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**Quality Assurance (Quality Control)**

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**Phases of Quality Assurance**

Acceptance sampling Process control Continuous improvement Inspection before/after production Corrective action during Quality built into the process The least progressive The most

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**Inspection How Much/How Often Where/When Centralized vs. On-site**

Inputs Transformation Outputs Acceptance sampling Process control

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**Inspection Costs Cost Total Cost Cost of inspection Cost of passing**

defectives Optimal Amount of Inspection

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**Where to Inspect in the Process**

Raw materials and purchased parts Finished products Before a costly operation Before an irreversible process Before a covering process

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**Examples of Inspection Points**

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**Statistical Process Control**

The Control Process Define Measure Compare to a standard Evaluate Take corrective action Evaluate corrective action

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**Statistical Process Control**

Variations and Control Random variation: Natural variations in the output of process, created by countless minor factors Assignable variation: A variation whose source can be identified

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**Sampling Distribution**

Process distribution Mean

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**Normal Distribution Mean -3s -2s +2s +3s 95.5% 99.7%**

s = Standard deviation

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**Control Limits (Type I Error)**

Mean LCL UCL a/2 a = Probability of Type I error

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**Control Limits Sampling distribution Process distribution Mean**

Lower control limit Upper control limit

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**Mean Charts Two approaches:**

If the process standard deviation (s) is available (x If the process standard deviation is not available (use sample range to approximate the process variability)

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**Mean charts (SD of process available)**

Upper control limit (UCL) = average sample mean + z (S.D. of sample mean) Lower control limit (LCL) = average sample mean - z (S.D. of sample mean)

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**Mean charts (SD of process not available)**

UCL = average of sample mean + A2 (average of sample range) LCL = average of sample mean - A2 (average of sample range) A2 is a parameter depending on the sample size and is obtainable from table.

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Example Means of sample taken from a process for making aluminum rods is 2 cm and the SD of the process is 0.1cm (assuming a normal distribution). Find the 3-sigma (99.7%) control limits assuming sample size of 16 are taken.

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**Example (solution) x = SD of sample mean distribution z = 3**

= SD of process / (sample size) = 0.1 / (16) = 0.025 z = 3 UCL = 2 + 3(0.025) = 2.075 LCL = = 1.925

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Example(p.427) Twenty samples of size 8 have been taken from a process. The average sample range of the 20 samples is 0.016cm and the average mean is 3cm. Determine the 3-sigma control limits.

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**Example Average sample mean = 3cm Average sample range = 0.016cm**

Sample size = 8 A2 = 0.37 (From Table 9-2) UCL = (0.016) = 3.006 LCL = (0.016) = 2.994

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Control Chart Abnormal variation due to assignable sources Out of control 1020 UCL 1010 1000 Mean Normal variation due to chance 990 LCL 980 Abnormal variation due to assignable sources 970 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sample number

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**Observations from Sample Distribution**

UCL LCL 1 2 3 4 Sample number

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**Mean and Range Charts Detects shift x-Chart Does not detect shift**

UCL LCL x-Chart Detects shift UCL LCL Does not detect shift R-chart

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**Mean and Range Charts Does not detect shift x-Chart R-chart**

UCL LCL UCL LCL Does not detect shift x-Chart UCL LCL R-chart Detects shift

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**Control Chart for Attributes**

p-Chart - Control chart used to monitor the proportion of defectives in a process c-Chart - Control chart used to monitor the number of defects per unit

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**Use of p-Charts When observations can be placed into two categories.**

Good or bad Pass or fail Operate or do not operate When the data consists of multiple samples of several observations each

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p-chart The center line is the average fraction (defective) p in the population if p is known, or it can be estimated from samples is it is unknown. p = SD of sample distribution = {p(1-p)/n} UCLp = p + zp LCLp = p - zp

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Example (p.431) The following table indicates the defective items in 20 samples, each of size 100. Construct a control chart that will describe 95.5% of the chance variations of the process

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Example The following table indicates the defective items in 20 samples, each of size 100. Construct a control chart that will describe 95.5% of the chance variations of the process No. of defective items

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Example (solution) Population mean not available, to be estimated from sample mean Total No. of defective items = 220 Estimate sample mean = 220/{20(100)}=.11 SD of sample = {.11(1-.11)/100}= 0.03 z = 2 (2-sigma) UCLp = (.03) = 0.17 LCLp = (.03) = 0.05 Thus a control chart can be plotted (p.431)

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Use of c-Charts Use only when the number of occurrences per unit of measure can be counted; nonoccurrences cannot be counted. Scratches, chips, dents, or errors per item Cracks or faults per unit of distance Calls, complaints, failures per unit of time

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**Process Capability Process variability matches specifications**

Lower Specification Upper Specification Process variability matches specifications Lower Specification Upper Specification Process variability well within specifications Lower Specification Upper Specification Process variability exceeds specifications

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