Final decision for electronic components supplier

Description:

Since our organization ensures the quality of manufactured boards but purchases the electrical components that are mounted on the boards from hundreds of suppliers. There are several electrical components on each board, deviations from designed specifications quickly add up, ultimately resulting in defective boards. To circumvent this, our organization enters into contracts with their suppliers in which they “guarantee” that the mean of their supplied product meets a designed target.

To make a fair decision and minimize the cost of sampling we designed this experiment:

\[ Ho:\mu=3.2\] \[ Ha:\mu\ne3.2 \]

First, we define the sample size of the resistor that we needed.

knitr::opts_chunk$set(echo = TRUE)
data <- c(3.14, 3.22, 3.30, 3.52, 3.05, 3.10, 3.54, 3.39, 3.19, 2.87, 3.23, 2.87, 2.91, 3.07, 3.29)
summary(data)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   2.870   3.060   3.190   3.179   3.295   3.540
sd(data) 
## [1] 0.2107967
Effect <- 0.1 / 0.21

library(pwr)
pwr.t.test(d=Effect, power= 0.9, sig.level=0.05, type= "one.sample", alternative= "two.sided")
## 
##      One-sample t test power calculation 
## 
##               n = 48.2995
##               d = 0.4761905
##       sig.level = 0.05
##           power = 0.9
##     alternative = two.sided
p.t.two <- pwr.t.test(d=Effect, power=0.9, type="one.sample", alternative = "two.sided")
plot(p.t.two)

Thus we collected the data and tested the resistance.

knitr::opts_chunk$set(echo = TRUE)
data1<-c(3.28, 3.24, 3.43, 3.15, 3.19, 3.21, 3.12, 3.10, 3.17, 3.01, 3.27, 3.07, 3.13, 3.12, 3.20, 3.37, 3.33, 3.12, 3.30, 3.31, 2.98, 3.21,
3.20, 3.39, 3.17, 3.20, 3.21, 3.29, 3.08, 3.11, 3.08, 3.18, 3.10, 3.16, 3.24, 3.44, 3.29, 3.18, 3.11, 3.29, 3.19, 3.21, 3.24, 3.14,
3.24, 3.22, 3.16, 3.19, 3.09)
t.test(data1, mu=3.2, alternative = "two.sided" )
## 
##  One Sample t-test
## 
## data:  data1
## t = -0.12967, df = 48, p-value = 0.8974
## alternative hypothesis: true mean is not equal to 3.2
## 95 percent confidence interval:
##  3.169682 3.226644
## sample estimates:
## mean of x 
##  3.198163

Parameters:

\[ p_{-value}=0,8974, t=-0.12967, mean=3.198163\]

Conclusion

We recommend keeping the supplier because the mean of the samples was 3.198 ohms which are very close to the optimum value defined as 3.2. The data reported above include a 90% of significance.

R CODE Used

#Sample size and power
data <- c(3.14, 3.22, 3.30, 3.52, 3.05, 3.10, 3.54, 3.39, 3.19, 2.87, 3.23, 2.87, 2.91, 3.07, 3.29)
summary(data)
sd(data) #probability to chose poorly 
Effect <- 0.1 / 0.21

library(pwr)
pwr.t.test(d=Effect, power= 0.9, sig.level=0.05, type= "one.sample", alternative= "two.sided")
p.t.two <- pwr.t.test(d=Effect, power=0.9, type="one.sample", alternative = "two.sided")
plot(p.t.two)

#Hypothesis test
data1<-c(3.28, 3.24, 3.43, 3.15, 3.19, 3.21, 3.12, 3.10, 3.17, 3.01, 3.27, 3.07, 3.13, 3.12, 3.20, 3.37, 3.33, 3.12, 3.30, 3.31, 2.98, 3.21,
3.20, 3.39, 3.17, 3.20, 3.21, 3.29, 3.08, 3.11, 3.08, 3.18, 3.10, 3.16, 3.24, 3.44, 3.29, 3.18, 3.11, 3.29, 3.19, 3.21, 3.24, 3.14,
3.24, 3.22, 3.16, 3.19, 3.09)
t.test(data1, mu=3.2, alternative = "two.sided" )