Quality Control - Southern Oregon University



Quality Control

Purpose of QC

• To assure that the process is performing in an acceptable manner

• Done through monitoring the process via inspection

Quality Assurance Relies on inspection

• Inspection after production (acceptance sampling)

• Inspection during production (statistical process control, or SPC)

Basic Issues in Inspection:

1) How much and how often to inspect

2) At what points in the process to inspect

3) Whether to inspect in a centralized or on-site location

4) Whether to inspect attributes (counting something) or variables (measure something)

Where to inspect:

• Raw materials and purchased parts

• Finished products

• Before a costly operation

• Before an irreversible process

• Before covering a process

Key Concepts:

• Variation is the enemy of quality

• Every process exhibits some form of variation

• The degree of this variation is a measure of the capability of the process

• Process variation can be classified as:

o common cause variation - inherent in system

o special cause variation - presence is detected using SPC

Control Charts

• Key tool for monitoring and controlling processes. A control chart is a time-ordered plot of sample statistics

• Purpose: used for detecting presence of special cause variation.

• Components of a Control Chart

1) Upper Control Limit

2) Middle Value

3) Lower Control Limit

Possible Errors in SPC

▪ Type I error

▪ Type II error

Managerial Considerations Concerning Control Charts

1. At what points in the process to use control charts

2. What size samples to take

3. What type of control chart

Four Common Types of Charts

A. Control charts for Variables

(1) Mean chart (a.k.a x-bar chart) - used to monitor the average of the process

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(2) Range chart (a.k.a. R-chart) - used to monitor the variability of the process

B. Control charts for Attributes

(1) p-chart (proportion chart) - used to monitor the proportion of defectives

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(2) c-chart (used when the goal is to control the number of defects per unit

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Charts Illustrating a Process Not in Control

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Table for A2, D3 and D4

|  |  |  |  |

| | |Factor for R Chart |

|Number of Observations|Factor for |Lower Control |Upper Control |

|in Subgroup |x-bar Chart |Limit |Limit |

|n |A2 |D3 |D4 |

| | | | |

|2 |1.88 |0.00 |3.27 |

|3 |1.02 |0.00 |2.57 |

|4 |0.73 |0.00 |2.28 |

|5 |0.58 |0.00 |2.11 |

|6 |0.48 |0.00 |2.00 |

|7 |0.42 |0.08 |1.92 |

|8 |0.37 |0.14 |1.86 |

|9 |0.34 |0.18 |1.82 |

|10 |0.31 |0.22 |1.78 |

|11 |0.29 |0.26 |1.74 |

|12 |0.27 |0.28 |1.72 |

|13 |0.25 |0.31 |1.69 |

|14 |0.24 |0.33 |1.67 |

|15 |0.22 |0.35 |1.65 |

|16 |0.21 |0.36 |1.64 |

|17 |0.20 |0.38 |1.62 |

|18 |0.19 |0.39 |1.61 |

|19 |0.19 |0.40 |1.60 |

|20 |0.18 |0.41 |1.59 |

|  |  |  |  |

| | | | |

Problems

4 – Control charts for Variables – Mean and Range charts

6 – Control chart for Attributes – p-chart

7 – Control chart for Attributes – c-chart

8 – How many to produce given a certain production survival rate

[pic] Problem 10.4 (p. 462)

Computer upgrades have a nominal time of 80 minutes. Samples of 5 observations each have been taken, and the results are listed below. Determine the upper and lower control limits for mean and range charts, and decide if the process is in control.

|SAMPLE |

|1 |2 |3 |4 |5 |6 |

|79.2 |80.5 |79.8 |78.9 |80.5 |79.7 |

|78.8 |78.7 |79.4 |79.4 |79.6 |80.6 |

|80.0 |81.0 |80.4 |79.7 |80.4 |80.5 |

|78.4 |80.4 |80.3 |79.4 |80.8 |80.0 |

|81.0 |80.1 |80.8 |80.6 |78.8 |81.1 |

Excel Solution

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[pic]Problem 10.6 (463)

A medical facility does MRIs for sports injuries. Occasionally a test yields inconclusive results and must be repeated. Using the following sample data and n=200, determine the upper and lower control limits for the fraction of retests using two-sigma limits.

Is the process in control? If not eliminate any values that are outside the limits and compute the revised limits.

| |SAMPLE |

| |

| |

|The postmaster of a small western city receives a certain number of complaints each day |

|about mail delivery. Assume that the distribution of daily complaints is Poisson. Construct |

|a control chart with three sigma limits using the following data. Is the process in control? |

| |SAMPLE |

|1 |2 |3 |4 |5 |6 |7 |8 |9 |10 |11 |12 |13 |14 | |Number of complaints |4 |10 |14 |8 |9 |6 |5 |12 |13 |7 |6 |4 |2 |10 | |

Excel Solution

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[pic]Problem 18

A production process consists of a three-step operation. The scrap rate is 10 percent for the first step and 6 percent for the other two steps.

(a) If the desired daily output is 450 units, how many units must be started to allow for loss due to scrap?

(b) If the scrap rate for each step would be cut in half, how many units would this save in terms of the scrap allowance?

(c ) If the scrap represents a cost of $10 per unit, how much is it costing the company per day for the original scrap rate?

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