QUALITY CONTROL AND SPC. CHAPTER 16. DAVID A. COLLIER AND JAMES R. EVANS. LO1 Describe quality control system and key issues in manufacturing and service. LO2 Explain types of variation and the role of statistical process control .
DAVID A. COLLIER AND JAMES R. EVANS
LO1Describe quality control system and key issues in manufacturing and service.
LO2Explain types of variation and the role of statistical process control.
LO3Describe how to construct and interpret simple control charts for both continuous and discrete data.
LO4Describe practical issues in implementing SPC.
LO5Explain process capability and calculate process capability indexes.
marriott has become infamous for its obsessively detailed standard operating procedures (SOPs), which result in hotels that travelers either love for their consistent good quality or hate for their bland uniformity. “This is a company that has more controls, more systems, and more procedural manuals than anyone—except the government,” says one industry veteran. “And they actually comply with them.” Housekeepers work with a 114-point checklist. One SOP: Server knocks three times. After knocking, the associate should immediately identify themselves in a clear voice, saying, “Room Service!” The guest’s name is never mentioned outside the door. Although people love to make fun of such procedures, they are a serious part of Marriott’s business, and SOPs are designed to protect the brand. Recently, Marriott has removed some of the rigid guidelines for owners of hotels it manages, empowering them to make some of their own decisions on details.
What do youthink?
What opportunities for improved quality control or use of SOPs can you think of at your college or university (e.g., bookstore, cafeteria)?
The task of quality control is to ensure that a good or service conforms to specifications and meets customer requirements by monitoring and measuring processes and making any necessary adjustments to maintain a specified level of performance.
If a defect or service error is identified and corrected in the design stage, it might cost $1 to fix. If it is first detected during the production process, it might cost $10 to fix. However, if the defect is not discovered until it reaches the customer, it might cost $100 to correct.
Two basic mistakes when attempting to control a process:
Adjusting a process that is already in control.
Failing to correct a process that is out of control.
Goodman Tire periodically tests its tires for tread wear under simulated road conditions. The company collects twenty samples, each containing three radial tires from different shifts over several days of operations. The overall mean is computed as 31.88, and the average range is 10.8.
Exhibit 16.1 Excel Template for Goodman Tire x-bar and R-Charts
Control limits are:
Exhibit 16.2 R-Chart for Goodman Tire Example
Exhibit 16.3 x-Chart for Goodman Tire Example
A process is said to be “in control” when the control chart has the following characteristics:
Rules for identifying a shift in the process:
8 points in a row above or below the center line.
10 of 11 consecutive points above or below the center line.
12 of 14 consecutive points above or below the center line.
2 of 3 consecutive points in the outer one-third region between the center line and one of the control limits.
4 of 5 consecutive points in the outer two-thirds region between the center line and one of the control limits.
Exhibit Extra Illustration of Some Rules for Identifying Out-of-Control Conditions
The operators of automated sorting machines in a post office must read the ZIP code on letters and divert the letters to the proper carrier routes. Over a month’s time, 25 samples of 100 letters were chosen, and the number of errors was recorded.
The average proportion defective, p is computed as 0.022. The standard deviation is:
UCL = .022 + 3(.01467) = .066, and LCL = .022 - 3(.01467) =
-.022. Since the LCL is negative and the actual proportion nonconforming cannot be less than zero, the LCL is set equal to zero.
Data and Calculations for the p-Chart Solved Problem
Exhibit 16.5 p-Chart for Solved Problem
UCLc= c + 3
LCLc= c - 3
The total number of machine failures over a 25-day period is 45.
The average number of failures per day, c, is 45/25 = 1.8.
Control limits for the c-chart are:
Machine Failure Data for c-Chart Solved Problem
Exhibit 16.7 c-Chart for Machine Failures
SPC is a useful methodology for processes that operate at a low sigma level (less than or equal to 3-sigma).
For processes with a high sigma level (greater than 3-sigma), few defects will be discovered even with large sample sizes.
More advanced tools are necessary.
The relationship between the natural variation and specifications is often quantified by a measure known as the process capability index.
Cp = (UTL – LTL)[16.9]
UTL = Upper tolerance limit
LTL = Lower tolerance limit
σ = Standard deviation of the process (or an estimate based on the sample standard deviation, s)
Exhibit 16.8 c-Process Capability versus Design Specifications
One-sided process capability indexes consider off-centering in a process:
Cpu = (UTL – µ)/3σ (upper one-sided index) [16.10]
Cpl= (µ – LTL)/3σ (lower one-sided index) [16.11]
Cpk = min (Cpl, Cpu) [16.12]
A controlled process shows an overall mean of 2.50 and an average range of 0.42. Samples of size 4 were used to construct the control charts. If specifications are 2.60 ± 0.25, how well can this process meet them? What are the process capability indexes?
Exhibit 16.9 Comparison of Observed Variation and Design Specifications for Solved Problem