Lesson 7.1 Quality Control Today we will learn to… > use quality control charts to determine if a manufacturing process is out of control

A business hires someone to be in charge of “quality control” to ensure that they produce a quality product.

X Charts The X Chart is used to analyze the means of measured values to determine if a quality product is being produced.

R charts The R Chart is used to analyze the ranges of measured values to determine if the manufacturing process is consistent.

Step 1 – compute the mean and range of each sample Step 3 – compute upper and lower control limits Step 2 – compute the Grand Mean ( X GM ) and the mean of the ranges (R) Step 4 – plot control charts Step 5 – analyze the charts

LCL x UCL x X GM control chart for a process that is in control

LCL x UCL x X GM control chart for a process that is out of control

Two types of variation that can occur in manufacturing process: 1) chance variation – random problem & cannot be eliminated entirely 2) assignable-cause variation – not random & must be eliminated to maintain quality of product Why is a process out of control?

A manufacturer of rope tests the breaking strength of 6 samples of 5 ropes. Sample Breaking Strength (pounds) Step 1 – 46 X R mean & range of samples n = 5

X GM = R =  49  3 3 Step 2 – the mean of the means the mean of the ranges

Step 3 – A is a constant obtained from the Quality Control Table where n is the number of items in one sample. UCL x = X GM + A R LCL x = X GM – A R compute the upper control limit and the lower control limit

Step 3 – compute the upper control limit and the lower control limit 49 + (0.577)(3) = (0.577)(3) = 47.3 Step 4 –  51  47 UCL x = X GM + A R LCL x = X GM – A R draw the chart

the quality is out of control =49 X GM =51 UCL x =47 LCL x X Chart

Step 3 – D 4 and D 3 are constants obtained from the Quality Control Table where n is the number of items in one sample. UCL R = D 4 R LCL R = D 3 R compute the upper control limit and the lower control limit

UCL R = D 4 R LCL R = D 3 R n =D 4 = R = D 3 = (2.115)(3) = (0)(3) = Step 4 –draw the chart  6 6

The process is consistent! = 3 R =6.3 UCL R =0 LCL R R chart

A battery is designed to last for 200 hours. Ten samples of six batteries each were selected and tested. Construct and analyze a quality control X chart for the data. n = 6

Sample XR Battery Tests X GM = R = How is this chart different from the first chart?

Step 3 – compute the upper control limit and the lower control limit UCL x = X GM + A R LCL x = X GM – A R (0.483)(2.1) = (0.483)(2.1) = n = 6 A =0.483 X GM = 2.1R = 202.0

The battery performance is = 202 X GM = 203 UCL x = 201 LCL x out of control (not consistent) R chart

X charts R charts In control  Out of control  In control  Out of control  quality is consistent quality is NOT consistent quality of product is acceptable quality of product is NOT acceptable

Lesson 7.2 Quality Control Today we will learn to… > use quality control charts to determine if a manufacturing process is out of control

X chart R chart Analysis? In control Out of control In control Out of control Product quality acceptable, manufacturing process consistent Product quality acceptable, manufacturing process not consistent Product quality not acceptable, manufacturing process consistent Product quality not acceptable, manufacturing process not consistent

Lesson 7.3 Attribute Charts Today we will learn to… > use attribute charts to determine if a manufacturing process is out of control

Attribute Charts are used to determine if manufactured items are within the acceptable limits of defects. When manufacturing items, there is always some level of “acceptable” defects.

Two types of charts are used to measure attributes. p charts and c charts The c chart is used to analyze the quality of and item by counting the number of defects per item The p chart is used to analyze the percent of defects per sample.

A company manufactures ball point pens. Five samples of 50 pens each are selected, and the number of defective pens in each sample is recorded. n = 50

SampleSize # of defective pens % Step 1 – find proportion of defective parts for each sample

Step 2 – find the mean for the proportions of defective parts p = p = 0.06 n = 50

Step 3 – find the UCL p and LCL p UCL p = p + 3 p (1 – p ) n n LCL p = p – 3 ♪♫ Memories ♪♫ -3σ -2σ -1σ  +1σ +2σ +3σ

Step 3 – find the UCL p and LCL p UCL p = 0.06 (1 – 0.06 ) LCL p = 0.06 (1 – 0.06 ) – 3 UCL p = LCL p = 0.16 – Since proportions cannot be negative, we use zero. = 0

=0.16 = 0.06 =0 p UCL p LCL p The number of defects per sample is acceptable. Step 4 – Draw the p chart

C alculators are manufactured and checked for defects. Twelve of the defective calculators are checked for the number of defects per calculator. The defects might include soldering, lettering, cracked cases, and memory error.

The number of defects per calculator are: 6, 3, 2, 5, 6, 7, 4, 3, 7, 8, 9, 5 Step 1 – find the average number of defects per item, c. c = 65  12 =5.42  5

Step 2 – Find UCL c and LCL c = = UCL c = c + 3 c LCL c = c – 3 c 11.7  – 1.71= 0 Since proportions cannot be negative, zero is used. 12

= 12 = 5 = 0 c UCL c LCL c Since all points fall within the limits, The number of defects per calculator is acceptable. Step 3 – Draw the c chart

p charts c charts In control  Out of control  In control  Out of control  % of defective products is acceptable % of defective products NOT acceptable # of defects per item is acceptable # of defects per item is NOT acceptable