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

2024
Views:

232

Pages:

23
Author:

coolcait7128jzy

Chapter 6 - Part 2 SPC – Attribute Control Charts Use of c-Charts • When we are interested in monitoring number of defects on a given unit of product or service. Scratches, chips, dents on an airplane wing • Errors on an invoice • Pot holes on a 5-mile section of highway • Complaints received per day • • Opportunity for a defect must be infinite. • Probability of a defect on any one location or any one point in time must be small. c-Chart c-chart notation: c = number of defects k = number of samples c - bar = c = estimated mean number of defects c-Chart A car company wants to monitor the number of paint defects on a certain new model of one of its cars. • Each day one car in inspected. • The results after 5 days are shown on the next slide. • c-Chart Day 1 2 3 4 5 Sum c c-bar c 5 2 8 7 11 33 6.60 c-bar 6.6 6.6 6.6 6.6 6.6 LCL 0 0 0 0 0 UCL 14.307 14.307 14.307 14.307 14.307 c-Chart - Mean c ∑ c= k c 33 ∑ = = 6.6 c= k 5 c-Chart – Control Limits LCL = c − 3 c UCL = c + 3 c c-Chart – Control Limits LCL = c − 3 c = 6.6 − 3 6.6 = −1.107 or 0 UCL = c + 3 c = 6.6 + 3 6.6 = 14.307 c-Chart for Number of Paint Defects c, number of defects 16 14 12 c 10 LCL 8 UCL 6 c-bar 4 2 0 1 2 3 Car 4 5 Conclusion Process shows upward trend. • Even though trend is within the control limits, the process is out of control. • Mean is shifting upward • This is due to an unfavorable special cause. • Must identify special cause and eliminate it from process. • Who is responsible for finding and eliminating special cause? • u-Chart • With a c chart, the sample size is one unit. • A u-chart is like a c-chart, except that the sample size is greater than one unit. • As a result, a u-chart tracks the number of defects per unit. • A c-chart monitors the number of defects on one unit. u-Chart •A car company monitors the number of paint defects per car by taking a sample of 5 cars each day over the next 6 days. • The results are shown on next side. u-Chart Day 1 2 3 4 5 6 Sum u u-bar n 5 5 5 5 5 5 c 45 58 48 53 68 44 u=c/n 9.0 11.6 9.6 10.6 13.6 8.8 63.2 10.5 u-bar 10.5 10.5 10.5 10.5 10.5 10.5 LCL 6.18 6.18 6.18 6.18 6.18 6.18 UCL 14.888 14.888 14.888 14.888 14.888 14.888 u-Chart u ∑ u = k u 63.2 ∑ = = 10.5 u = k 6 u-Chart u LCL = u − 3 n u UCL = u + 3 n u-Chart u LCL = u − 3 n 10.5 = 10.5 − 3 = 6.18 5 u UCL = u + 3 n 10.5 = 10.5 + 3 = 14.89 5 u-Chart u-Chart c, number of defects Number of Paint Defects Per Car 16 14 12 LCL 10 UCL 8 6 u u-bar 4 2 0 1 2 3 4 Car 5 6 Conclusion The process appears stable. • We can therefore get a statistically valid estimate the process mean number of defects per car. • Our estimate of the mean number of paint defects per car is 10.5, the center line on the control chart. • Thus, we expect each car to have, on average, 10.5 paint defects. • Conclusion Although the process is stable, the number of defects per car is too high. • Deming calls this a stable process for the production of defective product. • Important take away: • A stable process (process in control) is not necessarily a good process because it can be in control at the wrong level. • A stable process is predictable, but this doesn’t mean that what is being predicted is favorable. • u-Chart vs. c-Chart c u= n If n = 1, u = c and u = c. Control limits of the two chart will therefore be the same. Sample Size Control Chart When To Use Sample Size p-Chart Monitor the proportion of defectives in a process At least 50 c-Chart Monitor the number of defects 1 u-chart Monitor the number of defects per unit >1 In Practice You need 25 to 30 samples before computing initial control limits. • When a special cause occurs, you should eliminate that sample and re-compute control limits if • Special cause is identified • Eliminated or made part of process • To identify special causes, workers must keep log sheet, where they record any changes they make to the process. • Tracking Improvements UCL LCL UCL LCL Process centered Process not centered and stable and not stable UCL LCL Additional improvements made to the process