroups) = k = 5 • X = number of defective bulbs in a sample • p = sample fraction defective = ??? • p-bar = estimated process fraction defective • P = process fraction defective (unknown) • p-bar is an estimate of P Inspection Results Day 1 2 3 4 5 n 100 100 100 100 100 X 20 5 30 35 24 Compute p and p-bar Day 1 2 3 4 5 Sum p-bar n 100 100 100 100 100 X 20 5 30 35 24 p=X/n 0.20 0.05 0.30 0.35 0.24 1.14 0.23 p-bar (Estimated Process Fraction Defective) p ∑ p - bar = p = k p 1.14 ∑ = = 0.23 p= k 5 p-Chart Control Limits p (1 − p ) UCL = p + 3 n p (1 − p ) LCL = p − 3 n p-Chart - Control Limits .23(1 − .23) UCL = .23 + 3 = .356 100 .23(1 − .23) LCL = .23 − 3 = .104 100 p-Chart for Bulbs 0.4 p 0.3 LCL UCL 0.2 p-bar p 0.1 0 1 2 3 Day 4 5 Interpretation The estimated fraction of defective bulbs produced is .23. • On Day 2, p was below the LCL. • This means that a special cause occurred on that day to cause the process to go out of control. • The special cause shifted the process fraction defective downward. • This special cause was therefore favorable and should be ??? • Interpretation After Day 2, the special cause lost its impact because on Day 4, the process appears to be back in control and at old fraction defective of .23. • Until the special cause is identified and made part of the process, the process will be unstable and unpredictable. • It is therefore impossible to obtain a statistical valid estimate of the process fraction defective because it can change from day to day. • Trend Within Control Limits Process fractions defective is shifting (trending) upward P Sampling Distribution P UCL p-Chart LCL P P P = process fraction defective Applications • Think of an application of a p-chart in: Sales • Shipping department • Law •