Latihan 3.8

Soal

The time to failure in hours of an electronic component subjected to an accelerated life test is shown in Table 3E.1. To accelerate the failure test, the units were tested at an elevated temperature.

  1. Calculate the sample average and standard deviation.

  2. Construct a histogram.

  3. Construct a stem-and-leaf plot.

  4. Find the sample median and the lower and upper quartiles.

data38 <- c(
  127,124,121,118,
  125,123,136,131,
  131,120,140,125,
  124,119,137,133,
  129,128,125,141,
  121,133,124,125,
  142,137,128,140,
  151,124,129,131,
  160,142,130,129,
  125,123,122,126
)
length(data38)
## [1] 40

(a) Sample Average and Standard Deviation

mean(data38)
## [1] 129.975

Berdasarkan hasil perhitungan menggunakan R, diperoleh sample average sebesar 129.975 jam.

sd(data38)
## [1] 8.914084

Sample standard deviation yang diperoleh adalah 8.914084 jam.

(b) Histogram

hist(data38,
     breaks = seq(115,165,by=5),
     main = "Histogram Electronic Component Failure Time",
     xlab = "Failure Time (hours)",
     ylab = "Frequency")

Berdasarkan histogram, sebagian besar waktu kegagalan komponen berada pada kisaran 120–140 jam. Terdapat beberapa pengamatan dengan waktu kegagalan yang relatif tinggi.

(c) Stem-and-Leaf Plot

stem(data38)
## 
##   The decimal point is 1 digit(s) to the right of the |
## 
##   11 | 89
##   12 | 0112334444
##   12 | 555556788999
##   13 | 011133
##   13 | 677
##   14 | 00122
##   14 | 
##   15 | 1
##   15 | 
##   16 | 0

(d) Sample Median and Quartiles

median(data38)
## [1] 128
quantile(data38)
##     0%    25%    50%    75%   100% 
## 118.00 124.00 128.00 133.75 160.00

Berdasarkan hasil perhitungan, diperoleh: - Kuartil bawah (Q1) = 124 jam - Median = 128 jam - Kuartil atas (Q3) = 133.75 jam



# Latihan 3.10

Soal

An article in Quality Engineering (Vol. 4, 1992, pp. 487–495) presents viscosity data from a batch chemical process. A sample of these data is presented in Table 3E.3 (read down,then across). (a)Construct a stem-and-leaf display for the viscos ity data. (b)Construct a frequency distribution and histogram. (c)Convert the stem-and-leaf plot in part (a) into an ordered stem-and-leaf plot. Use this graph to assist in locating the median and the upper and lower quartiles of the viscosity data. (d)What are the tenth and ninetieth percentiles of viscosity?

data310 <- c(
  13.3,14.9,15.8,16.0,
  14.5,13.7,13.7,14.9,
  15.3,15.2,15.1,13.6,
  15.3,14.5,13.4,15.3,
  14.3,15.3,14.1,14.3,
  14.8,15.6,14.8,15.6,
  15.2,15.8,14.3,16.1,
  14.5,13.3,14.3,13.9,
  14.6,14.1,16.4,15.2,
  14.1,15.4,16.9,14.4,
  14.3,15.2,14.2,14.0,
  16.1,15.2,16.9,14.4,
  13.1,15.9,14.9,13.7,
  15.5,16.5,15.2,13.8,
  12.6,14.8,14.4,15.6,
  14.6,15.1,15.2,14.5,
  14.3,17.0,14.6,12.8,
  15.4,14.9,16.4,16.1,
  15.2,14.8,14.2,16.6,
  16.8,14.0,15.7,15.6
)
length(data310)
## [1] 80

(a) Stem-and-Leaf Display

stem(data310)
## 
##   The decimal point is at the |
## 
##   12 | 68
##   13 | 1334
##   13 | 677789
##   14 | 0011122333333444
##   14 | 555566688889999
##   15 | 1122222222333344
##   15 | 566667889
##   16 | 011144
##   16 | 56899
##   17 | 0

Berdasarkan stem-and-leaf display, data viscosity tersebar pada nilai sekitar 12,6 hingga 17,0.

(b) Frequency Distribution and Histogram

breaks310 <- seq(12.5, 17.5, by = 0.5)

freq310 <- hist(data310,
                breaks = breaks310,
                plot = FALSE)

freq310$counts
##  [1]  2  4  8 18 11 17  9  6  5  0
freq_table310 <- data.frame(
  Interval = paste(
    head(freq310$breaks, -1),
    "-",
    tail(freq310$breaks, -1)
  ),
  Frequency = freq310$counts
)

freq_table310
##     Interval Frequency
## 1  12.5 - 13         2
## 2  13 - 13.5         4
## 3  13.5 - 14         8
## 4  14 - 14.5        18
## 5  14.5 - 15        11
## 6  15 - 15.5        17
## 7  15.5 - 16         9
## 8  16 - 16.5         6
## 9  16.5 - 17         5
## 10 17 - 17.5         0
hist(data310,
     breaks = breaks310,
     main = "Histogram Viscosity",
     xlab = "Viscosity",
     ylab = "Frequency")

Berdasarkan histogram, sebagian besar data viscosity berada pada kisaran 14,0 hingga 15,5. Distribusi data terlihat terkonsentrasi di sekitar nilai tersebut, dengan beberapa pengamatan pada nilai yang lebih rendah maupun lebih tinggi.

(c) Ordered Stem-and-Leaf, Median, and Quartiles

stem(sort(data310))
## 
##   The decimal point is at the |
## 
##   12 | 68
##   13 | 1334
##   13 | 677789
##   14 | 0011122333333444
##   14 | 555566688889999
##   15 | 1122222222333344
##   15 | 566667889
##   16 | 011144
##   16 | 56899
##   17 | 0

Data yang telah diurutkan digunakan untuk membantu menentukan median serta kuartil bawah dan kuartil atas.

median(data310)
## [1] 14.9

Median dari data viscosity adalah 14,9.

quantile(data310)
##     0%    25%    50%    75%   100% 
## 12.600 14.300 14.900 15.525 17.000

Berdasarkan hasil perhitungan menggunakan R, diperoleh kuartil bawah (Q1) sebesar 14,3, median sebesar 14,9, dan kuartil atas (Q3) sebesar 15,525.

(d) Tenth and Ninetieth Percentiles

quantile(data310, probs = c(0.10, 0.90))
##   10%   90% 
## 13.70 16.13

Berdasarkan hasil perhitungan menggunakan R, diperoleh persentil ke-10 (P10) sebesar 13,70 dan persentil ke-90 (P90) sebesar 16,13.